diff --git a/Fixed_time_NN.slx b/Fixed_time_NN.slx new file mode 100644 index 0000000..822eeae Binary files /dev/null and b/Fixed_time_NN.slx differ diff --git a/Fixed_time_NNcontroller.m b/Fixed_time_NNcontroller.m new file mode 100644 index 0000000..2cf54e3 --- /dev/null +++ b/Fixed_time_NNcontroller.m @@ -0,0 +1,265 @@ +function [sys,x0,str,ts] = Fixed_time_NNcontroller(t,x,u,flag) +% 以下程序是 基于RBF神经网络的直接鲁棒自适应控制 +switch flag + case 0 %初始化 + [sys,x0,str,ts]=mdlInitializeSizes; + case 1 %连续状态计算 + sys=mdlDerivatives(t,x,u); + case {2,4,9} %离散状态计算，下一步仿真时刻，终止仿真设定 + sys=[]; + case 3 %输出信号计算 + sys=mdlOutputs(t,x,u); + otherwise + DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag)); +end + +function [sys,x0,str,ts]=mdlInitializeSizes %系统的初始化 +global c1 b1 c2 b2 node gama1 gama2 xite belta lg +% 神经网络采用2-7-1结构 +node = 7; +c1 = 0.5*[-2 -1.5 -1 0 1 1.5 2; + -2 -1.5 -1 0 1 1.5 2; + -2 -1.5 -1 0 1 1.5 2; + -2 -1.5 -1 0 1 1.5 2]; % 高斯函数的中心点矢量 维度 IN * MID 2*7 +b1 = 20; % 高斯函数的基宽 维度MID * 1 b的选择很重要 b越大 网路对输入的映射能力越大 +gama1 = 10; +lg = 2; +xite = 20; % 控制器的参数 + +c2 = 1.8*[-2 -1.5 -1 0 1 1.5 2; + -2 -1.5 -1 0 1 1.5 2; + -2 -1.5 -1 0 1 1.5 2; + -2 -1.5 -1 0 1 1.5 2]; % 高斯函数的中心点矢量 维度 IN * MID 2*7 +b2 = 4; % 高斯函数的基宽 维度MID * 1 b的选择很重要 b越大 网路对输入的映射能力越大 + +gama2 = 0.01; +belta = 2; +sizes = simsizes; +sizes.NumContStates = node*6; %设置系统连续状态的变量 +sizes.NumDiscStates = 0; %设置系统离散状态的变量 +sizes.NumOutputs = 4; %设置系统输出的变量 +sizes.NumInputs = 7; %设置系统输入的变量 +sizes.DirFeedthrough = 1; %如果在输出方程中显含输入变量u，则应该将本参数设置为1 +sizes.NumSampleTimes = 1; % 模块采样周期的个数 + % 需要的样本时间，一般为1. + % 猜测为如果为n，则下一时刻的状态需要知道前n个状态的系统状态 +sys = simsizes(sizes); +x0 = 0.1*[ones(node*4,1); 2*ones(node*1,1);3*ones(node*1,1)]; % 系统初始状态变量 代表W和V向量 +str = []; % 保留变量，保持为空 +ts = [0 0]; % 采样时间[t1 t2] t1为采样周期，如果取t1=-1则将继承输入信号的采样周期；参数t2为偏移量，一般取为0 + + +function sys = mdlDerivatives(t,x,u) %该函数仅在连续系统中被调用，用于产生控制系统状态的导数 +global c1 b1 c2 b2 node gama1 gama2 xite belta lg +% 仿真中应根据网络输入值的有效映射范围来设计 c和b 从而保证有效的高斯映射 不合适的b或c均会导致结果不正确 +yd1 = 0.5*sin(pi*t); +dyd1 = 0.5*pi*cos(pi*t); +ddyd1 = -0.5*pi*pi*sin(pi*t); + +yd2 = 0.5*sin(pi*t); +dyd2 = 0.5*pi*cos(pi*t); +ddyd2 = -0.5*pi*pi*sin(pi*t); + +q1 = u(1); +q2 = u(2); +dq1 = u(3); +dq2 = u(4); + +e1 = yd1 - q1; +e2 = yd2 - q2; +de1 = dyd1 - dq1; +de2 = dyd2 - dq2; +e = [e1;e2]; +de = [de1;de2]; + +% 参数的定义 +q = 3; +p = 5; + +% 滑模面 +s1 = e1 + 1/belta*abs(de1)^(p/q)*sign(de1); +s2 = e2 + 1/belta*abs(de2)^(p/q)*sign(de2); +s = [s1; s2]; + +coe1 = p/(belta*q)*de1^(p-q)^(1/q); % 必大于0 +coe2 = p/(belta*q)*de2^(p-q)^(1/q); % 必大于0 + +Input = [q1;q2;dq1;dq2]; +% --------------------------------------------- W权值的更新 +hf1 = zeros(node , 1); %7*1矩阵 +hf2 = zeros(node , 1); %7*1矩阵 +for i =1:node + hf1(i) = exp(-(norm(Input - c1(:,i))^2) / (2*b1^2)); + hf2(i) = exp(-(norm(Input - c1(:,i))^2) / (2*b1^2)); +end +W1 = x(1:node); % 7*1矩阵 +W2 = x(node+1:2*node); % 7*1矩阵 + +fx1 = W1' * hf1; +fx2 = W2' * hf2; + +fx = [fx1; fx2]; % 2*1 +dw_fx1 = -gama1 * s1 * coe1 * hf1; % 7*1矩阵 +dw_fx2 = -gama1 * s2 * coe2 * hf2; % 7*1矩阵 + +for i = 1:node + sys(i) = dw_fx1(i); + sys(i+node) = dw_fx2(i); +end +% ------------------------------------------------- V权值的更新 +hg11 = zeros(node , 1); %7*1矩阵 +hg12 = zeros(node , 1); %7*1矩阵 +hg21 = zeros(node , 1); %7*1矩阵 +hg22 = zeros(node , 1); %7*1矩阵 +for i =1:node + hg11(i) = exp(-(norm(Input - c2(:,i))^2) / (2*b2^2)); + hg12(i) = exp(-(norm(Input - c2(:,i))^2) / (2*b2^2)); + hg21(i) = exp(-(norm(Input - c2(:,i))^2) / (2*b2^2)); + hg22(i) = exp(-(norm(Input - c2(:,i))^2) / (2*b2^2)); +end +V11 = x(node*2+1:node*3); +V12 = x(node*3+1:node*4); +V21 = x(node*4+1:node*5); +V22 = x(node*5+1:node*6); + +gx11 = V11' * hg11; +gx12 = V12' * hg12; +gx21 = V21' * hg21; +gx22 = V22' * hg22; + +gx = [gx11 gx12; gx21 gx22]; +% 控制器的设计 +p1 = 2.9; +p2 = 0.76; +p3 = 0.87; +p4 = 3.04; + +M = [p1+p2+2*p3*cos(q2) p2+p3*cos(q2); + p2+p3*cos(q2) p2]; +% 控制器的设计 +g = inv(M); +temp1 = -belta*q/p* (abs(de1)^(2-p/q)*sign(de1)) + fx(1) - (lg+xite)*sign(s1) - ddyd1; +temp2 = -belta*q/p* (abs(de2)^(2-p/q)*sign(de2)) + fx(2) - (lg+xite)*sign(s2) - ddyd2; +temp = [temp1; temp2]; +tau = -inv(gx) * temp; + +dw_g11 = -gama2 * s1 * coe1 * hg11 * tau(1); +dw_g12 = -gama2 * s1 * coe1 * hg12 * tau(1); + +dw_g21 = -gama2 * s2 * coe2 * hg21 * tau(2); +dw_g22 = -gama2 * s2 * coe2 * hg22 * tau(2); + +for i = 1 : node + sys(i+node*2) = dw_g11(i); + sys(i+node*3) = dw_g12(i); + sys(i+node*4) = dw_g21(i); + sys(i+node*5) = dw_g22(i); +end + +function sys = mdlOutputs(t,x,u) %产生（传递）系统输出 +global c1 b1 c2 b2 node gama1 gama2 xite belta lg +% 角度跟踪指令 +yd1 = 0.5*sin(pi*t); +dyd1 = 0.5*pi*cos(pi*t); +ddyd1 = -0.5*pi*pi*sin(pi*t); + +yd2 = 0.5*sin(pi*t); +dyd2 = 0.5*pi*cos(pi*t); +ddyd2 = -0.5*pi*pi*sin(pi*t); + +q1 = u(1); +q2 = u(2); +dq1 = u(3); +dq2 = u(4); + +e1 = yd1 - q1; +e2 = yd2 - q2; +de1 = dyd1 - dq1; +de2 = dyd2 - dq2; +e = [e1;e2]; +de = [de1;de2]; +ddyd = [ddyd1; ddyd2]; + +% 参数的定义 +q = 3; +p = 5; + +% 滑模面 +s1 = e1 + 1/belta*abs(de1)^(p/q)*sign(de1); +s2 = e2 + 1/belta*abs(de2)^(p/q)*sign(de2); +s = [s1; s2]; + +Input = [q1;q2;dq1;dq2]; +% ------------------------------------------- W权值 +hf1 = zeros(node , 1); %7*1矩阵 +hf2 = zeros(node , 1); %7*1矩阵 +for i =1:node + hf1(i) = exp(-(norm(Input - c1(:,i))^2) / (2*b1^2)); + hf2(i) = exp(-(norm(Input - c1(:,i))^2) / (2*b1^2)); +end +W1 = x(1:node); % 7*1矩阵 +W2 = x(node+1:2*node); % 7*1矩阵 + +coe1 = p/(belta*q)*de1^(p-q)^(1/q); % 必大于0 +coe2 = p/(belta*q)*de2^(p-q)^(1/q); % 必大于0 + +fx1 = W1' * hf1; +fx2 = W2' * hf2; + +fx = [fx1; fx2]; % 2*1 + +% ------------------------------------------- V权值 +hg11 = zeros(node , 1); %7*1矩阵 +hg12 = zeros(node , 1); %7*1矩阵 +hg21 = zeros(node , 1); %7*1矩阵 +hg22 = zeros(node , 1); %7*1矩阵 +for i =1:node + hg11(i) = exp(-(norm(Input - c2(:,i))^2) / (2*b2^2)); + hg12(i) = exp(-(norm(Input - c2(:,i))^2) / (2*b2^2)); + hg21(i) = exp(-(norm(Input - c2(:,i))^2) / (2*b2^2)); + hg22(i) = exp(-(norm(Input - c2(:,i))^2) / (2*b2^2)); +end +V11 = x(node*2+1:node*3); +V12 = x(node*3+1:node*4); +V21 = x(node*4+1:node*5); +V22 = x(node*5+1:node*6); + +gx11 = V11' * hg11; +gx12 = V12' * hg12; +gx21 = V21' * hg21; +gx22 = V22' * hg22; + +gx = [gx11 gx12; gx21 gx22]; +p1 = 2.9; +p2 = 0.76; +p3 = 0.87; +p4 = 3.04; + +M = [p1+p2+2*p3*cos(q2) p2+p3*cos(q2); + p2+p3*cos(q2) p2]; +% 控制器的设计 +g = inv(M); + +temp1 = -belta*q/p* (abs(de1)^(2-p/q)*sign(de1)) + fx(1) - (lg+xite)*sign(s1) - ddyd1; +temp2 = -belta*q/p* (abs(de2)^(2-p/q)*sign(de2)) + fx(2) - (lg+xite)*sign(s2) - ddyd2; +temp = [temp1; temp2]; +tau = - inv(gx) * temp; + +sys(1) = tau(1); +sys(2) = tau(2); +sys(3) = fx1; +sys(4) = fx2; + + + + + + + + + + + + + + diff --git a/Fixed_time_NNplant.m b/Fixed_time_NNplant.m new file mode 100644 index 0000000..0e01500 --- /dev/null +++ b/Fixed_time_NNplant.m @@ -0,0 +1,78 @@ +function [sys,x0,str,ts] = Fixed_time_NNplant(t,x,u,flag) +switch flag + case 0 %初始化 + [sys,x0,str,ts]=mdlInitializeSizes; + case 1 %连续状态计算 + sys=mdlDerivatives(t,x,u); + case {2,4,9} %离散状态计算，下一步仿真时刻，终止仿真设定 + sys=[]; + case 3 %输出信号计算 + sys=mdlOutputs(t,x,u); + otherwise + DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag)); +end + +function [sys,x0,str,ts]=mdlInitializeSizes %系统的初始化 +sizes = simsizes; +sizes.NumContStates = 4; %设置系统连续状态的变量 +sizes.NumDiscStates = 0; %设置系统离散状态的变量 +sizes.NumOutputs = 4; %设置系统输出的变量 +sizes.NumInputs = 4; %设置系统输入的变量 +sizes.DirFeedthrough = 0; %如果在输出方程中显含输入变量u，则应该将本参数设置为1 +sizes.NumSampleTimes = 1; % 模块采样周期的个数 + % 需要的样本时间，一般为1. + % 猜测为如果为n，则下一时刻的状态需要知道前n个状态的系统状态 +sys = simsizes(sizes); +x0 = [0.09 -0.09 0 0]; % 系统初始状态变量 +str = []; % 保留变量，保持为空 +ts = [0 0]; % 采样时间[t1 t2] t1为采样周期，如果取t1=-1则将继承输入信号的采样周期；参数t2为偏移量，一般取为0 + + +function sys=mdlDerivatives(t,x,u) %该函数仅在连续系统中被调用，用于产生控制系统状态的导数 +tau1 = u(1); %力矩1 +tau2 = u(2); %力矩2 + +q1 = x(1); % 关节角一 +q2 = x(2); % 关节角二 +dq1 = x(3); % 关节角速度一 +dq2 = x(4); % 关节角速度一 +q = [q1; q2]; +dq = [dq1; dq2]; + +% 参数的定义 +p1 = 2.9; +p2 = 0.76; +p3 = 0.87; +p4 = 3.04; +p5 = 0.87; +g = 9.8; + +d = sin(10*x(1))+cos(x(2)); %干扰 +% f = [u(3); u(4)]; %LuGre摩擦力 +f = [0.02*sign(dq1);0.02*sign(dq2)]; +M = [p1+p2+2*p3*cos(q2) p2+p3*cos(q2); + p2+p3*cos(q2) p2]; +C = [-p3*dq2*sin(q2) -p3*(dq1+dq2)*sin(q2); + p3*dq1*sin(q2) 0]; +G = [p4*g*cos(q1)+p5*g*cos(q1+q2); + p5*g*cos(q1+q2)]; + +tau = [tau1; tau2]; + +ddq = inv(M) * (tau - C*dq - G - d - f); + +sys(1) = x(3); +sys(2) = x(4); +sys(3) = ddq(1); +sys(4) = ddq(2); + + +function sys=mdlOutputs(t,x,u) %产生（传递）系统输出 + +sys(1) = x(1); %q1 +sys(2) = x(2); %q2 +sys(3) = x(3); %dq1 +sys(4) = x(4); %dq2 + + +