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diff --git a/matlab_implementation/ACE1_comparison.png b/matlab_implementation/ACE1_comparison.png
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diff --git a/matlab_implementation/ACE2.txt b/matlab_implementation/ACE2.txt
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+++ b/matlab_implementation/ACE2.txt
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diff --git a/matlab_implementation/ACE2_comparison.png b/matlab_implementation/ACE2_comparison.png
new file mode 100644
index 0000000..50a8ba5
Binary files /dev/null and b/matlab_implementation/ACE2_comparison.png differ
diff --git a/matlab_implementation/RBF.asv b/matlab_implementation/RBF.asv
new file mode 100644
index 0000000..c295955
--- /dev/null
+++ b/matlab_implementation/RBF.asv
@@ -0,0 +1,125 @@
+% Defining the class RBF
+classdef RBF<handle
+
+    % Defining variables for the class
+    properties 
+
+        X; % Variable for state
+        h; % Variable for number of hidden layers
+        mu; % Variable for mean
+        sigma; % Variable for variance
+        K; % Variable for K values of PID
+        Vprev; % Variable for previous value of value function
+        V; % Variable for value of value function
+        w; % Variable for Actor weight matrix
+        v; % Variable for Critic weight matrix
+        output; % Variable for hidden layer
+        aw; % Variable for learning parameter
+        av; % Variable for learning parameter
+        au; % Variable for learning parameter
+        asig; % Variable for learning parameter
+        gamma; % Variable for discount factor in RL
+
+    end
+    methods
+
+        % Defining the RBF constructor
+        function self = RBF(aw , av , au , asig , gamma,h )
+
+            self.X = zeros(3,1); % Initializing X
+            self.h = h; % Initializing for number of hidden layers h
+            self.mu = zeros(3,h); % Initializing mean (mu)
+            self.sigma = ones(1,h); % Initializing variance (sigma)
+            self.K = zeros(3,1); % Initializing K
+            self.Vprev = 0; % Initializing previous value function
+            self.V  = 0; % Initializing value function
+            self.w = zeros(3,h); % Initializing w
+            self.v = zeros(1,h); % Initializing v
+            self.output = ones(h,1); % Initializing output
+            self.aw = aw; % Initializing learning parameter aw
+            self.av = av; % Initializing learning parameter av
+            self.au = au; % Initializing learning parameter au
+            self.asig = asig; % Initializing learning parameter asig
+            self.gamma = gamma; % Initializing learning parameter gamma
+            
+        end
+
+        % Defining the function for the hidden layer of the RBF 
+        function self = HiddenLayer(self)
+
+            % Looping over h hidden layers
+            for i = 1:self.h 
+
+                % Gaussian Function (Equation 26 in the paper)
+                self.output(i) = exp(- (norm( self.X - self.mu(:,i) )^2 )/(2*self.sigma(i)^2) );
+            end
+        end
+
+        % Defining the function for output layer of the RBF
+        function self = OutputLayer(self)
+
+            % Equation 27 in the paper
+            self.K = self.w*self.output;
+
+            % Equating previous value function value to current value function value
+            self.Vprev = self.V;
+
+            % Equation 28 in the paper
+            self.V = self.v*self.output;
+        end
+
+        function self = Update(self, y_ref , Y, y1, y2 , y3 , delU )
+
+            % TD Error (Equation 30 in the paper)
+            del_TD = 0.5 * ( y_ref - Y )^2 + self.gamma*self.V - self.Vprev;
+
+            % Finding delY/delU
+            delY_delU = (Y - y1 )/delU ;
+
+            % Finding the gradient of the weight matrix
+            w_gradient = del_TD *delY_delU* ( [ (y1 - y2) ; -self.X(1) ; (y1 - 2*y2 + y3) ]*self.output');
+
+            % Update rule for w (Equation 32 in the paper)
+            self.w = self.w - self.aw * w_gradient;
+
+            % Finding the gradient of the mean (mu) matrix
+            mu_gradient = del_TD* (repmat(self.X,1,self.h) - self.mu).*(  (( self.output.*(self.v') )./( (self.sigma).^2 )')' );
+
+            % Update rule for mean (Equation 34 in the paper)
+            self.mu = self.mu + self.au*mu_gradient;
+
+            temp = zeros(1,self.h);
+
+            for j = 1: self.h
+
+                temp(j) = norm( self.X - self.mu(:,j) )^2;
+
+            end
+            % Finding gradient for updating sigma (variance)
+            sig_gradient =  (del_TD) * temp.* ((( self.output.*(self.v') )./( (self.sigma).^3 )')');
+
+            % Update rule for sigma (Equation 35 in the paper)
+            self.sigma = self.sigma + self.asig*sig_gradient;
+
+            % Update rule for critic weights, value function (Equation 33 in the paper)
+            self.v = self.v + self.av*del_TD*self.output';
+
+        end
+        
+        % Defining function to initialize weights
+        function self = initialize_weights(self,area)
+
+            % Initialize the weights for area 1
+            if area == 1
+                self.w = readmatrix('w_matrix1.txt');
+
+            % Initialize the weights for area 2
+            elseif area == 2
+                self.w = readmatrix('w_matrix2.txt');
+            end 
+        end
+    end
+end
+
+
+
diff --git a/matlab_implementation/RBF.m b/matlab_implementation/RBF.m
new file mode 100644
index 0000000..c295955
--- /dev/null
+++ b/matlab_implementation/RBF.m
@@ -0,0 +1,125 @@
+% Defining the class RBF
+classdef RBF<handle
+
+    % Defining variables for the class
+    properties 
+
+        X; % Variable for state
+        h; % Variable for number of hidden layers
+        mu; % Variable for mean
+        sigma; % Variable for variance
+        K; % Variable for K values of PID
+        Vprev; % Variable for previous value of value function
+        V; % Variable for value of value function
+        w; % Variable for Actor weight matrix
+        v; % Variable for Critic weight matrix
+        output; % Variable for hidden layer
+        aw; % Variable for learning parameter
+        av; % Variable for learning parameter
+        au; % Variable for learning parameter
+        asig; % Variable for learning parameter
+        gamma; % Variable for discount factor in RL
+
+    end
+    methods
+
+        % Defining the RBF constructor
+        function self = RBF(aw , av , au , asig , gamma,h )
+
+            self.X = zeros(3,1); % Initializing X
+            self.h = h; % Initializing for number of hidden layers h
+            self.mu = zeros(3,h); % Initializing mean (mu)
+            self.sigma = ones(1,h); % Initializing variance (sigma)
+            self.K = zeros(3,1); % Initializing K
+            self.Vprev = 0; % Initializing previous value function
+            self.V  = 0; % Initializing value function
+            self.w = zeros(3,h); % Initializing w
+            self.v = zeros(1,h); % Initializing v
+            self.output = ones(h,1); % Initializing output
+            self.aw = aw; % Initializing learning parameter aw
+            self.av = av; % Initializing learning parameter av
+            self.au = au; % Initializing learning parameter au
+            self.asig = asig; % Initializing learning parameter asig
+            self.gamma = gamma; % Initializing learning parameter gamma
+            
+        end
+
+        % Defining the function for the hidden layer of the RBF 
+        function self = HiddenLayer(self)
+
+            % Looping over h hidden layers
+            for i = 1:self.h 
+
+                % Gaussian Function (Equation 26 in the paper)
+                self.output(i) = exp(- (norm( self.X - self.mu(:,i) )^2 )/(2*self.sigma(i)^2) );
+            end
+        end
+
+        % Defining the function for output layer of the RBF
+        function self = OutputLayer(self)
+
+            % Equation 27 in the paper
+            self.K = self.w*self.output;
+
+            % Equating previous value function value to current value function value
+            self.Vprev = self.V;
+
+            % Equation 28 in the paper
+            self.V = self.v*self.output;
+        end
+
+        function self = Update(self, y_ref , Y, y1, y2 , y3 , delU )
+
+            % TD Error (Equation 30 in the paper)
+            del_TD = 0.5 * ( y_ref - Y )^2 + self.gamma*self.V - self.Vprev;
+
+            % Finding delY/delU
+            delY_delU = (Y - y1 )/delU ;
+
+            % Finding the gradient of the weight matrix
+            w_gradient = del_TD *delY_delU* ( [ (y1 - y2) ; -self.X(1) ; (y1 - 2*y2 + y3) ]*self.output');
+
+            % Update rule for w (Equation 32 in the paper)
+            self.w = self.w - self.aw * w_gradient;
+
+            % Finding the gradient of the mean (mu) matrix
+            mu_gradient = del_TD* (repmat(self.X,1,self.h) - self.mu).*(  (( self.output.*(self.v') )./( (self.sigma).^2 )')' );
+
+            % Update rule for mean (Equation 34 in the paper)
+            self.mu = self.mu + self.au*mu_gradient;
+
+            temp = zeros(1,self.h);
+
+            for j = 1: self.h
+
+                temp(j) = norm( self.X - self.mu(:,j) )^2;
+
+            end
+            % Finding gradient for updating sigma (variance)
+            sig_gradient =  (del_TD) * temp.* ((( self.output.*(self.v') )./( (self.sigma).^3 )')');
+
+            % Update rule for sigma (Equation 35 in the paper)
+            self.sigma = self.sigma + self.asig*sig_gradient;
+
+            % Update rule for critic weights, value function (Equation 33 in the paper)
+            self.v = self.v + self.av*del_TD*self.output';
+
+        end
+        
+        % Defining function to initialize weights
+        function self = initialize_weights(self,area)
+
+            % Initialize the weights for area 1
+            if area == 1
+                self.w = readmatrix('w_matrix1.txt');
+
+            % Initialize the weights for area 2
+            elseif area == 2
+                self.w = readmatrix('w_matrix2.txt');
+            end 
+        end
+    end
+end
+
+
+
diff --git a/matlab_implementation/TwoAreaPS.asv b/matlab_implementation/TwoAreaPS.asv
new file mode 100644
index 0000000..13ce0bc
--- /dev/null
+++ b/matlab_implementation/TwoAreaPS.asv
@@ -0,0 +1,116 @@
+% Defining class TwoAreaPS
+classdef TwoAreaPS<handle
+
+    % Defining the variables for the class
+    properties
+
+        yt_a1; % Defining variable yt for output of area 1 
+        yt_a2; % Defining variable yt for output of area 2
+        Xprev; % Defining variable for previous value of X
+        X; % Defining variable X
+        Y; % Defining variable Y
+        Tg; % Defining variable for governor time constant
+        Tp; % Defining variable for plant time constant
+        Tt; % Defining variable for turbine time constant
+        Kp; % Defining variable for PID parameter Kp
+        T12; % Defining variable for tie line power constant
+        a12; % Defining variable for a12
+        R; % Defining variable for regulation
+        beta1; % Defining variable for frequency bias constant of area 1
+        beta2; % Defining variable for frequency bias constant of area 2
+        T; % Defining variable for time step
+        A; % Defining variable for state space model matrix A
+        B; % Defining variable for state space model matrix B
+        C; % Defining variable for state space model matrix C
+        Ad; % Defining variable for discretization parameter 
+        Bd; % Defining variable for discretization parameter 
+
+    end
+    methods
+        function self = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  yt_a1, yt_a2)
+
+            self.yt_a1 = yt_a1; % Initializing variable for previous output value
+            self.yt_a2 = yt_a2; % Initializing variable for previous output value
+            self.Xprev = zeros( 7,1); % Initializing variable for input
+            self.X= zeros( 7,1); % Initializing variable for input
+            self.Y = zeros( 5,1 ); % Initializing variable for output
+            self.Tg = Tg; % Initializing variable for governor time constant
+            self.Tp = Tp ; % Initializing variable for plant time constant
+            self.Tt = Tt ; % Initializing variable for turbine time constant
+            self.Kp = Kp; % Initializing variable for PID parameter Kp
+            self.T12 = T12 ; % Initializing variable for tie line power constant
+            self.a12 = a12; % Initializing variable for a12
+            self.R = R ; % Initializing variable for regulation
+        
+            self.beta1 = beta1; % Initializing variable for frequency bias constant of area 1
+            self.beta2 = beta2; % Initializing variable for frequency bias constant of area 2
+        
+            self.T = T;
+        
+            self.CalcDiscreteCoef();
+        end
+
+        function self = CalcDiscreteCoef(self)
+            Tg = self.Tg;
+            Tp = self.Tp;
+            Tt = self.Tt;
+            Kp = self.Kp;
+            T12 = self.T12 ;
+            a12 = self.a12;
+            R = self.R ;
+            
+            % Defining state space model matrix A
+            self.A  = [ -1/Tp Kp/Tp  0  -Kp/Tp  0  0  0  ;
+                        0  -1/Tt  1/Tt  0  0 0  0  ; 
+                        -1/(R*Tg)  0  -1/Tg  0  0 0 0 ; 
+                        2*pi*T12  0  0  0  -2*pi*T12  0 0 ; 
+                        0  0  0  -Kp*a12/Tp  -1/Tp  Kp/Tp  0 ;  
+                        0   0 0 0 0  -1/Tt 1/Tt ; 
+                        0   0 0 0 -1/(R*Tg)  1/Tg  -1/Tg  ];
+               
+            % Defining state space model matrix B
+            self.B = [ 0 0 -Kp/Tp  0 ;
+                       0 0 0 0 ;
+                      1/Tg 0  0 0 ;
+                       0 0 0 0 ;
+                       0 0 0 0 ;
+                       0 0 0 0 ;
+                       0 1/Tg 0 -Kp/Tp ] ;
+    
+            % Defining state space model matrix C
+            self.C = [ self.beta1  0  0 1  0 0  0 ;
+                       0  0 0 1 self.beta2  0  0 ; 
+                       0  0 0 1 0 0 0 ; 
+                       1  0 0 0 0 0 0 ;
+                       0  0 0 0 1 0 0 ]    ;
+
+            % Calculating system matrix for discrete time (eq 8 in the paper)
+            self.Ad = expm(self.A*self.T);
+    
+            % Calculating input matrix for discrete time (eq 9 in the paper)
+            self.Bd = inv(self.A)*(self.Ad - eye(7) )*self.B;
+
+        end
+    
+        % Defining function output
+        function self = Output(self,Ut)
+
+            % Updating previous values for area 1
+            self.yt_a1 = [self.Y(1) self.yt_a1(1) self.yt_a1(2)];
+
+            % Updating previous values for area 2
+            self.yt_a2 = [self.Y(2) self.yt_a2(1) self.yt_a2(2)];
+
+            % System equation (Equation 4 in the paper)
+            self.X = self.Ad*self.Xprev +self.Bd*Ut;
+
+            % Output equation (Equation 5 in the paper)
+            self.Y = self.C*self.Xprev;
+
+            % Updating previous values for X 
+            self.Xprev = self.X;
+
+        end
+        
+    end
+end
\ No newline at end of file
diff --git a/matlab_implementation/TwoAreaPS.m b/matlab_implementation/TwoAreaPS.m
new file mode 100644
index 0000000..13ce0bc
--- /dev/null
+++ b/matlab_implementation/TwoAreaPS.m
@@ -0,0 +1,116 @@
+% Defining class TwoAreaPS
+classdef TwoAreaPS<handle
+
+    % Defining the variables for the class
+    properties
+
+        yt_a1; % Defining variable yt for output of area 1 
+        yt_a2; % Defining variable yt for output of area 2
+        Xprev; % Defining variable for previous value of X
+        X; % Defining variable X
+        Y; % Defining variable Y
+        Tg; % Defining variable for governor time constant
+        Tp; % Defining variable for plant time constant
+        Tt; % Defining variable for turbine time constant
+        Kp; % Defining variable for PID parameter Kp
+        T12; % Defining variable for tie line power constant
+        a12; % Defining variable for a12
+        R; % Defining variable for regulation
+        beta1; % Defining variable for frequency bias constant of area 1
+        beta2; % Defining variable for frequency bias constant of area 2
+        T; % Defining variable for time step
+        A; % Defining variable for state space model matrix A
+        B; % Defining variable for state space model matrix B
+        C; % Defining variable for state space model matrix C
+        Ad; % Defining variable for discretization parameter 
+        Bd; % Defining variable for discretization parameter 
+
+    end
+    methods
+        function self = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  yt_a1, yt_a2)
+
+            self.yt_a1 = yt_a1; % Initializing variable for previous output value
+            self.yt_a2 = yt_a2; % Initializing variable for previous output value
+            self.Xprev = zeros( 7,1); % Initializing variable for input
+            self.X= zeros( 7,1); % Initializing variable for input
+            self.Y = zeros( 5,1 ); % Initializing variable for output
+            self.Tg = Tg; % Initializing variable for governor time constant
+            self.Tp = Tp ; % Initializing variable for plant time constant
+            self.Tt = Tt ; % Initializing variable for turbine time constant
+            self.Kp = Kp; % Initializing variable for PID parameter Kp
+            self.T12 = T12 ; % Initializing variable for tie line power constant
+            self.a12 = a12; % Initializing variable for a12
+            self.R = R ; % Initializing variable for regulation
+        
+            self.beta1 = beta1; % Initializing variable for frequency bias constant of area 1
+            self.beta2 = beta2; % Initializing variable for frequency bias constant of area 2
+        
+            self.T = T;
+        
+            self.CalcDiscreteCoef();
+        end
+
+        function self = CalcDiscreteCoef(self)
+            Tg = self.Tg;
+            Tp = self.Tp;
+            Tt = self.Tt;
+            Kp = self.Kp;
+            T12 = self.T12 ;
+            a12 = self.a12;
+            R = self.R ;
+            
+            % Defining state space model matrix A
+            self.A  = [ -1/Tp Kp/Tp  0  -Kp/Tp  0  0  0  ;
+                        0  -1/Tt  1/Tt  0  0 0  0  ; 
+                        -1/(R*Tg)  0  -1/Tg  0  0 0 0 ; 
+                        2*pi*T12  0  0  0  -2*pi*T12  0 0 ; 
+                        0  0  0  -Kp*a12/Tp  -1/Tp  Kp/Tp  0 ;  
+                        0   0 0 0 0  -1/Tt 1/Tt ; 
+                        0   0 0 0 -1/(R*Tg)  1/Tg  -1/Tg  ];
+               
+            % Defining state space model matrix B
+            self.B = [ 0 0 -Kp/Tp  0 ;
+                       0 0 0 0 ;
+                      1/Tg 0  0 0 ;
+                       0 0 0 0 ;
+                       0 0 0 0 ;
+                       0 0 0 0 ;
+                       0 1/Tg 0 -Kp/Tp ] ;
+    
+            % Defining state space model matrix C
+            self.C = [ self.beta1  0  0 1  0 0  0 ;
+                       0  0 0 1 self.beta2  0  0 ; 
+                       0  0 0 1 0 0 0 ; 
+                       1  0 0 0 0 0 0 ;
+                       0  0 0 0 1 0 0 ]    ;
+
+            % Calculating system matrix for discrete time (eq 8 in the paper)
+            self.Ad = expm(self.A*self.T);
+    
+            % Calculating input matrix for discrete time (eq 9 in the paper)
+            self.Bd = inv(self.A)*(self.Ad - eye(7) )*self.B;
+
+        end
+    
+        % Defining function output
+        function self = Output(self,Ut)
+
+            % Updating previous values for area 1
+            self.yt_a1 = [self.Y(1) self.yt_a1(1) self.yt_a1(2)];
+
+            % Updating previous values for area 2
+            self.yt_a2 = [self.Y(2) self.yt_a2(1) self.yt_a2(2)];
+
+            % System equation (Equation 4 in the paper)
+            self.X = self.Ad*self.Xprev +self.Bd*Ut;
+
+            % Output equation (Equation 5 in the paper)
+            self.Y = self.C*self.Xprev;
+
+            % Updating previous values for X 
+            self.Xprev = self.X;
+
+        end
+        
+    end
+end
\ No newline at end of file
diff --git a/matlab_implementation/TwoAreaPS_PID.asv b/matlab_implementation/TwoAreaPS_PID.asv
new file mode 100644
index 0000000..e92367c
--- /dev/null
+++ b/matlab_implementation/TwoAreaPS_PID.asv
@@ -0,0 +1,162 @@
+% Load Disturbance for area 1
+PL1 = 0;
+% Load Disturbance for area 2
+PL2 = 0;
+
+% Defining and initializing variables
+ut1 = []; % Variable for control signal for area 1
+ut2 = []; % Variable for control signal for area 2
+pl1 = []; % Variable for load disturbance for area 1
+pl2 = []; % Variable for load disturbance for area 2
+ACE1 = []; % Variable for area control error for area 1
+ACE2 = []; % Variable for area control error for area 2
+TieLine = []; % Variable for TieLine Power
+Freq1 =[]; % Variable for Frequency change for area 2
+Freq2 = [];% Variable for Frequency change  for area 2
+time = []; % Variable for time 
+
+
+Tg = 0.08; % Initializing variable for governor time constant
+Tp = 20; % Initializing variable for plant time constant 
+Tt = 0.3; % Initializing variable for Turbine time constant 
+Kp = 120; % Initliazing PID parameter K
+T12 = 0.545/(2*pi); % Initializing variable for Tie line power constant 
+a12 = -1; 
+R = 5; % Initializing variable for Regulation 
+T = 1/80; 
+dt = 1/80;
+beta1 = 0.425; % Initializing variable for Frequency bias constant of area 1
+beta2 = 0.425; % Initializing variable for Frequency bias constant of area 2
+
+% Defining object System for the class TwoAreaPS
+System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+
+
+KP1 = 1.723845;
+KI1 = 0.014555;
+KD1 = 17.936909;
+
+KP2 = 0.106744;
+KI2 = 0.006323;
+KD2 = 15.023620;
+
+ut_1 = 0;
+ut_2 = 0;
+
+t = 200;
+
+y = [];
+x = [];
+
+for i = 1:t/dt
+    % Finding error signal e_t for area 1
+    e_t_a1 = 0 - System.yt_a1(1);
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+    % Finding double derivate of the output (delta square y) for area 1
+    del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+
+    % Controller definition (Equation 22 in the paper) for area 1
+    ut_1 = ut_1 + (KI1*e_t_a1 - KP1*del_y_a1 - KD1*del2_y_a1);
+     % Controller definition (Equation 22 in the paper) for area 2
+    ut_2 = ut_2 + (KI2*e_t_a2 - KP2*del_y_a2 - KD2*del2_y_a2);
+
+    % Defining control signal ut1 for area 1
+    ut1 = [ut1 ut_1];
+    % Defining control signal ut2 for area 2
+    ut2 = [ut2 ut_2];
+    
+    if (i*dt >=40 && i*dt <= 80)
+        PL1 = 0.003;
+    elseif( i*dt > 80 && i*dt <= 120)
+        PL1 = 0.006;
+    elseif( i*dt > 120 && i*dt <= 160)
+        PL1 = 0.009;
+    else
+        PL1 =  0;
+    end
+        
+    PL2 =  0;
+
+    pl1 = [pl1 PL1];
+    pl2 = [pl2 PL2];
+    
+    % Defining control signal Ut
+    Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+
+    System.Output(Ut);
+   
+    % Defining ACE for area 1
+    ACE1 = [ACE1 System.Y(1)];
+    % Defining ACE for area 2
+    ACE2 = [ACE2 System.Y(2)];
+    % Defining Tie Line Power
+    TieLine = [ TieLine System.Y(3)];
+    % Defining Frequency Change for area 1
+    Freq1 = [ Freq1 System.Y(4)];
+    % Defining Frequency Change for area 2
+    Freq2 = [ Freq2 System.Y(5)];
+    % Defining variable time for our time period
+    time = [time i*dt];
+    
+    ITAE = [];
+    ITAE = [ITAE, dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+
+    ISTE = [];
+    ISTE = [ISTE, dt*(i*dt)*( System.Y(1)^2 + System.Y(2)^2 )];
+
+    IAE = [];
+    IAE = [IAE, dt*( abs(System.Y(1)) + abs(System.Y(2)) ) ];
+
+    ISE = [];
+    ISE = [ISE, dt*( System.Y(1)^2 + System.Y(2)^2 ) ];
+end
+
+fprintf('IAE is');
+disp(sum(IAE));
+fprintf('ISE is');
+disp(sum(ISE));
+fprintf('ISTE is');
+disp(sum(ISTE));
+fprintf('ITAE is');
+disp(sum(ITAE));
+
+figure(1);
+subplot(2,1,1);
+plot(time,pl1 );
+title(' Area 1 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+subplot(2,1,2);
+plot(time, pl2);
+title('Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+figure(2);
+subplot(2,1,1);
+plot(time,ut1 );
+title(' Area 1 Control Signal vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+subplot(2,1,2);
+plot(time, ut2);
+title('Area 2 Control Signal  vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+
+figure(3);
+subplot(2,1,1);
+plot(time, ACE1);
+title(' Area 1 ACE vs Time for PSO Tuned PID')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+subplot(2,1,2);
+plot(time, ACE2);
+title('Area 2 ACE vs Time for PSO Tuned PID')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+
+ACE1_pso  = ACE1;
+ACE2_pso = ACE2;
+
diff --git a/matlab_implementation/TwoAreaPS_PID.m b/matlab_implementation/TwoAreaPS_PID.m
new file mode 100644
index 0000000..e92367c
--- /dev/null
+++ b/matlab_implementation/TwoAreaPS_PID.m
@@ -0,0 +1,162 @@
+% Load Disturbance for area 1
+PL1 = 0;
+% Load Disturbance for area 2
+PL2 = 0;
+
+% Defining and initializing variables
+ut1 = []; % Variable for control signal for area 1
+ut2 = []; % Variable for control signal for area 2
+pl1 = []; % Variable for load disturbance for area 1
+pl2 = []; % Variable for load disturbance for area 2
+ACE1 = []; % Variable for area control error for area 1
+ACE2 = []; % Variable for area control error for area 2
+TieLine = []; % Variable for TieLine Power
+Freq1 =[]; % Variable for Frequency change for area 2
+Freq2 = [];% Variable for Frequency change  for area 2
+time = []; % Variable for time 
+
+
+Tg = 0.08; % Initializing variable for governor time constant
+Tp = 20; % Initializing variable for plant time constant 
+Tt = 0.3; % Initializing variable for Turbine time constant 
+Kp = 120; % Initliazing PID parameter K
+T12 = 0.545/(2*pi); % Initializing variable for Tie line power constant 
+a12 = -1; 
+R = 5; % Initializing variable for Regulation 
+T = 1/80; 
+dt = 1/80;
+beta1 = 0.425; % Initializing variable for Frequency bias constant of area 1
+beta2 = 0.425; % Initializing variable for Frequency bias constant of area 2
+
+% Defining object System for the class TwoAreaPS
+System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+
+
+KP1 = 1.723845;
+KI1 = 0.014555;
+KD1 = 17.936909;
+
+KP2 = 0.106744;
+KI2 = 0.006323;
+KD2 = 15.023620;
+
+ut_1 = 0;
+ut_2 = 0;
+
+t = 200;
+
+y = [];
+x = [];
+
+for i = 1:t/dt
+    % Finding error signal e_t for area 1
+    e_t_a1 = 0 - System.yt_a1(1);
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+    % Finding double derivate of the output (delta square y) for area 1
+    del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+
+    % Controller definition (Equation 22 in the paper) for area 1
+    ut_1 = ut_1 + (KI1*e_t_a1 - KP1*del_y_a1 - KD1*del2_y_a1);
+     % Controller definition (Equation 22 in the paper) for area 2
+    ut_2 = ut_2 + (KI2*e_t_a2 - KP2*del_y_a2 - KD2*del2_y_a2);
+
+    % Defining control signal ut1 for area 1
+    ut1 = [ut1 ut_1];
+    % Defining control signal ut2 for area 2
+    ut2 = [ut2 ut_2];
+    
+    if (i*dt >=40 && i*dt <= 80)
+        PL1 = 0.003;
+    elseif( i*dt > 80 && i*dt <= 120)
+        PL1 = 0.006;
+    elseif( i*dt > 120 && i*dt <= 160)
+        PL1 = 0.009;
+    else
+        PL1 =  0;
+    end
+        
+    PL2 =  0;
+
+    pl1 = [pl1 PL1];
+    pl2 = [pl2 PL2];
+    
+    % Defining control signal Ut
+    Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+
+    System.Output(Ut);
+   
+    % Defining ACE for area 1
+    ACE1 = [ACE1 System.Y(1)];
+    % Defining ACE for area 2
+    ACE2 = [ACE2 System.Y(2)];
+    % Defining Tie Line Power
+    TieLine = [ TieLine System.Y(3)];
+    % Defining Frequency Change for area 1
+    Freq1 = [ Freq1 System.Y(4)];
+    % Defining Frequency Change for area 2
+    Freq2 = [ Freq2 System.Y(5)];
+    % Defining variable time for our time period
+    time = [time i*dt];
+    
+    ITAE = [];
+    ITAE = [ITAE, dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+
+    ISTE = [];
+    ISTE = [ISTE, dt*(i*dt)*( System.Y(1)^2 + System.Y(2)^2 )];
+
+    IAE = [];
+    IAE = [IAE, dt*( abs(System.Y(1)) + abs(System.Y(2)) ) ];
+
+    ISE = [];
+    ISE = [ISE, dt*( System.Y(1)^2 + System.Y(2)^2 ) ];
+end
+
+fprintf('IAE is');
+disp(sum(IAE));
+fprintf('ISE is');
+disp(sum(ISE));
+fprintf('ISTE is');
+disp(sum(ISTE));
+fprintf('ITAE is');
+disp(sum(ITAE));
+
+figure(1);
+subplot(2,1,1);
+plot(time,pl1 );
+title(' Area 1 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+subplot(2,1,2);
+plot(time, pl2);
+title('Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+figure(2);
+subplot(2,1,1);
+plot(time,ut1 );
+title(' Area 1 Control Signal vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+subplot(2,1,2);
+plot(time, ut2);
+title('Area 2 Control Signal  vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+
+figure(3);
+subplot(2,1,1);
+plot(time, ACE1);
+title(' Area 1 ACE vs Time for PSO Tuned PID')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+subplot(2,1,2);
+plot(time, ACE2);
+title('Area 2 ACE vs Time for PSO Tuned PID')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+
+ACE1_pso  = ACE1;
+ACE2_pso = ACE2;
+
diff --git a/matlab_implementation/TwoAreaPS_PID_2.asv b/matlab_implementation/TwoAreaPS_PID_2.asv
new file mode 100644
index 0000000..95286e4
--- /dev/null
+++ b/matlab_implementation/TwoAreaPS_PID_2.asv
@@ -0,0 +1,192 @@
+% Load Disturbance for area 1
+PL1 = 0;
+% Load Disturbance for area 2
+PL2 = 0;
+
+% Defining and initializing variables
+ut1 = []; % Variable for control signal for area 1
+ut2 = []; % Variable for control signal for area 2
+pl1 = []; % Variable for load disturbance for area 1
+pl2 = []; % Variable for load disturbance for area 2
+ACE1 = []; % Variable for area control error for area 1
+ACE2 = []; % Variable for area control error for area 2
+TieLine = []; % Variable for TieLine Power
+Freq1 =[]; % Variable for Frequency change for area 2
+Freq2 = [];% Variable for Frequency change  for area 2
+time = []; % Variable for time 
+
+
+Tg = 0.08; % Initializing variable for governor time constant
+Tp = 20; % Initializing variable for plant time constant 
+Tt = 0.3; % Initializing variable for Turbine time constant 
+Kp = 120; % Initliazing PID parameter K
+T12 = 0.545/(2*pi); % Initializing variable for Tie line power constant 
+a12 = -1; 
+R = 5; % Initializing variable for Regulation 
+T = 1/80; 
+dt = 1/80;
+beta1 = 0.425; % Initializing variable for Frequency bias constant of area 1
+beta2 = 0.425; % Initializing variable for Frequency bias constant of area 2
+
+% Defining object System for the class TwoAreaPS
+System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+
+
+KP1 = 1.723845;
+KI1 = 0.014555;
+KD1 = 17.936909;
+
+KP2 = 0.106744;
+KI2 = 0.006323;
+KD2 = 15.023620;
+
+ut_1 = 0;
+ut_2 = 0;
+
+t = 200;
+
+y = [];
+x = [];
+
+for i = 1:t/dt
+    % Finding error signal e_t for area 1
+    e_t_a1 = 0 - System.yt_a1(1);
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+    % Finding double derivate of the output (delta square y) for area 1
+    del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+
+    e_t_a2 = 0 - System.yt_a2(1);
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a2 =  System.yt_a2(1) - System.yt_a2(2);
+    % Finding double derivate of the output (delta square y) for area 1
+    del2_y_a2 = System.yt_a2(1) - 2*System.yt_a2(2) + System.yt_a2(3);
+    
+    % Controller definition (Equation 22 in the paper) for area 1
+    ut_1 = ut_1 + (KI1*e_t_a1 - KP1*del_y_a1 - KD1*del2_y_a1);
+     % Controller definition (Equation 22 in the paper) for area 2
+    ut_2 = ut_2 + (KI2*e_t_a2 - KP2*del_y_a2 - KD2*del2_y_a2);
+
+    % Defining control signal ut1 for area 1
+    ut1 = [ut1 ut_1];
+    % Defining control signal ut2 for area 2
+    ut2 = [ut2 ut_2];
+    
+    if (i*dt >=40 && i*dt <= 80)
+        PL1 = 0.003;
+    elseif( i*dt > 80 && i*dt <= 120)
+        PL1 = 0.006;
+    elseif( i*dt > 120 && i*dt <= 160)
+        PL1 = 0.009;
+    else
+        PL1 =  0;
+    end
+        
+    PL2 =  0;
+
+    pl1 = [pl1 PL1];
+    pl2 = [pl2 PL2];
+    
+    % Defining control signal Ut
+    Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+
+    System.Output(Ut);
+   
+    % Defining ACE for area 1
+    ACE1 = [ACE1 System.Y(1)];
+    % Defining ACE for area 2
+    ACE2 = [ACE2 System.Y(2)];
+    % Defining Tie Line Power
+    TieLine = [ TieLine System.Y(3)];
+    % Defining Frequency Change for area 1
+    Freq1 = [ Freq1 System.Y(4)];
+    % Defining Frequency Change for area 2
+    Freq2 = [ Freq2 System.Y(5)];
+    % Defining variable time for our time period
+    time = [time i*dt];
+    
+    ITAE = [];
+    ITAE = [ITAE, dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+
+    ISTE = [];
+    ISTE = [ISTE, dt*(i*dt)*( System.Y(1)^2 + System.Y(2)^2 )];
+
+    IAE = [];
+    IAE = [IAE, dt*( abs(System.Y(1)) + abs(System.Y(2)) ) ];
+
+    ISE = [];
+    ISE = [ISE, dt*( System.Y(1)^2 + System.Y(2)^2 ) ];
+end
+
+fprintf('IAE is');
+disp(sum(IAE));
+fprintf('ISE is');
+disp(sum(ISE));
+fprintf('ISTE is');
+disp(sum(ISTE));
+fprintf('ITAE is');
+disp(sum(ITAE));
+
+figure(1);
+subplot(2,1,1);
+plot(time,pl1 );
+title(' Area 1 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+subplot(2,1,2);
+plot(time, pl2);
+title('Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+figure(2);
+subplot(2,1,1);
+plot(time,ut1 );
+title(' Area 1 Control Signal vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+subplot(2,1,2);
+plot(time, ut2);
+title('Area 2 Control Signal  vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+
+figure(3);
+subplot(2,1,1);
+plot(time, ACE1);
+title(' Area 1 ACE vs Time')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+subplot(2,1,2);
+plot(time, ACE2);
+title('Area 2 ACE vs Time')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+
+
+figure(4);
+subplot(2,1,1);
+plot(time, Freq1);
+title(' Area 1 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+subplot(2,1,2);
+plot(time, Freq2);
+title('Area 2 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+
+figure(5);
+plot(time, TieLine);
+title('Tie Line Power vs Time')
+xlabel('Time(s)')
+ylabel('Tie Line Power (pu)')
+
+ACE1_pso = ACE1;
+ACE2_pso = ACE2;
+pso_freq1 = Freq1;
+pso_freq2 = Freq2;
+pso_tileine = TieLine;
+pso_ut1= ut1 ;
+pso_ut2 = ut2 ; 
+
diff --git a/matlab_implementation/TwoAreaPS_PID_2.m b/matlab_implementation/TwoAreaPS_PID_2.m
new file mode 100644
index 0000000..95286e4
--- /dev/null
+++ b/matlab_implementation/TwoAreaPS_PID_2.m
@@ -0,0 +1,192 @@
+% Load Disturbance for area 1
+PL1 = 0;
+% Load Disturbance for area 2
+PL2 = 0;
+
+% Defining and initializing variables
+ut1 = []; % Variable for control signal for area 1
+ut2 = []; % Variable for control signal for area 2
+pl1 = []; % Variable for load disturbance for area 1
+pl2 = []; % Variable for load disturbance for area 2
+ACE1 = []; % Variable for area control error for area 1
+ACE2 = []; % Variable for area control error for area 2
+TieLine = []; % Variable for TieLine Power
+Freq1 =[]; % Variable for Frequency change for area 2
+Freq2 = [];% Variable for Frequency change  for area 2
+time = []; % Variable for time 
+
+
+Tg = 0.08; % Initializing variable for governor time constant
+Tp = 20; % Initializing variable for plant time constant 
+Tt = 0.3; % Initializing variable for Turbine time constant 
+Kp = 120; % Initliazing PID parameter K
+T12 = 0.545/(2*pi); % Initializing variable for Tie line power constant 
+a12 = -1; 
+R = 5; % Initializing variable for Regulation 
+T = 1/80; 
+dt = 1/80;
+beta1 = 0.425; % Initializing variable for Frequency bias constant of area 1
+beta2 = 0.425; % Initializing variable for Frequency bias constant of area 2
+
+% Defining object System for the class TwoAreaPS
+System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+
+
+KP1 = 1.723845;
+KI1 = 0.014555;
+KD1 = 17.936909;
+
+KP2 = 0.106744;
+KI2 = 0.006323;
+KD2 = 15.023620;
+
+ut_1 = 0;
+ut_2 = 0;
+
+t = 200;
+
+y = [];
+x = [];
+
+for i = 1:t/dt
+    % Finding error signal e_t for area 1
+    e_t_a1 = 0 - System.yt_a1(1);
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+    % Finding double derivate of the output (delta square y) for area 1
+    del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+
+    e_t_a2 = 0 - System.yt_a2(1);
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a2 =  System.yt_a2(1) - System.yt_a2(2);
+    % Finding double derivate of the output (delta square y) for area 1
+    del2_y_a2 = System.yt_a2(1) - 2*System.yt_a2(2) + System.yt_a2(3);
+    
+    % Controller definition (Equation 22 in the paper) for area 1
+    ut_1 = ut_1 + (KI1*e_t_a1 - KP1*del_y_a1 - KD1*del2_y_a1);
+     % Controller definition (Equation 22 in the paper) for area 2
+    ut_2 = ut_2 + (KI2*e_t_a2 - KP2*del_y_a2 - KD2*del2_y_a2);
+
+    % Defining control signal ut1 for area 1
+    ut1 = [ut1 ut_1];
+    % Defining control signal ut2 for area 2
+    ut2 = [ut2 ut_2];
+    
+    if (i*dt >=40 && i*dt <= 80)
+        PL1 = 0.003;
+    elseif( i*dt > 80 && i*dt <= 120)
+        PL1 = 0.006;
+    elseif( i*dt > 120 && i*dt <= 160)
+        PL1 = 0.009;
+    else
+        PL1 =  0;
+    end
+        
+    PL2 =  0;
+
+    pl1 = [pl1 PL1];
+    pl2 = [pl2 PL2];
+    
+    % Defining control signal Ut
+    Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+
+    System.Output(Ut);
+   
+    % Defining ACE for area 1
+    ACE1 = [ACE1 System.Y(1)];
+    % Defining ACE for area 2
+    ACE2 = [ACE2 System.Y(2)];
+    % Defining Tie Line Power
+    TieLine = [ TieLine System.Y(3)];
+    % Defining Frequency Change for area 1
+    Freq1 = [ Freq1 System.Y(4)];
+    % Defining Frequency Change for area 2
+    Freq2 = [ Freq2 System.Y(5)];
+    % Defining variable time for our time period
+    time = [time i*dt];
+    
+    ITAE = [];
+    ITAE = [ITAE, dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+
+    ISTE = [];
+    ISTE = [ISTE, dt*(i*dt)*( System.Y(1)^2 + System.Y(2)^2 )];
+
+    IAE = [];
+    IAE = [IAE, dt*( abs(System.Y(1)) + abs(System.Y(2)) ) ];
+
+    ISE = [];
+    ISE = [ISE, dt*( System.Y(1)^2 + System.Y(2)^2 ) ];
+end
+
+fprintf('IAE is');
+disp(sum(IAE));
+fprintf('ISE is');
+disp(sum(ISE));
+fprintf('ISTE is');
+disp(sum(ISTE));
+fprintf('ITAE is');
+disp(sum(ITAE));
+
+figure(1);
+subplot(2,1,1);
+plot(time,pl1 );
+title(' Area 1 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+subplot(2,1,2);
+plot(time, pl2);
+title('Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+figure(2);
+subplot(2,1,1);
+plot(time,ut1 );
+title(' Area 1 Control Signal vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+subplot(2,1,2);
+plot(time, ut2);
+title('Area 2 Control Signal  vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+
+figure(3);
+subplot(2,1,1);
+plot(time, ACE1);
+title(' Area 1 ACE vs Time')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+subplot(2,1,2);
+plot(time, ACE2);
+title('Area 2 ACE vs Time')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+
+
+figure(4);
+subplot(2,1,1);
+plot(time, Freq1);
+title(' Area 1 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+subplot(2,1,2);
+plot(time, Freq2);
+title('Area 2 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+
+figure(5);
+plot(time, TieLine);
+title('Tie Line Power vs Time')
+xlabel('Time(s)')
+ylabel('Tie Line Power (pu)')
+
+ACE1_pso = ACE1;
+ACE2_pso = ACE2;
+pso_freq1 = Freq1;
+pso_freq2 = Freq2;
+pso_tileine = TieLine;
+pso_ut1= ut1 ;
+pso_ut2 = ut2 ; 
+
diff --git a/matlab_implementation/TwoArea_Adaptive.m b/matlab_implementation/TwoArea_Adaptive.m
new file mode 100644
index 0000000..53797b5
--- /dev/null
+++ b/matlab_implementation/TwoArea_Adaptive.m
@@ -0,0 +1,224 @@
+% Load disturbance for Area 1
+PL1 = 0;
+% Load disturbance for Area 2
+PL2 = 0;
+
+% Importing RBF Class
+import RBF.*
+
+% Defining an object (nn1) of the class RBF
+nn1 = RBF( 8e+1, 33.3e-2, 5e+1 , 9e-1, 0.95, 3);
+
+% Defining an object (nn2) of the class RBF
+nn2 = RBF( 8e+1, 33.3e-2, 5e+1 , 9e-1, 0.95, 3);
+
+% Defining and initializing variables
+ut1 = []; % Variable for control signal for area 1
+ut2 = []; % Variable for control signal for area 2
+pl1 = []; % Variable for load disturbance for area 1
+pl2 = []; % Variable for load disturbance for area 2
+ACE1 = []; % Variable for area control error for area 1
+ACE2 = []; % Variable for area control error for area 2
+TieLine = []; % Variable for TieLine Power
+Freq1 =[]; % Variable for Frequency change for area 2
+Freq2 = [];% Variable for Frequency change  for area 2
+time = []; % Variable for time 
+
+Kp_data = [];
+
+Tg = 0.08; % Initializing variable for governor time constant
+Tp = 20; % Initializing variable for plant time constant 
+Tt = 0.3; % Initializing variable for Turbine time constant 
+Kp = 120; % Initializing variable for PID parameter Kp
+T12 = 0.545/(2*pi); % Initializing variable for Tie line power constant 
+a12 = -1; % Initializing variable a12
+R = 5; % Initializing variable for Regulation 
+T = 1/80; % Initializing Time step
+dt = 1/80; % Initializing Time step
+beta1 = 0.425; % Initializing variable for Frequency bias constant of area 1
+beta2 = 0.425; % Initializing variable for Frequency bias constant of area 2
+
+% Defining object System for the class TwoAreaPS
+System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+
+% Initializing Ki
+Ki = 0 ;
+% Initializing Kd
+Kd = 0 ;
+% Initializing Kp
+Kp = 0 ;
+% Initializing weights
+nn1.initialize_weights(1);
+nn2.initialize_weights(2);
+
+% Initializing control signals
+ut_1 = 0;
+ut_2 = 0;
+
+% Duration of run
+t = 200;
+
+% Output variable
+y = [];
+
+for i = 1:t/dt
+    % Finding error signal e_t for area 1
+    e_t_a1 = 0 - System.yt_a1(1);
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+    % Finding double derivate of the output (delta square y) for area 1
+    del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+
+    % Defining the state space X for area 1
+    nn1.X = [ e_t_a1 ; -del_y_a1 ;  -del2_y_a1];
+    % Calling HiddenLayer function using object nn1
+    nn1.HiddenLayer();
+    % Calling OutputLayer function using object nn1
+    nn1.OutputLayer();
+
+    % Finding error signal e_t for area 2
+    e_t_a2 = 0 - System.yt_a2(1);
+    % Finding derivative of the output (delta y) for area 2
+    del_y_a2 =  System.yt_a2(1) - System.yt_a2(2);
+    % Finding double derivate of the output (delta square y) for area 2
+    del2_y_a2 = System.yt_a2(1) - 2*System.yt_a2(2) + System.yt_a2(3);
+
+    %  % Defining the state space X for area 2
+    nn2.X = [ e_t_a2 ; -del_y_a2 ; -del2_y_a2];
+    % Calling HiddenLayer function using object nn2
+    nn2.HiddenLayer();
+    % Calling OutputLayer function using object nn2
+    nn2.OutputLayer();
+
+    % Controller definition (Equation 22 in the paper) for area 1
+    ut_1 = ut_1 + (nn1.K(2)*e_t_a1 - nn1.K(1)*del_y_a1 - nn1.K(3)*del2_y_a1);
+     % Controller definition (Equation 22 in the paper) for area 2
+    ut_2 = ut_2 + (nn1.K(2)*e_t_a2 - nn1.K(1)*del_y_a2 - nn1.K(3)*del2_y_a2);
+
+    % Defining control signal ut1 for area 1
+    ut1 = [ut1 ut_1];
+    % Defining control signal ut2 for area 2
+    ut2 = [ut2 ut_2];
+    
+    % Load disturbances
+    if (i*dt >=40 && i*dt <= 80)
+        PL1 = 0.003;
+    elseif( i*dt > 80 && i*dt <= 120)
+        PL1 = 0.006;
+    elseif( i*dt > 120 && i*dt <= 160)
+        PL1 = 0.009;
+    else
+        PL1 =  0;
+    end
+        
+    PL2 =  0;
+
+    pl1 = [pl1 PL1];
+    pl2 = [pl2 PL2];
+    
+    % Defining control signal Ut
+    Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+
+    System.Output(Ut);
+    
+    % Calling Update function using the object nn1 for area 1
+    nn1.Update(0 ,System.Y(1), System.yt_a1(1), System.yt_a1(2), System.yt_a1(3));
+    % Calling Update function using the object nn2 for area 2
+    nn2.Update(0 ,System.Y(2), System.yt_a2(1), System.yt_a2(2), System.yt_a2(3) );
+
+    % Defining ACE for area 1
+    ACE1 = [ACE1 System.Y(1)];
+    % Defining ACE for area 2
+    ACE2 = [ACE2 System.Y(2)];
+    % Defining Tie Line Power
+    TieLine = [ TieLine System.Y(3)];
+    % Defining Frequency Change for area 1
+    Freq1 = [ Freq1 System.Y(4)];
+    % Defining Frequency Change for area 2
+    Freq2 = [ Freq2 System.Y(5)];
+    % Defining variable time for our time period
+    time = [time i*dt];
+    
+    % Metrics calculations
+
+    %Integral time absolute error(eq 38 in paper)
+    ITAE = [];
+    ITAE = [ITAE, dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+
+    % Integral time squared error(eq 36 in paper)
+    ITSE = [];
+    ITSE = [ITSE, dt*(i*dt)*( System.Y(1)^2 + System.Y(2)^2 )];
+
+    % Integral absolute error(eq 37 in paper)
+    IAE = [];
+    IAE = [IAE, dt*( abs(System.Y(1)) + abs(System.Y(2)) ) ];
+
+    % Integral Square error(eq 39 in paper)
+    ISE = [];
+    ISE = [ISE, dt*( System.Y(1)^2 + System.Y(2)^2 ) ];
+
+end
+
+fprintf('IAE is');
+disp(sum(IAE));
+fprintf('ISE is');
+disp(sum(ISE));
+fprintf('ITSE is');
+disp(sum(ITSE));
+fprintf('ITAE is');
+disp(sum(ITAE));
+
+figure(1);
+subplot(2,1,1);
+plot(time,pl1 );
+title(' Area 1 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+subplot(2,1,2);
+plot(time, pl2);
+title('Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+figure(2);
+subplot(2,1,1);
+plot(time,ut1 );
+title(' Area 1 Control Signal vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+subplot(2,1,2);
+plot(time, ut2);
+title('Area 2 Control Signal  vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+
+% Plotting ACE vs Time
+figure(3);
+subplot(2,1,1);
+plot(time, ACE1);
+title(' Area 1 ACE vs Time')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+subplot(2,1,2);
+plot(time, ACE2);
+title('Area 2 ACE vs Time')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+
+figure(4);
+subplot(2,1,1);
+plot(time, Freq1);
+title(' Area 1 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+subplot(2,1,2);
+plot(time, Freq2);
+title('Area 2 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+
+figure(5);
+plot(time, TieLine);
+title('Tie Line Power vs Time')
+xlabel('Time(s)')
+ylabel('Tie Line Power (pu)')
diff --git a/matlab_implementation/ace1.png b/matlab_implementation/ace1.png
new file mode 100644
index 0000000..9e9f91b
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diff --git a/matlab_implementation/ace2.png b/matlab_implementation/ace2.png
new file mode 100644
index 0000000..278dd03
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diff --git a/matlab_implementation/freq1.png b/matlab_implementation/freq1.png
new file mode 100644
index 0000000..14169cd
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diff --git a/matlab_implementation/freq1_comparison.png b/matlab_implementation/freq1_comparison.png
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index 0000000..9de0e3a
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diff --git a/matlab_implementation/freq2.png b/matlab_implementation/freq2.png
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index 0000000..edfa782
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diff --git a/matlab_implementation/main.asv b/matlab_implementation/main.asv
new file mode 100644
index 0000000..6dd36a5
--- /dev/null
+++ b/matlab_implementation/main.asv
@@ -0,0 +1,271 @@
+% Load disturbance for Area 1
+PL1 = 0;
+% Load disturbance for Area 2
+PL2 = 0;
+
+% Importing RBF Class
+import RBF.*
+
+% Defining an object (nn1) of the class RBF
+
+nn1 = RBF( 0.13,0.21,0.25,0.9,0.98, 3);
+
+% Defining an object (nn2) of the class RBF
+nn2 = RBF( 0.13,0.21,0.25,0.9,0.98, 3);
+
+% Defining and initializing variables
+ut1 = []; % Variable for control signal for area 1
+ut2 = []; % Variable for control signal for area 2
+pl1 = []; % Variable for load disturbance for area 1
+pl2 = []; % Variable for load disturbance for area 2
+ACE1 = []; % Variable for area control error for area 1
+ACE2 = []; % Variable for area control error for area 2
+TieLine = []; % Variable for TieLine Power
+Freq1 =[]; % Variable for Frequency change for area 2
+Freq2 = [];% Variable for Frequency change  for area 2
+time = []; % Variable for time 
+K = [];
+
+Tg = 0.08; % Initializing variable for governor time constant
+Tp = 20; % Initializing variable for plant time constant 
+Tt = 0.3; % Initializing variable for Turbine time constant 
+Kp = 120; % Initializing variable for PID parameter Kp
+T12 = 0.545/(2*pi); % Initializing variable for Tie line power constant 
+a12 = -1; % Initializing variable a12
+R = 5; % Initializing variable for Regulation 
+T = 1/80; % Initializing Time step
+dt = 1/80; % Initializing Time step
+beta1 = 0.425; % Initializing variable for Frequency bias constant of area 1
+beta2 = 0.425; % Initializing variable for Frequency bias constant of area 2
+
+% Defining object System for the class TwoAreaPS
+System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+
+% Initializing Ki
+Ki = 0 ;
+% Initializing Kd
+Kd = 0 ;
+% Initializing Kp
+Kp = 0 ;
+
+% Initializing weights
+nn1.initialize_weights(1);
+nn2.initialize_weights(2);
+
+% Initializing control signals
+ut_1 = 0;
+ut_2 = 0;
+
+% Duration of run
+t = 200;
+
+% Output variable
+y = [];
+
+for i = 1:t/dt
+
+    % Finding error signal e_t for area 1
+    e_t_a1 = 0 - System.yt_a1(1);
+
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+
+    % Finding second derivate of the output (delta square y) for area 1
+    del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+
+    % Defining the state X for area 1 controller
+    nn1.X = [ e_t_a1 ; -del_y_a1 ;  -del2_y_a1];
+
+    % Calling HiddenLayer function using object nn1
+    nn1.HiddenLayer();
+
+    % Calling OutputLayer function using object nn1
+    nn1.OutputLayer();
+
+    % Finding error signal e_t for area 2
+    e_t_a2 = 0 - System.yt_a2(1);
+
+    % Finding derivative of the output (delta y) for area 2
+    del_y_a2 =  System.yt_a2(1) - System.yt_a2(2);
+
+    % Finding second derivate of the output (delta square y) for area 2
+    del2_y_a2 = System.yt_a2(1) - 2*System.yt_a2(2) + System.yt_a2(3);
+
+    % Defining the state X for area 2 controller
+    nn2.X = [ e_t_a2 ; -del_y_a2 ; -del2_y_a2];
+
+    % Calling HiddenLayer function using object nn2
+    nn2.HiddenLayer();
+
+    % Calling OutputLayer function using object nn2
+    nn2.OutputLayer();
+
+    % Control signal (Equation 22 in the paper) for area 1
+    ut_1 = ut_1 + (nn1.K(2)*e_t_a1 - nn1.K(1)*del_y_a1 - nn1.K(3)*del2_y_a1);
+
+    % Control signal (Equation 22 in the paper) for area 2
+    ut_2 = ut_2 + (nn2.K(2)*e_t_a2 - nn2.K(1)*del_y_a2 - nn2.K(3)*del2_y_a2);
+
+    % Calculating delU1
+    delU1 =  (nn1.K(2)*e_t_a1 - nn1.K(1)*del_y_a1 - nn1.K(3)*del2_y_a1);
+
+    
+    K = [K nn1.K(3)];
+    % Calculating delU2
+    delU2 = (nn2.K(2)*e_t_a2 - nn2.K(1)*del_y_a2 - nn2.K(3)*del2_y_a2);
+
+
+    % Defining control signal ut1 for area 1
+    ut1 = [ut1 ut_1];
+
+    % Defining control signal ut2 for area 2
+    ut2 = [ut2 ut_2];
+    
+    % Load disturbances
+    if (i*dt >=40 && i*dt <= 80)
+        PL1 = 0.003;
+    elseif( i*dt > 80 && i*dt <= 120)
+        PL1 = 0.006;
+    elseif( i*dt > 120 && i*dt <= 160)
+        PL1 = 0.009;
+    else
+        PL1 =  0;
+    end
+        
+    PL2 =  0;
+
+    pl1 = [pl1 PL1];
+    pl2 = [pl2 PL2];
+    
+    % Defining control signal Ut
+    Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+
+    System.Output(Ut);
+    
+    % Calling Update function using the object nn1 for area 1
+    nn1.Update(0 ,System.Y(1), System.yt_a1(1), System.yt_a1(2), System.yt_a1(3),delU1+1);
+
+    % Calling Update function using the object nn2 for area 2
+    nn2.Update(0 ,System.Y(2), System.yt_a2(1), System.yt_a2(2), System.yt_a2(3),delU2+1 );
+
+    % Defining ACE for area 1
+    ACE1 = [ACE1 System.Y(1)];
+
+    % Defining ACE for area 2
+    ACE2 = [ACE2 System.Y(2)];
+
+    % Defining Tie Line Power
+    TieLine = [ TieLine System.Y(3)];
+
+    % Defining Frequency Change for area 1
+    Freq1 = [ Freq1 System.Y(4)];
+
+    % Defining Frequency Change for area 2
+    Freq2 = [ Freq2 System.Y(5)];
+
+    % Defining variable time for our time period
+    time = [time i*dt];
+    
+    % Metrics calculations
+
+    %Integral time absolute error(eq 38 in paper)
+    ITAE = [];
+    ITAE = [ITAE dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+
+    % Integral time squared error(eq 36 in paper)
+    ITSE = [];
+    ITSE = [ITSE dt*(i*dt)*( System.Y(1)^2 + System.Y(2)^2 )];
+
+    % Integral absolute error(eq 37 in paper)
+    IAE = [];
+    IAE = [IAE dt*( abs(System.Y(1)) + abs(System.Y(2)) ) ];
+
+    % Integral Square error(eq 39 in paper)
+    ISE = [];
+    ISE = [ISE dt*( System.Y(1)^2 + System.Y(2)^2 ) ];
+
+end
+
+% Displaying metrics values
+fprintf('IAE is');
+disp(sum(IAE));
+fprintf('ISE is');
+disp(sum(ISE));
+fprintf('ITSE is');
+disp(sum(ITSE));
+fprintf('ITAE is');
+disp(sum(ITAE));
+
+% disp(K);
+
+writematrix(ACE1,"ACE1.txt");
+writematrix(ACE2,"ACE2.txt");
+writematrix(time,"time.txt");
+
+% plotting load graph
+figure(1);
+plot(time,pl1 ,time,pl2);
+title(' Area 1 and Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+legend('Area 1', 'Area 2')
+
+% ylabel('Load (pu)')
+% subplot(2,1,2);
+% plot(time, pl2);
+% title('Area 2 Load vs Time')
+% xlabel('Time(s)')
+
+% plotting control signal graph
+figure(2);
+subplot(2,1,1);
+plot(time,ut1 );
+title(' Area 1 Control Signal vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+subplot(2,1,2);
+plot(time, ut2);
+title('Area 2 Control Signal  vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+
+% plotting ACE graph
+figure(3);
+subplot(2,1,1);
+plot(time, ACE1);
+title(' Area 1 ACE vs Time for Adaptive PID')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+subplot(2,1,2);
+plot(time, ACE2);
+title('Area 2 ACE vs Time Adaptive PID')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+
+figure(4);
+plot(time,K);
+title(' Area 1 and Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+% legend('Area 1', 'Area 2')
+
+figure(4);
+subplot(2,1,1);
+plot(time, Freq1);
+title(' Area 1 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+subplot(2,1,2);
+plot(time, Freq2);
+title('Area 2 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+
+figure(5);
+plot(time, TieLine);
+title('Tie Line Power vs Time')
+xlabel('Time(s)')
+ylabel('Tie Line Power (pu)')
+
diff --git a/matlab_implementation/main.m b/matlab_implementation/main.m
new file mode 100644
index 0000000..6dd36a5
--- /dev/null
+++ b/matlab_implementation/main.m
@@ -0,0 +1,271 @@
+% Load disturbance for Area 1
+PL1 = 0;
+% Load disturbance for Area 2
+PL2 = 0;
+
+% Importing RBF Class
+import RBF.*
+
+% Defining an object (nn1) of the class RBF
+
+nn1 = RBF( 0.13,0.21,0.25,0.9,0.98, 3);
+
+% Defining an object (nn2) of the class RBF
+nn2 = RBF( 0.13,0.21,0.25,0.9,0.98, 3);
+
+% Defining and initializing variables
+ut1 = []; % Variable for control signal for area 1
+ut2 = []; % Variable for control signal for area 2
+pl1 = []; % Variable for load disturbance for area 1
+pl2 = []; % Variable for load disturbance for area 2
+ACE1 = []; % Variable for area control error for area 1
+ACE2 = []; % Variable for area control error for area 2
+TieLine = []; % Variable for TieLine Power
+Freq1 =[]; % Variable for Frequency change for area 2
+Freq2 = [];% Variable for Frequency change  for area 2
+time = []; % Variable for time 
+K = [];
+
+Tg = 0.08; % Initializing variable for governor time constant
+Tp = 20; % Initializing variable for plant time constant 
+Tt = 0.3; % Initializing variable for Turbine time constant 
+Kp = 120; % Initializing variable for PID parameter Kp
+T12 = 0.545/(2*pi); % Initializing variable for Tie line power constant 
+a12 = -1; % Initializing variable a12
+R = 5; % Initializing variable for Regulation 
+T = 1/80; % Initializing Time step
+dt = 1/80; % Initializing Time step
+beta1 = 0.425; % Initializing variable for Frequency bias constant of area 1
+beta2 = 0.425; % Initializing variable for Frequency bias constant of area 2
+
+% Defining object System for the class TwoAreaPS
+System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+
+% Initializing Ki
+Ki = 0 ;
+% Initializing Kd
+Kd = 0 ;
+% Initializing Kp
+Kp = 0 ;
+
+% Initializing weights
+nn1.initialize_weights(1);
+nn2.initialize_weights(2);
+
+% Initializing control signals
+ut_1 = 0;
+ut_2 = 0;
+
+% Duration of run
+t = 200;
+
+% Output variable
+y = [];
+
+for i = 1:t/dt
+
+    % Finding error signal e_t for area 1
+    e_t_a1 = 0 - System.yt_a1(1);
+
+    % Finding derivative of the output (delta y) for area 1
+    del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+
+    % Finding second derivate of the output (delta square y) for area 1
+    del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+
+    % Defining the state X for area 1 controller
+    nn1.X = [ e_t_a1 ; -del_y_a1 ;  -del2_y_a1];
+
+    % Calling HiddenLayer function using object nn1
+    nn1.HiddenLayer();
+
+    % Calling OutputLayer function using object nn1
+    nn1.OutputLayer();
+
+    % Finding error signal e_t for area 2
+    e_t_a2 = 0 - System.yt_a2(1);
+
+    % Finding derivative of the output (delta y) for area 2
+    del_y_a2 =  System.yt_a2(1) - System.yt_a2(2);
+
+    % Finding second derivate of the output (delta square y) for area 2
+    del2_y_a2 = System.yt_a2(1) - 2*System.yt_a2(2) + System.yt_a2(3);
+
+    % Defining the state X for area 2 controller
+    nn2.X = [ e_t_a2 ; -del_y_a2 ; -del2_y_a2];
+
+    % Calling HiddenLayer function using object nn2
+    nn2.HiddenLayer();
+
+    % Calling OutputLayer function using object nn2
+    nn2.OutputLayer();
+
+    % Control signal (Equation 22 in the paper) for area 1
+    ut_1 = ut_1 + (nn1.K(2)*e_t_a1 - nn1.K(1)*del_y_a1 - nn1.K(3)*del2_y_a1);
+
+    % Control signal (Equation 22 in the paper) for area 2
+    ut_2 = ut_2 + (nn2.K(2)*e_t_a2 - nn2.K(1)*del_y_a2 - nn2.K(3)*del2_y_a2);
+
+    % Calculating delU1
+    delU1 =  (nn1.K(2)*e_t_a1 - nn1.K(1)*del_y_a1 - nn1.K(3)*del2_y_a1);
+
+    
+    K = [K nn1.K(3)];
+    % Calculating delU2
+    delU2 = (nn2.K(2)*e_t_a2 - nn2.K(1)*del_y_a2 - nn2.K(3)*del2_y_a2);
+
+
+    % Defining control signal ut1 for area 1
+    ut1 = [ut1 ut_1];
+
+    % Defining control signal ut2 for area 2
+    ut2 = [ut2 ut_2];
+    
+    % Load disturbances
+    if (i*dt >=40 && i*dt <= 80)
+        PL1 = 0.003;
+    elseif( i*dt > 80 && i*dt <= 120)
+        PL1 = 0.006;
+    elseif( i*dt > 120 && i*dt <= 160)
+        PL1 = 0.009;
+    else
+        PL1 =  0;
+    end
+        
+    PL2 =  0;
+
+    pl1 = [pl1 PL1];
+    pl2 = [pl2 PL2];
+    
+    % Defining control signal Ut
+    Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+
+    System.Output(Ut);
+    
+    % Calling Update function using the object nn1 for area 1
+    nn1.Update(0 ,System.Y(1), System.yt_a1(1), System.yt_a1(2), System.yt_a1(3),delU1+1);
+
+    % Calling Update function using the object nn2 for area 2
+    nn2.Update(0 ,System.Y(2), System.yt_a2(1), System.yt_a2(2), System.yt_a2(3),delU2+1 );
+
+    % Defining ACE for area 1
+    ACE1 = [ACE1 System.Y(1)];
+
+    % Defining ACE for area 2
+    ACE2 = [ACE2 System.Y(2)];
+
+    % Defining Tie Line Power
+    TieLine = [ TieLine System.Y(3)];
+
+    % Defining Frequency Change for area 1
+    Freq1 = [ Freq1 System.Y(4)];
+
+    % Defining Frequency Change for area 2
+    Freq2 = [ Freq2 System.Y(5)];
+
+    % Defining variable time for our time period
+    time = [time i*dt];
+    
+    % Metrics calculations
+
+    %Integral time absolute error(eq 38 in paper)
+    ITAE = [];
+    ITAE = [ITAE dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+
+    % Integral time squared error(eq 36 in paper)
+    ITSE = [];
+    ITSE = [ITSE dt*(i*dt)*( System.Y(1)^2 + System.Y(2)^2 )];
+
+    % Integral absolute error(eq 37 in paper)
+    IAE = [];
+    IAE = [IAE dt*( abs(System.Y(1)) + abs(System.Y(2)) ) ];
+
+    % Integral Square error(eq 39 in paper)
+    ISE = [];
+    ISE = [ISE dt*( System.Y(1)^2 + System.Y(2)^2 ) ];
+
+end
+
+% Displaying metrics values
+fprintf('IAE is');
+disp(sum(IAE));
+fprintf('ISE is');
+disp(sum(ISE));
+fprintf('ITSE is');
+disp(sum(ITSE));
+fprintf('ITAE is');
+disp(sum(ITAE));
+
+% disp(K);
+
+writematrix(ACE1,"ACE1.txt");
+writematrix(ACE2,"ACE2.txt");
+writematrix(time,"time.txt");
+
+% plotting load graph
+figure(1);
+plot(time,pl1 ,time,pl2);
+title(' Area 1 and Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+legend('Area 1', 'Area 2')
+
+% ylabel('Load (pu)')
+% subplot(2,1,2);
+% plot(time, pl2);
+% title('Area 2 Load vs Time')
+% xlabel('Time(s)')
+
+% plotting control signal graph
+figure(2);
+subplot(2,1,1);
+plot(time,ut1 );
+title(' Area 1 Control Signal vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+subplot(2,1,2);
+plot(time, ut2);
+title('Area 2 Control Signal  vs Time')
+xlabel('Time(s)')
+ylabel('Control Signal (pu)')
+
+% plotting ACE graph
+figure(3);
+subplot(2,1,1);
+plot(time, ACE1);
+title(' Area 1 ACE vs Time for Adaptive PID')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+subplot(2,1,2);
+plot(time, ACE2);
+title('Area 2 ACE vs Time Adaptive PID')
+xlabel('Time(s)')
+ylabel('ACE (pu)')
+
+figure(4);
+plot(time,K);
+title(' Area 1 and Area 2 Load vs Time')
+xlabel('Time(s)')
+ylabel('Load (pu)')
+
+% legend('Area 1', 'Area 2')
+
+figure(4);
+subplot(2,1,1);
+plot(time, Freq1);
+title(' Area 1 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+subplot(2,1,2);
+plot(time, Freq2);
+title('Area 2 Frequency Change vs Time')
+xlabel('Time(s)')
+ylabel('Frequency Change (pu)')
+
+figure(5);
+plot(time, TieLine);
+title('Tie Line Power vs Time')
+xlabel('Time(s)')
+ylabel('Tie Line Power (pu)')
+
diff --git a/matlab_implementation/mu_matrix1.txt b/matlab_implementation/mu_matrix1.txt
new file mode 100644
index 0000000..0ca5e55
--- /dev/null
+++ b/matlab_implementation/mu_matrix1.txt
@@ -0,0 +1,3 @@
+1.845599726003620614e-02 1.516044794402831306e-03 8.995979242641155338e+00
+5.780865431825088323e-03 4.713686580375981566e-03 3.674395894835833065e+00
+9.482924956430698771e+00 -2.785259136223135812e+00 4.344232482720499000e+00
diff --git a/matlab_implementation/mu_matrix2.txt b/matlab_implementation/mu_matrix2.txt
new file mode 100644
index 0000000..c1a46a7
--- /dev/null
+++ b/matlab_implementation/mu_matrix2.txt
@@ -0,0 +1,3 @@
+1.181781558224546773e-02 1.130746439805960235e-02 4.709530595006598652e+00
+6.339533643002934378e-03 3.406172729208175026e-03 3.687143721330234047e+00
+1.537852532877977518e+00 1.835690290426149396e+00 7.904398565729198189e+00
diff --git a/matlab_implementation/nonlinearmain.asv b/matlab_implementation/nonlinearmain.asv
new file mode 100644
index 0000000..eeee867
--- /dev/null
+++ b/matlab_implementation/nonlinearmain.asv
@@ -0,0 +1,4 @@
+yd = [ 2.1*ones(1,100) 3.5*ones(1,100) 2*ones(1,100) 3*ones(1,100)];
+[y,x,i] = nonlinearsystem(yd);
+
+plot(x,y)
\ No newline at end of file
diff --git a/matlab_implementation/nonlinearmain.m b/matlab_implementation/nonlinearmain.m
new file mode 100644
index 0000000..eeee867
--- /dev/null
+++ b/matlab_implementation/nonlinearmain.m
@@ -0,0 +1,4 @@
+yd = [ 2.1*ones(1,100) 3.5*ones(1,100) 2*ones(1,100) 3*ones(1,100)];
+[y,x,i] = nonlinearsystem(yd);
+
+plot(x,y)
\ No newline at end of file
diff --git a/matlab_implementation/nonlinearsystem.asv b/matlab_implementation/nonlinearsystem.asv
new file mode 100644
index 0000000..d18cd14
--- /dev/null
+++ b/matlab_implementation/nonlinearsystem.asv
@@ -0,0 +1,50 @@
+function [y, x, initial_states] = nonlinearsystem(yd)
+    import RBF.*
+    rbf = RBF(0.13,0.21,0.25,0.9,0.98,3);
+    t = 1;
+    yt_1 = 0.4;
+    yt_2 = 0.46;
+    yt_3 = 0.42;
+    initial_states = [yt_1, yt_2, yt_3];
+    dt = 1/400;
+
+    Ki = -0.07709546;
+    Kd = 0.58844546;
+    Kp = -0.01747239;
+
+    ut_1 = 0;
+
+    y = [];
+    x = [];
+
+    for i = 1:t/dt
+        e_t = yd(i) - yt_1;
+        del_y =  yt_1 - yt_2;
+        del2_y = yt_1 - 2*yt_2 + yt_3;
+        
+        rbf.X = [ e_t ; -del_y ;  -del2_y];
+        rbf.HiddenLayer();
+        rbf.OutputLayer();
+
+        ut_1 = ut_1 + rbf.K(2)*e_t - rbf.K(1)*del_y - rbf.K(3)*del2_y;
+        disp(rbf.K);
+%         [y1,y2,y3] = deal(yt_1 , yt_2, yt_3);
+
+
+        [yt_1 , yt_2, yt_3] = deal(yt_1*yt_2*(yt_1 + 2.5) / ( 1 + yt_1^2 + yt_2^2 )+ ut_1 , yt_1 , yt_2) ;
+
+        y0 = yt_1;
+
+
+        rbf.Update(yd(i),y0);
+
+        y = [y, yt_1];
+        x = [x, i];
+    end
+    
+
+    
+
+
+
+end
\ No newline at end of file
diff --git a/matlab_implementation/nonlinearsystem.m b/matlab_implementation/nonlinearsystem.m
new file mode 100644
index 0000000..d18cd14
--- /dev/null
+++ b/matlab_implementation/nonlinearsystem.m
@@ -0,0 +1,50 @@
+function [y, x, initial_states] = nonlinearsystem(yd)
+    import RBF.*
+    rbf = RBF(0.13,0.21,0.25,0.9,0.98,3);
+    t = 1;
+    yt_1 = 0.4;
+    yt_2 = 0.46;
+    yt_3 = 0.42;
+    initial_states = [yt_1, yt_2, yt_3];
+    dt = 1/400;
+
+    Ki = -0.07709546;
+    Kd = 0.58844546;
+    Kp = -0.01747239;
+
+    ut_1 = 0;
+
+    y = [];
+    x = [];
+
+    for i = 1:t/dt
+        e_t = yd(i) - yt_1;
+        del_y =  yt_1 - yt_2;
+        del2_y = yt_1 - 2*yt_2 + yt_3;
+        
+        rbf.X = [ e_t ; -del_y ;  -del2_y];
+        rbf.HiddenLayer();
+        rbf.OutputLayer();
+
+        ut_1 = ut_1 + rbf.K(2)*e_t - rbf.K(1)*del_y - rbf.K(3)*del2_y;
+        disp(rbf.K);
+%         [y1,y2,y3] = deal(yt_1 , yt_2, yt_3);
+
+
+        [yt_1 , yt_2, yt_3] = deal(yt_1*yt_2*(yt_1 + 2.5) / ( 1 + yt_1^2 + yt_2^2 )+ ut_1 , yt_1 , yt_2) ;
+
+        y0 = yt_1;
+
+
+        rbf.Update(yd(i),y0);
+
+        y = [y, yt_1];
+        x = [x, i];
+    end
+    
+
+    
+
+
+
+end
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/Particle.asv b/matlab_implementation/pso_with_two_area/Particle.asv
new file mode 100644
index 0000000..53905ed
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/Particle.asv
@@ -0,0 +1,39 @@
+classdef Particle
+    properties
+        fitness;
+        dim;
+        minx;
+        maxx;
+        position;
+        velocity;
+        best_part_pos;
+        best_part_fitnessVal;
+        rnd;
+    end
+    methods
+        function self = Particle(dim, minx, maxx)
+            rng('default')
+            self.rnd = rand();
+ 
+            self.position = zeros(1,dim);
+         
+            self.velocity = zeros(1,dim);
+         
+            self.best_part_pos = zeros(1,dim);
+         
+            for i = 1:dim
+                self.position(i) = ((maxx - minx) * self.rnd + minx);
+                self.velocity(i) = ((maxx - minx) * self.rnd + minx);
+             
+                self.fitness = system_with_pid(self.position) ;
+                
+                self.best_part_pos = self.position;
+                self.best_part_fitnessVal = self.fitness ;
+            end
+        end
+        
+    end
+end
+
+
+
diff --git a/matlab_implementation/pso_with_two_area/Particle.m b/matlab_implementation/pso_with_two_area/Particle.m
new file mode 100644
index 0000000..53905ed
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/Particle.m
@@ -0,0 +1,39 @@
+classdef Particle
+    properties
+        fitness;
+        dim;
+        minx;
+        maxx;
+        position;
+        velocity;
+        best_part_pos;
+        best_part_fitnessVal;
+        rnd;
+    end
+    methods
+        function self = Particle(dim, minx, maxx)
+            rng('default')
+            self.rnd = rand();
+ 
+            self.position = zeros(1,dim);
+         
+            self.velocity = zeros(1,dim);
+         
+            self.best_part_pos = zeros(1,dim);
+         
+            for i = 1:dim
+                self.position(i) = ((maxx - minx) * self.rnd + minx);
+                self.velocity(i) = ((maxx - minx) * self.rnd + minx);
+             
+                self.fitness = system_with_pid(self.position) ;
+                
+                self.best_part_pos = self.position;
+                self.best_part_fitnessVal = self.fitness ;
+            end
+        end
+        
+    end
+end
+
+
+
diff --git a/matlab_implementation/pso_with_two_area/pso.asv b/matlab_implementation/pso_with_two_area/pso.asv
new file mode 100644
index 0000000..c3ed1f8
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/pso.asv
@@ -0,0 +1,65 @@
+function best_swarm_pos = pso(max_iter, n, dim, minx, maxx)
+    w = 0.729;
+    c1 = 1.49445;
+    c2 = 1.49445;
+    
+    rng('default')
+    rnd = rand();
+    
+    swarm = [];
+    for i = 1:n
+        swarm = [swarm, Particle(dim, minx, maxx)];
+    end
+    
+    best_swarm_fitnessVal = Inf; 
+    
+    for i = 1:n 
+        if swarm(i).fitness < best_swarm_fitnessVal
+          best_swarm_fitnessVal = swarm(i).fitness;
+          best_swarm_pos = swarm(i).position;
+        end
+    end
+
+
+    Iter = 0;
+    while Iter < max_iter
+        
+        for i = 1:n
+        
+            for k = 1:dim
+                r1 = rand();   
+                r2 = rand();
+
+                
+                swarm(i).velocity(k) = ((w * swarm(i).velocity(k)) + (c1 * r1 * (swarm(i).best_part_pos(k) - swarm(i).position(k))) + (c2 * r2 * (best_swarm_pos(k) -swarm(i).position(k)))) ;
+                
+      
+                if swarm(i).velocity(k) < minx
+                  swarm(i).velocity(k) = minx;
+                elseif swarm(i).velocity(k) > maxx
+                  swarm(i).velocity(k) = maxx;
+                end
+            
+            
+            for k = 1:dim
+                swarm(i).position(k) = swarm(i).position(k) + swarm(i).velocity(k);
+            end
+            
+            swarm(i).fitness = system_with_pid(swarm(i).position);
+            
+            if swarm(i).fitness < swarm(i).best_part_fitnessVal
+                swarm(i).best_part_fitnessVal = swarm(i).fitness;
+                swarm(i).best_part_pos = swarm(i).position;
+            end
+            
+            if swarm(i).fitness < best_swarm_fitnessVal
+                best_swarm_fitnessVal = swarm(i).fitness;
+                best_swarm_pos = swarm(i).position;
+            end
+        
+        
+            end
+        end
+        Iter = Iter+1;
+    end
+end
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/pso.m b/matlab_implementation/pso_with_two_area/pso.m
new file mode 100644
index 0000000..c3ed1f8
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/pso.m
@@ -0,0 +1,65 @@
+function best_swarm_pos = pso(max_iter, n, dim, minx, maxx)
+    w = 0.729;
+    c1 = 1.49445;
+    c2 = 1.49445;
+    
+    rng('default')
+    rnd = rand();
+    
+    swarm = [];
+    for i = 1:n
+        swarm = [swarm, Particle(dim, minx, maxx)];
+    end
+    
+    best_swarm_fitnessVal = Inf; 
+    
+    for i = 1:n 
+        if swarm(i).fitness < best_swarm_fitnessVal
+          best_swarm_fitnessVal = swarm(i).fitness;
+          best_swarm_pos = swarm(i).position;
+        end
+    end
+
+
+    Iter = 0;
+    while Iter < max_iter
+        
+        for i = 1:n
+        
+            for k = 1:dim
+                r1 = rand();   
+                r2 = rand();
+
+                
+                swarm(i).velocity(k) = ((w * swarm(i).velocity(k)) + (c1 * r1 * (swarm(i).best_part_pos(k) - swarm(i).position(k))) + (c2 * r2 * (best_swarm_pos(k) -swarm(i).position(k)))) ;
+                
+      
+                if swarm(i).velocity(k) < minx
+                  swarm(i).velocity(k) = minx;
+                elseif swarm(i).velocity(k) > maxx
+                  swarm(i).velocity(k) = maxx;
+                end
+            
+            
+            for k = 1:dim
+                swarm(i).position(k) = swarm(i).position(k) + swarm(i).velocity(k);
+            end
+            
+            swarm(i).fitness = system_with_pid(swarm(i).position);
+            
+            if swarm(i).fitness < swarm(i).best_part_fitnessVal
+                swarm(i).best_part_fitnessVal = swarm(i).fitness;
+                swarm(i).best_part_pos = swarm(i).position;
+            end
+            
+            if swarm(i).fitness < best_swarm_fitnessVal
+                best_swarm_fitnessVal = swarm(i).fitness;
+                best_swarm_pos = swarm(i).position;
+            end
+        
+        
+            end
+        end
+        Iter = Iter+1;
+    end
+end
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/pso_example.asv b/matlab_implementation/pso_with_two_area/pso_example.asv
new file mode 100644
index 0000000..8b792bf
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/pso_example.asv
@@ -0,0 +1,63 @@
+% Initialization
+% Parameters
+clear
+clc
+iterations = 50;
+W = 0.9;
+C1 = 2.0;
+C2 = 2.0;
+n = 49;
+% ---- initial swarm position -----
+index = 1;
+for i = 1 : 7
+    for j = 1 : 7
+        particle(index, 1, 1) = i;
+        particle(index, 1, 2) = j;
+        index = index + 1;
+    end
+end
+particle(:, 4, 1) = 1000;          % best value so far
+particle(:, 2, :) = 0;             % initial velocity
+%% Iterations
+for iter = 1 : iterations
+%-- evaluating position & quality ---
+        for i = 1 : n
+        particle(i, 1, 1) = particle(i, 1, 1) + particle(i, 2, 1)/1.3;     %update x position
+        particle(i, 1, 2) = particle(i, 1, 2) + particle(i, 2, 2)/1.3;     %update y position
+        Kp = particle(i, 1, 1);
+        Ki = particle(i, 1, 2);
+        Gc=tf([Kp Ki],[1 0]);
+        G=tf(1,[1 2 3]);
+        Q=feedback(Gc*G,1);
+        Z=stepinfo(Q);
+        a=Z.RiseTime;
+        b=Z.SettlingTime;
+        % Z.Overshoot=350;
+        c=Z.Overshoot;
+        d=Z.Undershoot;
+        % e=Z.SettlingMax;
+        % alpha=0.5;
+        F = min((a)+min(c)+min(b)+min(d));          % fitness evaluation
+                
+        if F < particle(i, 4, 1)                 % if new position is better
+            particle(i, 3, 1) = particle(i, 1, 1);    % update best x,
+            particle(i, 3, 2) = particle(i, 1, 2);    % best y postions
+            particle(i, 4, 1) = F;               % and best value
+        end
+    end
+    [temp, gbest] = min(particle(:, 4, 1));        % global best position
+    %--- updating velocity vectors
+    for i = 1 : n
+        particle(i, 2, 1) = rand*W*particle(i, 2, 1) + C1*rand*(particle(i, 3, 1) - particle(i, 1, 1)) + C2*rand*(particle(gbest, 3, 1) - particle(i, 1, 1));   %x velocity component
+        particle(i, 2, 2) = rand*W*particle(i, 2, 2) + C1*rand*(particle(i, 3, 2) - particle(i, 1, 2)) + C2*rand*(particle(gbest, 3, 2) - particle(i, 1, 2));   %y velocity component
+    end
+    %% Plotting the swarm
+    disp(gbest)
+    clf    
+    plot(particle(:, 1, 1), particle(:, 1, 2), 'x')   
+    axis([-2 10 -2 10]);
+    pause(0)
+    
+end
+disp('best value is')
+disp(gbest)
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/pso_example.m b/matlab_implementation/pso_with_two_area/pso_example.m
new file mode 100644
index 0000000..8b792bf
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/pso_example.m
@@ -0,0 +1,63 @@
+% Initialization
+% Parameters
+clear
+clc
+iterations = 50;
+W = 0.9;
+C1 = 2.0;
+C2 = 2.0;
+n = 49;
+% ---- initial swarm position -----
+index = 1;
+for i = 1 : 7
+    for j = 1 : 7
+        particle(index, 1, 1) = i;
+        particle(index, 1, 2) = j;
+        index = index + 1;
+    end
+end
+particle(:, 4, 1) = 1000;          % best value so far
+particle(:, 2, :) = 0;             % initial velocity
+%% Iterations
+for iter = 1 : iterations
+%-- evaluating position & quality ---
+        for i = 1 : n
+        particle(i, 1, 1) = particle(i, 1, 1) + particle(i, 2, 1)/1.3;     %update x position
+        particle(i, 1, 2) = particle(i, 1, 2) + particle(i, 2, 2)/1.3;     %update y position
+        Kp = particle(i, 1, 1);
+        Ki = particle(i, 1, 2);
+        Gc=tf([Kp Ki],[1 0]);
+        G=tf(1,[1 2 3]);
+        Q=feedback(Gc*G,1);
+        Z=stepinfo(Q);
+        a=Z.RiseTime;
+        b=Z.SettlingTime;
+        % Z.Overshoot=350;
+        c=Z.Overshoot;
+        d=Z.Undershoot;
+        % e=Z.SettlingMax;
+        % alpha=0.5;
+        F = min((a)+min(c)+min(b)+min(d));          % fitness evaluation
+                
+        if F < particle(i, 4, 1)                 % if new position is better
+            particle(i, 3, 1) = particle(i, 1, 1);    % update best x,
+            particle(i, 3, 2) = particle(i, 1, 2);    % best y postions
+            particle(i, 4, 1) = F;               % and best value
+        end
+    end
+    [temp, gbest] = min(particle(:, 4, 1));        % global best position
+    %--- updating velocity vectors
+    for i = 1 : n
+        particle(i, 2, 1) = rand*W*particle(i, 2, 1) + C1*rand*(particle(i, 3, 1) - particle(i, 1, 1)) + C2*rand*(particle(gbest, 3, 1) - particle(i, 1, 1));   %x velocity component
+        particle(i, 2, 2) = rand*W*particle(i, 2, 2) + C1*rand*(particle(i, 3, 2) - particle(i, 1, 2)) + C2*rand*(particle(gbest, 3, 2) - particle(i, 1, 2));   %y velocity component
+    end
+    %% Plotting the swarm
+    disp(gbest)
+    clf    
+    plot(particle(:, 1, 1), particle(:, 1, 2), 'x')   
+    axis([-2 10 -2 10]);
+    pause(0)
+    
+end
+disp('best value is')
+disp(gbest)
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/pso_example_2.asv b/matlab_implementation/pso_with_two_area/pso_example_2.asv
new file mode 100644
index 0000000..48af1f7
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/pso_example_2.asv
@@ -0,0 +1,114 @@
+clear
+clc
+num_particles = 50;           % Size of the swarm " no of birds "
+max_iter = 50;                    % Maximum number of "birds steps"
+dim = 6;                % Dimension of the problem
+
+c2 = 1.49445;          % PSO parameter C1
+c1 = 1.49445;        % PSO parameter C2
+w = 0.729;           % pso momentum or inertia
+fitness = zeros(num_particles,max_iter);
+
+                                       %-----------------------------%
+                                       %    initialize the parameter %
+                                       %-----------------------------%
+
+R1 = rand(dim, num_particles);
+R2 = rand(dim, num_particles);
+current_fitness = zeros(num_particles,1);
+
+                                 %------------------------------------------------%
+                                 % Initializing swarm and velocities and position %
+                                 %------------------------------------------------%
+
+current_position = 10 * (rand(dim, num_particles)-0.5);
+velocity = 0.3 * randn(dim, num_particles) ;
+local_best_position  = current_position ;
+
+
+                                 %-------------------------------------------%
+                                 %     Evaluate initial population           %
+                                 %-------------------------------------------%
+
+for i = 1 : num_particles
+    current_fitness(i) = system_with_pid(current_position(:,i));
+end
+
+
+local_best_fitness  = current_fitness ;
+[global_best_fitness,g] = min(local_best_fitness) ;
+
+for i = 1 : num_particles
+    global_best_position(:,i) = local_best_position(:,g) ;
+end
+%                                                %-------------------%
+%                                                %  VELOCITY UPDATE  %
+%                                                %-------------------%
+% 
+% velocity = w *velocity + c1*(R1.*(local_best_position-current_position)) + c2*(R2.*(global_best_position-current_position));
+% 
+%                                                %------------------%
+%                                                %   SWARMUPDATE    %
+%                                                %------------------%
+% 
+% 
+% current_position = current_position + velocity ;
+
+                                               %------------------------%
+                                               %  evaluate a new swarm   %
+                                               %------------------------%
+iter = 0 ;        % Iterations’counter
+while  ( iter < max_iter )
+    if mod(iter,10)==0 && iter>1 
+%         fprintf('Iter = %d', iter);
+%         fprintf('Best fitness = %.7f', current_global_best_fitness);
+        disp(iter);
+        disp(current_global_best_fitness);
+    end
+    iter = iter + 1;
+    
+    for i = 1 : num_particles
+        current_fitness(i) = system_with_pid(current_position(:,i)) ;
+    end
+    
+    
+    for i = 1 : num_particles
+        if current_fitness(i) < local_best_fitness(i)
+            local_best_fitness(i)  = current_fitness(i);
+            local_best_position(:,i) = current_position(:,i)   ;
+        end
+        fitness(i,iter) = local_best_fitness(i);
+    end
+    
+    
+    [current_global_best_fitness,g] = min(local_best_fitness);
+    
+    
+    if current_global_best_fitness < global_best_fitness
+        global_best_fitness = current_global_best_fitness;
+    
+        for i = 1 : num_particles
+            global_best_position(:,i) = local_best_position(:,g);
+        end
+    
+    end
+    
+    
+    velocity = w *velocity + c1*(R1.*(local_best_position-current_position)) + c2*(R2.*(global_best_position-current_position));
+    current_position = current_position + velocity;
+
+
+    
+
+
+end % end of while loop its mean the end of all step that the birds move it
+
+
+xx = fitness(:,max_iter);
+% disp(current_global_best_fitness);
+disp(xx);
+[Y,I] = min(xx);
+% disp(Y);
+disp(current_position(:,I));
+
+%
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/pso_example_2.m b/matlab_implementation/pso_with_two_area/pso_example_2.m
new file mode 100644
index 0000000..48af1f7
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/pso_example_2.m
@@ -0,0 +1,114 @@
+clear
+clc
+num_particles = 50;           % Size of the swarm " no of birds "
+max_iter = 50;                    % Maximum number of "birds steps"
+dim = 6;                % Dimension of the problem
+
+c2 = 1.49445;          % PSO parameter C1
+c1 = 1.49445;        % PSO parameter C2
+w = 0.729;           % pso momentum or inertia
+fitness = zeros(num_particles,max_iter);
+
+                                       %-----------------------------%
+                                       %    initialize the parameter %
+                                       %-----------------------------%
+
+R1 = rand(dim, num_particles);
+R2 = rand(dim, num_particles);
+current_fitness = zeros(num_particles,1);
+
+                                 %------------------------------------------------%
+                                 % Initializing swarm and velocities and position %
+                                 %------------------------------------------------%
+
+current_position = 10 * (rand(dim, num_particles)-0.5);
+velocity = 0.3 * randn(dim, num_particles) ;
+local_best_position  = current_position ;
+
+
+                                 %-------------------------------------------%
+                                 %     Evaluate initial population           %
+                                 %-------------------------------------------%
+
+for i = 1 : num_particles
+    current_fitness(i) = system_with_pid(current_position(:,i));
+end
+
+
+local_best_fitness  = current_fitness ;
+[global_best_fitness,g] = min(local_best_fitness) ;
+
+for i = 1 : num_particles
+    global_best_position(:,i) = local_best_position(:,g) ;
+end
+%                                                %-------------------%
+%                                                %  VELOCITY UPDATE  %
+%                                                %-------------------%
+% 
+% velocity = w *velocity + c1*(R1.*(local_best_position-current_position)) + c2*(R2.*(global_best_position-current_position));
+% 
+%                                                %------------------%
+%                                                %   SWARMUPDATE    %
+%                                                %------------------%
+% 
+% 
+% current_position = current_position + velocity ;
+
+                                               %------------------------%
+                                               %  evaluate a new swarm   %
+                                               %------------------------%
+iter = 0 ;        % Iterations’counter
+while  ( iter < max_iter )
+    if mod(iter,10)==0 && iter>1 
+%         fprintf('Iter = %d', iter);
+%         fprintf('Best fitness = %.7f', current_global_best_fitness);
+        disp(iter);
+        disp(current_global_best_fitness);
+    end
+    iter = iter + 1;
+    
+    for i = 1 : num_particles
+        current_fitness(i) = system_with_pid(current_position(:,i)) ;
+    end
+    
+    
+    for i = 1 : num_particles
+        if current_fitness(i) < local_best_fitness(i)
+            local_best_fitness(i)  = current_fitness(i);
+            local_best_position(:,i) = current_position(:,i)   ;
+        end
+        fitness(i,iter) = local_best_fitness(i);
+    end
+    
+    
+    [current_global_best_fitness,g] = min(local_best_fitness);
+    
+    
+    if current_global_best_fitness < global_best_fitness
+        global_best_fitness = current_global_best_fitness;
+    
+        for i = 1 : num_particles
+            global_best_position(:,i) = local_best_position(:,g);
+        end
+    
+    end
+    
+    
+    velocity = w *velocity + c1*(R1.*(local_best_position-current_position)) + c2*(R2.*(global_best_position-current_position));
+    current_position = current_position + velocity;
+
+
+    
+
+
+end % end of while loop its mean the end of all step that the birds move it
+
+
+xx = fitness(:,max_iter);
+% disp(current_global_best_fitness);
+disp(xx);
+[Y,I] = min(xx);
+% disp(Y);
+disp(current_position(:,I));
+
+%
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/pso_main.asv b/matlab_implementation/pso_with_two_area/pso_main.asv
new file mode 100644
index 0000000..75a812f
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/pso_main.asv
@@ -0,0 +1,12 @@
+
+dim = 6;
+% fitness = @system_with_pid;
+ 
+num_particles = 40;
+max_iter = 50;
+ 
+ 
+best_position = pso(max_iter, num_particles, dim, -1, 1);
+disp(best_position);
+fitnessVal = system_with_pid(best_position);
+disp(fitnessVal);
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/pso_main.m b/matlab_implementation/pso_with_two_area/pso_main.m
new file mode 100644
index 0000000..582a027
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/pso_main.m
@@ -0,0 +1,11 @@
+
+dim = 6;
+ 
+num_particles = 40;
+max_iter = 50;
+ 
+ 
+best_position = pso(max_iter, num_particles, dim, -1, 1);
+disp(best_position);
+fitnessVal = system_with_pid(best_position);
+disp(fitnessVal);
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/system_with_pid.asv b/matlab_implementation/pso_with_two_area/system_with_pid.asv
new file mode 100644
index 0000000..accfbd2
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/system_with_pid.asv
@@ -0,0 +1,87 @@
+function fitness = system_with_pid(k_values)
+    PL1 = 0;
+    PL2 = 0;
+    import RBF.*
+    
+    
+    ut1 = [];
+    ut2 = [];
+    pl1 = []; 
+    pl2 = [];
+    ACE1 = []; 
+    ACE2 = [];
+    time = [];
+    
+    Tg = 0.08;
+    Tp = 20;
+    Tt = 0.3;
+    Kp = 120;
+    T12 = 0.545/(2*pi);
+    a12 = -1;
+    R = 5;
+    T = 1/80;
+    dt = 1/80;
+    beta1 = 0.425;
+    beta2 = 0.425;
+    
+    
+    System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+    
+    KP1 = k_values(1);
+    KI1 = k_values(2);
+    KD1 = k_values(3);
+    
+    KP2 = k_values(4);
+    KI2 = k_values(5);
+    KD2 = k_values(6);
+    
+    
+    
+    ut_1 = 0;
+    ut_2 = 0;
+    
+    t = 200;
+    
+    y = [];
+    x = [];
+    
+    for i = 1:t/dt
+        e_t_a1 = 0 - System.yt_a1(1);
+        del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+        del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+    
+        e_t_a2 = 0 - System.yt_a2(1);
+        del_y_a2 =  System.yt_a2(1) - System.yt_a2(2);
+        del2_y_a2 = System.yt_a2(1) - 2*System.yt_a2(2) + System.yt_a2(3);
+    
+        ut_1 = ut_1 + KI1*e_t_a1 - KP1*del_y_a1 - KD1*del2_y_a1;
+    
+        ut_2 = ut_2 + KI2*e_t_a2 - KP2*del_y_a2 - KD2*del2_y_a2;
+    
+        ut1 = [ut1 ut_1];
+        ut2 = [ut2 ut_2];
+        
+        if (i*dt >=40 && i*dt <= 80)
+            PL1 = 0.003;
+        elseif( i*dt > 80 && i*dt <= 120)
+            PL1 = 0.006;
+        elseif( i*dt > 120 && i*dt <= 160)
+            PL1 = 0.009;
+        else
+            PL1 =  0;
+        end
+            
+        PL2 =  0;
+    
+        pl1 = [pl1 PL1];
+        pl2 = [pl2 PL2];
+    
+        Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+    
+        System.Output(Ut);
+        performance_index = [];
+        performance_index = [performance_index, dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+    end
+
+    fitness = sum(performance_index);
+end
\ No newline at end of file
diff --git a/matlab_implementation/pso_with_two_area/system_with_pid.m b/matlab_implementation/pso_with_two_area/system_with_pid.m
new file mode 100644
index 0000000..accfbd2
--- /dev/null
+++ b/matlab_implementation/pso_with_two_area/system_with_pid.m
@@ -0,0 +1,87 @@
+function fitness = system_with_pid(k_values)
+    PL1 = 0;
+    PL2 = 0;
+    import RBF.*
+    
+    
+    ut1 = [];
+    ut2 = [];
+    pl1 = []; 
+    pl2 = [];
+    ACE1 = []; 
+    ACE2 = [];
+    time = [];
+    
+    Tg = 0.08;
+    Tp = 20;
+    Tt = 0.3;
+    Kp = 120;
+    T12 = 0.545/(2*pi);
+    a12 = -1;
+    R = 5;
+    T = 1/80;
+    dt = 1/80;
+    beta1 = 0.425;
+    beta2 = 0.425;
+    
+    
+    System = TwoAreaPS( Tg, Tp, Tt, Kp, T12, a12, R, T, beta1, beta2,  [0,0,0],[0,0,0] );
+    
+    KP1 = k_values(1);
+    KI1 = k_values(2);
+    KD1 = k_values(3);
+    
+    KP2 = k_values(4);
+    KI2 = k_values(5);
+    KD2 = k_values(6);
+    
+    
+    
+    ut_1 = 0;
+    ut_2 = 0;
+    
+    t = 200;
+    
+    y = [];
+    x = [];
+    
+    for i = 1:t/dt
+        e_t_a1 = 0 - System.yt_a1(1);
+        del_y_a1 =  System.yt_a1(1) - System.yt_a1(2);
+        del2_y_a1 = System.yt_a1(1) - 2*System.yt_a1(2) + System.yt_a1(3);
+    
+        e_t_a2 = 0 - System.yt_a2(1);
+        del_y_a2 =  System.yt_a2(1) - System.yt_a2(2);
+        del2_y_a2 = System.yt_a2(1) - 2*System.yt_a2(2) + System.yt_a2(3);
+    
+        ut_1 = ut_1 + KI1*e_t_a1 - KP1*del_y_a1 - KD1*del2_y_a1;
+    
+        ut_2 = ut_2 + KI2*e_t_a2 - KP2*del_y_a2 - KD2*del2_y_a2;
+    
+        ut1 = [ut1 ut_1];
+        ut2 = [ut2 ut_2];
+        
+        if (i*dt >=40 && i*dt <= 80)
+            PL1 = 0.003;
+        elseif( i*dt > 80 && i*dt <= 120)
+            PL1 = 0.006;
+        elseif( i*dt > 120 && i*dt <= 160)
+            PL1 = 0.009;
+        else
+            PL1 =  0;
+        end
+            
+        PL2 =  0;
+    
+        pl1 = [pl1 PL1];
+        pl2 = [pl2 PL2];
+    
+        Ut = [ ut_1 ; ut_2 ; PL1 ; PL2 ];
+    
+        System.Output(Ut);
+        performance_index = [];
+        performance_index = [performance_index, dt*(i*dt)*( abs(System.Y(1)) + abs(System.Y(2)))];
+    end
+
+    fitness = sum(performance_index);
+end
\ No newline at end of file
diff --git a/matlab_implementation/sigma_matrix1.txt b/matlab_implementation/sigma_matrix1.txt
new file mode 100644
index 0000000..064ae20
--- /dev/null
+++ b/matlab_implementation/sigma_matrix1.txt
@@ -0,0 +1 @@
+1.958288059466925191e+00 2.405280511179789561e-03 4.456775142277715318e+00
diff --git a/matlab_implementation/sigma_matrix2.txt b/matlab_implementation/sigma_matrix2.txt
new file mode 100644
index 0000000..d75c6ad
--- /dev/null
+++ b/matlab_implementation/sigma_matrix2.txt
@@ -0,0 +1 @@
+4.844955477517413733e+00 1.878559667561860547e+00 4.493629460068961912e+00
diff --git a/matlab_implementation/tieline.png b/matlab_implementation/tieline.png
new file mode 100644
index 0000000..7a71fba
Binary files /dev/null and b/matlab_implementation/tieline.png differ
diff --git a/matlab_implementation/time.txt b/matlab_implementation/time.txt
new file mode 100644
index 0000000..4b7eeab
--- /dev/null
+++ b/matlab_implementation/time.txt
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diff --git a/matlab_implementation/twoarea_pso.asv b/matlab_implementation/twoarea_pso.asv
new file mode 100644
index 0000000..3c70442
--- /dev/null
+++ b/matlab_implementation/twoarea_pso.asv
@@ -0,0 +1,61 @@
+% Initialization
+% Parameters
+clear
+clc
+iterations = 50;
+W = 0.9;
+C1 = 2.0;
+C2 = 2.0;
+n = 49;
+% ---- initial swarm position -----
+index = 1;
+for i = 1 : 7
+    for j = 1 : 7
+        particle(index, 1, 1) = i;
+        particle(index, 1, 2) = j;
+        index = index + 1;
+    end
+end
+particle(:, 4, 1) = 1000;          % best value so far
+particle(:, 2, :) = 0;             % initial velocity
+%% Iterations
+for iter = 1 : iterations
+%-- evaluating position & quality ---
+        for i = 1 : n
+        particle(i, 1, 1) = particle(i, 1, 1) + particle(i, 2, 1)/1.3;     %update x position
+        particle(i, 1, 2) = particle(i, 1, 2) + particle(i, 2, 2)/1.3;     %update y position
+        Kp = particle(i, 1, 1);
+        Ki = particle(i, 1, 2);
+        Gc=tf([Kp Ki],[1 0]);
+        G=tf(1,[1 2 3]);
+        Q=feedback(Gc*G,1);
+        Z=stepinfo(Q);
+        a=Z.RiseTime;
+        b=Z.SettlingTime;
+        % Z.Overshoot=350;
+        c=Z.Overshoot;
+        d=Z.Undershoot;
+        % e=Z.SettlingMax;
+        % alpha=0.5;
+        F = min((a)+min(c)+min(b)+min(d));          % fitness evaluation
+                
+        if F < particle(i, 4, 1)                 % if new position is better
+            particle(i, 3, 1) = particle(i, 1, 1);    % update best x,
+            particle(i, 3, 2) = particle(i, 1, 2);    % best y postions
+            particle(i, 4, 1) = F;               % and best value
+        end
+    end
+    [temp, gbest] = min(particle(:, 4, 1));        % global best position
+    %--- updating velocity vectors
+    for i = 1 : n
+        particle(i, 2, 1) = rand*W*particle(i, 2, 1) + C1*rand*(particle(i, 3, 1) - particle(i, 1, 1)) + C2*rand*(particle(gbest, 3, 1) - particle(i, 1, 1));   %x velocity component
+        particle(i, 2, 2) = rand*W*particle(i, 2, 2) + C1*rand*(particle(i, 3, 2) - particle(i, 1, 2)) + C2*rand*(particle(gbest, 3, 2) - particle(i, 1, 2));   %y velocity component
+    end
+    %% Plotting the swarm
+    disp(gbest)
+    clf    
+    plot(particle(:, 1, 1), particle(:, 1, 2), 'x')   
+    axis([-2 150 -2 150]);
+    pause(0)
+    
+end
diff --git a/matlab_implementation/untitled8.png b/matlab_implementation/untitled8.png
new file mode 100644
index 0000000..2d85293
Binary files /dev/null and b/matlab_implementation/untitled8.png differ
diff --git a/matlab_implementation/untitled9.png b/matlab_implementation/untitled9.png
new file mode 100644
index 0000000..2780889
Binary files /dev/null and b/matlab_implementation/untitled9.png differ
diff --git a/matlab_implementation/ut1.png b/matlab_implementation/ut1.png
new file mode 100644
index 0000000..e792771
Binary files /dev/null and b/matlab_implementation/ut1.png differ
diff --git a/matlab_implementation/ut2.png b/matlab_implementation/ut2.png
new file mode 100644
index 0000000..7689bc4
Binary files /dev/null and b/matlab_implementation/ut2.png differ
diff --git a/matlab_implementation/v_matrix1.txt b/matlab_implementation/v_matrix1.txt
new file mode 100644
index 0000000..c0dd1d6
--- /dev/null
+++ b/matlab_implementation/v_matrix1.txt
@@ -0,0 +1 @@
+-5.119681902619694497e-02 -5.677065117500559865e-02 4.543883283077812529e-01
diff --git a/matlab_implementation/v_matrix2.txt b/matlab_implementation/v_matrix2.txt
new file mode 100644
index 0000000..4985c9f
--- /dev/null
+++ b/matlab_implementation/v_matrix2.txt
@@ -0,0 +1 @@
+2.018131229130886925e-02 -6.464005328840795317e-02 2.501364485888891293e-02
diff --git a/matlab_implementation/w_matrix1.asv b/matlab_implementation/w_matrix1.asv
new file mode 100644
index 0000000..3b17609
--- /dev/null
+++ b/matlab_implementation/w_matrix1.asv
@@ -0,0 +1,3 @@
+1.907601000e+000 1.572228000e+000 0.076839000e+000
+57.048960000e-003 0.000382030e+000 -2.1046990e-002
+6.4872820900e+001 -2.5643675742e+001 1.65372754e-001
diff --git a/matlab_implementation/w_matrix1.txt b/matlab_implementation/w_matrix1.txt
new file mode 100644
index 0000000..3b17609
--- /dev/null
+++ b/matlab_implementation/w_matrix1.txt
@@ -0,0 +1,3 @@
+1.907601000e+000 1.572228000e+000 0.076839000e+000
+57.048960000e-003 0.000382030e+000 -2.1046990e-002
+6.4872820900e+001 -2.5643675742e+001 1.65372754e-001
diff --git a/matlab_implementation/w_matrix2.asv b/matlab_implementation/w_matrix2.asv
new file mode 100644
index 0000000..8c42bac
--- /dev/null
+++ b/matlab_implementation/w_matrix2.asv
@@ -0,0 +1,3 @@
+-5.2316153 5.415998 0.86425342
+4.624684 0.2412 -4.857954
+43.1839379 -25.6099376 -3.75358525
diff --git a/matlab_implementation/w_matrix2.txt b/matlab_implementation/w_matrix2.txt
new file mode 100644
index 0000000..cccdb95
--- /dev/null
+++ b/matlab_implementation/w_matrix2.txt
@@ -0,0 +1,3 @@
+-5.231615300e+000 5.415998000e+000 0.864253420e+000
+4.624684000e+000 0.241200000e+000 -4.857954000e+000
+43.183937900e+000 -25.609937600e+000 -3.753585250e+000
diff --git a/RBF.py b/python_implementation/RBF.py
similarity index 100%
rename from RBF.py
rename to python_implementation/RBF.py
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