Hi, I'd like to regulate an output of a second-order system using MPC. But I always get a result with a huge undershoot. Could anyone let me know how to remove this undershoot? I've changed weight matrices and prediction/control horizons, but still failed to get a good result. Below is the MATLAB code I've made. Thank you.
clear all; clc;
A=[1 1;0 1];
B=[0.5;1];
C=[1 0];
D=zeros(1,1);
IC=[1;0];
Ts=0.1;
SYS=ss(A,B,C,D,Ts);
MSYS = minreal(SYS);
np=10; % prediction horizon
nc=4; % control horizon
mpcobj=mpc(MSYS,Ts,np,nc);
Q=1.e+3;
R=1.e+0;
mpcobj.Weights.OutputVariables={Q};
mpcobj.Weights.ManipulatedVariables={R};
Tstop=20;
Tf=round(Tstop/Ts);
r=zeros(Tf,1);
options=mpcsimopt(mpcobj);
options.PlantInitialState=IC;
[y,t,u]=sim(mpcobj,Tf,r,options);
figure;
subplot(1,2,1);plot(t,u);xlabel('Time');ylabel('Control');
subplot(1,2,2);plot(t,y);xlabel('Time');ylabel('Output');
Dear David Cho,
Improve the performance of the MPC command
-Reduce the sampling periods to meet the requirements of ultra-fast systems.
-Expand the area of application including:
- Control of electric motors and generators
- Embedded Vehicle System, Autonomous Vehicle and Aeronautics...
-Integration of a larger number of constraints with the aim of respecting them.
For more details and information about this subject I suggest you to see links and attached files in topics.
- Introducing Model Predictive Control for Improving Power Plant ...
folk.ntnu.no/skoge/prost/proceedings/ifac2008/data/.../0311.pdf
- Fast Model Predictive Control Using Online ... - Stanford University
https://www.stanford.edu/~boyd/papers/pdf/fast_mpc.pdf
- Performance improvement in MPC with time-varying horizon via ...
ieeexplore.ieee.org/document/6870915/ -
- Performance evaluation of an improved model predictive control with ...
ieeexplore.ieee.org/document/7931947/
- Improved model predictive control for high voltage quality in microgrid ...
ieeexplore.ieee.org/document/8096768/ -
Bestregards
Dear Dr. Kirchsteiger, thank you very much for your answer! It really works and significantly reduces the undershoot. But I couldn't completely remove the undershoot (without adding a constraint on y).
I also would like to greatly thank to Dr. Lafifi for introducing me good references on MPC. I really appreciate it.
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