imc.rar_IMC_control_predictive_predictive control

clear all; close all; %% create grid for direction plot [Q1,Q2]=meshgrid(-1.5:.3:1.5,-0.7:.14:0.7); %% create matrices with elements of vector Qd Qd1=zeros(size(Q1)); Qd2=zeros(size(Q2)); for i=1:11; for j=1:11; Qdot=duffing(0,[Q1(i,j);Q2(i,j)]); Qd1(i,j)=Qdot(1); Qd2(i,j)=Qdot(2); end end %% plot direction plot figure(1); quiver(Q1,Q2,Qd1,Qd2); xlabel('q_1'); ylabel('q_2') title('Direction field of Duffing equation'); %% create time vector and numerical solution with ode45 [t, Q]=ode45('duffing',[0 30],[1.5;0]); %% plot trajectory in time figure(2) plot(t,Q(:,1)) xlabel('t'); ylabel('q_1'); figure(3) plot(t,Q(:,2)) xlabel('t'); ylabel('q_2'); %% plot trajectory in phase space figure(4); quiver(Q1,Q2,Qd1,Qd2); xlabel('q_1=x'); ylabel('q_2=dotx') title('Solution curve in phase plane'); hold on; plot(Q(:,1),Q(:,2),'k');