Model Predictive Control System Design and Implementation Using ...

1.4 Receding Horizon Control 21
r=ones(N_sim,1);
u=0; % u(k-1) =0
y=0;
5. From the receding horizon control, at sample time kk, theΔU vector is
calculated using the set-point signal r(kk) and the state vector Xf.Then,
Δu(kk) is taken as the first element of ΔU;andu(kk) =u(kk−1)+Δu(k).
The weight factor is selected as 0.1.
6. Continue entering the following program into the file:
for kk=1:N_sim;
DeltaU=inv(Phi_Phi+0.1*eye(Nc,Nc))*(Phi_R*r(kk)-Phi_F*Xf);
deltau=DeltaU(1,1);
u=u+deltau;
u1(kk)=u;
y1(kk)=y;
7. The plant state and output are simulated using the control signal generated;
the state variable used in the feedback mechanism is updated as Xf.
8. Continue entering the following program into the file:
xm_old=xm;
xm=Ap*xm+Bp*u;
y=Cp*xm;
Xf=[xm-xm_old;y];
end
9. The input and output signals are plotted against samples.
10. Continue entering the following program into the file:
k=0:(N_sim-1);
figure
subplot(211)
plot(k,y1)
xlabel(’Sampling Instant’)
legend(’Output’)
subplot(212)
plot(k,u1)
xlabel(’Sampling Instant’)
legend(’Control’)
11. Save the program in the same directory as the one that contains the function.
Run the program.
12. Change the weight r w in the design to 2 and observe that the closed-loop
response speed is slower.
13. Create your own plant using different Ap, Bp and Cp, and experiment
with different prediction and control horizons.