一阶倒立摆模糊控制matlab仿真.doc

一阶倒立摆模糊控制仿真实验分析报告%mainclearclose all%load table.matglobal Table;global RULE;global UCenter;global Width;global num;global RuleMatch; %前件匹配方式 0 取小； 1乘积global Defuzzy; %反模糊化方法 0: COG ; 1:COA; 2:MAXglobal g0;global g1;global h;x=0.4,0,0;RuleMatch = 1; %前件匹配方式 0 取小； 1乘积Defuzzy = 0;%反模糊化方法 0: COG ; 1:COA; 2:MAXg0=1.5;g1=0.1;h=1;% u=0;% Table = u;% m,n=size(u);% num = (m-1)/2;%u=;RULE =2, 2, 2, 1, 0; . 2, 2, 1, 0,-1;. 2, 1, 0,-1,-2;. 1, 0,-1,-2,-2;. 0,-1,-2,-2,-2;% % RULE =2,2,1,1,0; .% 2,1,1,0,-1;.% 1,1,0,-1,-1;. % 1,0,-1,-1,-2;.% 0,-1,-1,-2,-2;RULE=RULE + 3*ones(size(RULE);%原始的 %UCenter=-20,-10,0,10,20;%改进的%UCenter=-25,-15,0,15,25; UCenter=-20,-15,0,15,20;Width(1)=(UCenter(5)-UCenter(4)/2;Width(2)=(UCenter(5)-UCenter(3);Width(3)=(UCenter(4)-UCenter(3)*2;Width(4)=Width(2);Width(5)=Width(1); x=x; t,y= ode45(P_Pendulum,0,5,x);% t,y= ode45(P_Pendulum_tab,0,10,x);% y2=y.*y;% inty = intnum(t,y2)% % int_e2 = inty(1)+inty(2);% int_u2 = inty(3);%int_y2 = sum(y.2);%int_e2 = int_y2(1)+int_y2(2);%int_u2 = int_y2(3);figuresubplot(2,1,1)plot(t,y(:,1 ),r,t,y(:,2),k)%xlabel(t(sec)% str1 = sprintf(x(0)=%2.2f,%2.2f,x(1),x(2);% Title(str1,Interpreter,latex,fontsize,14)% % str1=sprintf(t(sec)-index:$inteT(t)e(t)dt=$ %f, int_e2);%str1 = $inte2dt$% text(6,0,str1,Interpreter,latex,fontsize,14)% % xlabel(str1,Interpreter,latex,fontsize,14)legend(x1(rad), x2(rad/s)title(输出隶属函数中心值：-20,-15,0,15,20)subplot(2,1,2)plot(t,y(:,3),r)xlabel(t(sec)ylabel(u(N)% str1=sprintf(t(sec)-index:$intu2(t)dt$= %f, int_u2);% %H = Title(str1,Interpreter,latex,fontsize,14)% xlabel(str1,Interpreter,latex,fontsize,14)% inverted pendulum stabilized% program on 2006,10,26function xdot = P_Pendulum(t,x)global RULE;global UCenter;global step;global k;global Kc;global QQ;global Width;global RuleMatch; %前件匹配方式 0 取小； 1乘积global Defuzzy; %反模糊化方法 0: COG ; 1:COA; 2:MAXglobal g0;global g1;global h;M = 1;m =0.5;g = 9.8;l = 0.5;a = 1/(m+M);%计算隶属度mu_e= emembershipdegree(-x(1)*g0);mu_de = demembershipdegree(-x(2)*g1);%pausemu_e_id = find(mu_e0);mu_de_id = find(mu_de0);eLen= length(mu_e_id);deLen = length(mu_de_id);mu_pre= zeros(1,4);fuzzy_out = zeros(1,4);weight = zeros(1,4);in =1;%规则匹配for (i=1:eLen) for(j=1:deLen) switch RuleMatch case 0 %前件采用取小推理 mu_pre(in)= min(mu_e(mu_e_id(i),mu_de(mu_de_id(j); case 1 %前件采用乘积推理 mu_pre(in)= mu_e(mu_e_id(i)*mu_de(mu_de_id(j); end %计算规则匹配度 fuzzy_out(in) = RULE(mu_e_id(i),mu_de_id(j); in=in+1; endendnRule = eLen *deLen; u = 0;summu =0;%反模糊化for(i=1:nRule) switch Defuzzy case 0 %按照重心法计算(COG) weight(i)= Width(fuzzy_out(i)*(mu_pre(i)-mu_pre(i)*mu_pre(i)/2); case 1 % 按照中心平均法 weight(i)=mu_pre(i); case 2 % 取大法(大中求中) max_v,max_id = max(mu_pre); weight(max_id)=1; end u = weight(i)*UCenter(fuzzy_out(i)+u; summu =summu + weight(i);end %u=0;u=h*u/summu;if (u20) u=20;endif (u2.5 & t20) % u=20;% end% % if (u-20)% u=-20;% end% xdot(1)=x(2);% xdot(2)=(g*sin(x(1)-a*m*l*x(2)*x(2)*sin(2*x(1)/2-a*cos(x(1)*x(3)/(4*l/3-a*m*l*cos(x(1)*cos(x(1);% xdot(3)=-100*x(3)+100*u;% x(3) = u;xdot(1)=x(2);xdot(2)=(g*sin(x(1)-a*m*l*x(2)*x(2)*sin(2*x(1)/2-a*cos(x(1)*x(3)/(4*l/3-a*m*l*cos(x(1)*cos(x(1);xdot(3)=-100*x(3)+100*u;xdot = xdot;function y = emembershipdegree(x)y=zeros(1,5);if (x= -pi/2) y(1) =1 ; elseif (x=-pi/4) y(1) = abs(x+pi/4)/(pi/4); y(2) = 1-abs(x+pi/4)/(pi/4);elseif (x= 0) y(2) = 1-abs(x+pi/4)/(pi/4); y(3) = 1- abs(x)/(pi/4);elseif (x=pi/4) y(3) = 1- abs(x)/(pi/4); y(4) = 1-abs(x-pi/4)/(pi/4);elseif (xpi/2) y(5) =1;endfunction y = demembershipdegree(x)y=zeros(1,5);if (x= -pi/4) y(1) =1 ; elseif (x=-pi/8) y(1) = abs(x+pi/8)/(pi/8); y(2) = 1-abs(x+pi/8)/(pi/8);elseif (x= 0) y(2) = 1-abs(x+pi/8)/(pi/8); y(3) = 1- abs(x)/(pi/8);elseif (x=pi/8) y(3) = 1- abs(x)/(pi/8); y(4) = 1-abs(x-pi/8)/(pi/8);elseif (xpi/4) y(5) =1;endfunction y = umembershipdegree(x)y=zeros(1,5);if (x= -30) y(1) =0 ; elseif (x=-20) y(1) = 1-abs(x+20)/(10);elseif (x=-10) y(1) = 1-abs(x+20)/(10); y(2) = 1-abs(x+10)/(10);elseif (x= 0) y(2) = 1-abs(x+10)/(10); y(3) = 1- abs(x)/(10);elseif (x=10) y(3) = 1- abs(x)/(10); y(4) = 1-abs(x-10)/(10);elseif (x30)elseif (x30) y(5) =0;end不同的推理方式，反模糊化方法初始值：x0=0.1 0 序号前件隶属度计算方法蕴含方法反模糊化方法误差性能指标控制量性能指标稳定时间性能描述1取小取小COG0.0326.905s收敛慢2乘积取小COG0.0306.465s收敛慢3取小取小COA0.05812.72发散4乘积取小COA0.07816.82发散5取小取小MAX0.75234.44剧烈振荡6乘积取小MAX0.75234.44剧烈振荡不同的初始条件前件隶属度函数计算方法：乘积模糊蕴含关系计算方法：取小反模糊化方法：COG 序号初始值误差性能指标控制量性能指标稳定时间性能描述10.1 ,0 (5.73)0.0306.465s收敛慢20.2 ,0 (11.46 )0.1737.8收敛慢30.3 ,0 (17.19 )1.74412.7发散40.4 ,0 (22.92 )134.81301.9发散结论：当初始角达到一定程度时，控制力趋向饱和，系统不稳定。控制器参数调整对比前件隶属度函数计算方法：乘积蕴含运算：取小反模糊化方法：COG初始条件：0.1，0 序号g0g1h误差性能指标控制量性能指标调节时间11110.0326.455s210.510.01994.095s310.210.01191.954.5s410.110.01241.332.1s 序号g0g1h误差性能指标控制量性能指标调节时间110.110.0121.332.121.50.110.0201.181.5s31.80.110.0261.371.8s420.110.0301.551.6s 序号g0g1h误差性能指标控制量性能指标调节时间11.50.110.0201.181.5s21.50.140.0353.320.52s31.50.170.0385.610.56s41.50.1100.0397.570.62s量化因子：g0=1.5,g1=0.1,h=1 序号初始值误差性能指标控制量性能指标调节时间10.1 ,00.0200.0301.186.461.4s20.2 ,00.0670.174.9437.81.7s30.3 ,00.141.7413.94412.71.9s40.4 ,00.24134.834.181301.92.0s初始角达到一定程度依然不稳定分析：在相同的初始条件下，模糊控制器的控制效果与量化因子有关，可以通过对量化因子的整定调节控制性能。g0保持不变，g1增大时对系统输出状态变化的抑制能力增大，但会使系统的响应速度减慢，系统达到稳态的过渡时间变长，g1减小时系统输出量的振荡幅度增大；g1保持不变，g0增大时系统响应速度加快，系统输出量的震荡幅度增大，g0过大会时系统不稳定。干扰抑制能力对比前件隶属度函数计算方法：乘积模糊蕴含关系计算方法：取小反模糊化方法：COG量化因子：g0=1.5,g1=0.1干扰：在时间区间2.5,2.6秒之间对控制量施加20N正方向干扰。初始值：0.4,0 序号g0g1h误差性能指标控制量性能指标收敛时间11.50.11123.6847.9干扰后剧烈波动，失稳21.50.140.6668.3干扰后波动偏大，恢复时间偏大31.50.170.5864.6干扰后波动较小，恢复时间较短41.50.1100.5