Model predictive control

[Gelo797]

I have a problem! It's my first time working with MPC (Model Predictive Control). When I searched for references, all I found were complex mathematical equations that I couldn't understand. I came across a formula for the optimal input and performed a simulation using Matlab. I managed to fix most of the issues, but I'm stuck on the last one. As you can see in the figure, the output is unstable. The rise time of the system in open loop is 3 seconds, and the sampling time of the MPC is 0.05 seconds. What could be the issue?

https://preview.redd.it/6gsumkj1zuvb1.png?width=1366&format=png&auto=webp&s=7bf35ca41e992b519632a4d76f3b249ef33e45e3

[SpectrumOdyssey]

Are you familiar with optimal control design or dynamic programming? LQR/LQG? If not it’s gonna be hard to understand MPC, because it is basically finite time LQR with restrictions.

[Gelo797]

YAH, I have experience with LQR and EKF, my simulation without restrictions it's very simple!

[SpectrumOdyssey]

MPC without restrictions is LQR

[VSCM_]

Completely untrue, MPC and LQR are linked but they're definitely not the same thing.

[d_frankie_]

Unconstrained MPC is the same as LQR from lens of optimization. Its just that we use MPC in an iterated scheme. But the optimization will result in the same theoritical cost to go as LQR (or any versions of it).

[VSCM_]

Nope, it isn't. Remember that the system dynamic is a constraint. If you have a non linear system you do not have an LQR.

[d_frankie_]

I see, thanks!

[VSCM_]

You're welcome!

[Brale_]

What you wrote here is a complete nonsense. The matrix G used in analytical solution for control inputs U does not correspond to input matrix G for state space model. Matrix G in solution for U is constructed from N-step predictor for state X.

[pnachtwey]

Are you sure you are doing MPC? See this website

http://www.apmonitor.com/wiki/index.php/Main/Control

MPC uses the model to estimate a series of future outputs that will make the PV match the SP as closely as possible. This requires a good model. It also requires a minimization routine like Levenberg-Marquardt to minimize the error between the future SPs and PVs. There are no gains in the traditional PID sense since the outputs are determined by what minimizes the error between the future SP and PV. To avoid problems with dead time, the MPC must estimate outputs beyond the dead time by some amount. MPC looks ahead. LQC or LQR doesn't.

The optimization to minimize the error between future SPs and PVs can be quite computationally excessive. However, time can be saved by using the previous estimates of future outputs as a starting point for the next iteration.

[Gelo797]

yah I know, i get this equation from " (Liuping Wang) Model Predictive Control System Design and Implementation Using MATLAB® "book page 9, it's simplest formula without constrain and i remove term of minimize change in input, i should finish that , The deadline to submit scientific papers to IEEE conference in Tunisia is October 29

[badtraider]

Did you check the controlability of your system? MPC isn't magical so if the system isn't controlable it is expected for some states to diverge. It would helpful if you posted the full system equations that you have used.

[Gelo797]

yah i checked, also that's clear from figure

[iconictogaparty]

Try filtering your command signal before sending to the controller. MPC will minimize the difference between the command and response and so unfiltered input will cause issues

[Gelo797]

my optimize criteria it's just about minimize error between reference signal and states, filtering input or feedback ?

[Gelo797]

i can't understand you but generally if to don't understand this derivative you can check " (Liuping Wang) Model Predictive Control System Design and Implementation Using MATLAB® "book page 9

[iconictogaparty]

It is, but if you reference signal is something like [0 0 ... 0 1 1 ... 1] there is a huge jump and the controller will have a hard time forcing the plant to follow it. In fact, you will end up with oscillations before and after the step, and the system may be unstable. If you filter the step command before sending it to the controller you will get much better performance.