matlab基于差分进化的PID控制

clear all; close all; global TE G ts Size=50; %样本个数 D=4; %每个样本有４个固定点,即分成4段 F=0.5; %变异因子 CR=0.9; %交叉因子 Nmax=30; %DE优化次数 TE=1; %参考轨迹参数TE thd=0.50; aim=[TE;thd];%摆线路径终点 start=[0;0];%路径起点 tmax=3*TE; %仿真时间 ts=0.001; %Sampling time G=tmax/ts; %仿真时间为G=3000 %***************摆线参考轨迹*************% th0=0; dT=TE/1000; %将TE分为1000个点，每段长度(步长)为dT for k=1:1:G t(k)=k*dT; %t(1)=0.001;t(2)=0.002;..... if t(k)<TE thr(k)=(thd-th0)*(t(k)/TE-1/(2*pi)*sin(2*pi*t(k)/TE))+th0; %不含原点的参考轨迹(1) else thr(k)=thd; end end %***************初始化路径**************% for i=1:Size for j=1:D Path(i,j)=rand*(thd-th0)+th0; end end %**********差分进化计算***************% for N=1:Nmax %**************变异**************% for i=1:Size r1=ceil(Size*rand); r2=ceil(Size*rand); r3=ceil(Size*rand); while(r1==r2||r1==r3||r2==r3||r1==i||r2==i||r3==i)%选取不同的r1,r2,r3，且不等于i r1=ceil(Size*rand); r2=ceil(Size*rand); r3=ceil(Size*rand); end for j=1:D mutate_Path(i,j)=Path(r1,j)+F.*(Path(r2,j)-Path(r3,j));%选择前半部分产生变异个体 end %****************交叉****************% for j=1:D if rand<=CR cross_Path(i,j)=mutate_Path(i,j); else cross_Path(i,j)=Path(i,j); end end %先进行三次样条插值，此为D=4时的特殊情况% XX(1)=0;XX(2)=200*dT;XX(3)=400*dT;XX(4)=600*dT;XX(5)=800*dT;XX(6)=1000*dT; YY(1)=th0;YY(2)=cross_Path(i,1);YY(3)=cross_Path(i,2);YY(4)=cross_Path(i,3);YY(5)=cross_Path(i,4);YY(6)=thd; dY=[0 0]; cross_Path_spline=spline(XX,YY,linspace(0,1,1000));%输出插值拟合后的曲线，注意步长nt的一致,此时输出1000个点 YY(2)=Path(i,1);YY(3)=Path(i,2);YY(4)=Path(i,3);YY(5)=Path(i,4); Path_spline=spline(XX,YY,linspace(0,1,1000)); %*** 计算指标并比较***% for k=1:1000 distance_cross(i,k)=abs(cross_Path_spline(k)-thr(k)); %计算交叉后的轨迹与参考轨迹的距离值 distance_Path(i,k)=abs(Path_spline(k)-thr(k)); %计算插值后的轨迹与参考轨迹的距离值 end new_object = chap10_6obj(cross_Path_spline,distance_cross(i,:),0); %计算交叉后的能量消耗最低及路径逼近最佳值的和 formal_object = chap10_6obj(Path_spline,distance_Path(i,:),0); %计算插值后的能量消耗最低及路径逼近最佳值的和 %%%%%%%%%% 选择算法 %%%%%%%%%%% if new_object<=formal_object Fitness(i)=new_object; Path(i,:)=cross_Path(i,:); else Fitness(i)=formal_object; Path(i,:)=Path(i,:); end end [iteraion_fitness(N),flag]=min(Fitness);%记下第NC次迭代的最小数值及其维数 lujing(N,:)=Path(flag,:) %第NC次迭代的最佳路径 fprintf('N=%d Jmin=%g\n',N,iteraion_fitness(N)); end [Best_fitness,flag1]=min(iteraion_fitness); Best_solution=lujing(flag1,:); YY(2)=Best_solution(1);YY(3)=Best_solution(2);YY(4)=Best_solution(3);YY(5)=Best_solution(4); Finally_spline=spline(XX,YY,linspace(0,1,1000)); chap10_6obj(Finally_spline,distance_Path(Size,:),1); figure(3); plot((0:0.001:1),[0,thr(1:1:1000)],'k','linewidth',2); xlabel('Time (s)');ylabel('Ideal Path'); hold on; plot((0:0.2:1), YY,'ko','linewidth',2); hold on; plot((0:0.001:1),[0,Finally_spline],'k-.','linewidth',2); xlabel('Time (s)');ylabel('Optimized Path'); legend('Ideal Path','Interpolation points','Optimized Path'); figure(4); plot((1:Nmax),iteraion_fitness,'k','linewidth',2); xlabel('Time (s)');ylabel('Fitness Change');