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Model Predictive Control of Multi-Input, Multi-Output (MIMO) systems

version 1.1 (512 KB) by

Quadratic Programming is used to simulate Model Predictive Control of MIMO systems



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These scripts set up and simulate Model Predictive Control of a general Multi-Input, Multi-Output (MIMO) Control system, when the linearized state-space model (or transfer function) is given as input to the functions. However, the plant model can be nonlinear in general.

Quadratic programming is used to make the input and output variables reach their set-points in the desired time horizon.

The description of the files is as follows:
run_MPC.m: The main file that sets up and runs the simulation.
MPC_simulation.m: Iterates through time and implements the present time input variables that are found at each iterate.
MPC_calculation: The MPC controller that solves the quadratic problem with looking at a forward time horizon based on the linearized model of the plant.
MPC_plant.m: Implements the present time input vector in the plant. In general, the plant model can be nonlinear.
Addnoise.m: A function to add noise to the main signal (output of the plant), based on the order of magnitude of the signal, and noise percentage (noise std)

The formulation and original code (for SISO systems) is by Elling W. Jacobsen from KTH university, Sweden. The formulation is included in the files. The code is modified and generalized for MIMO systems by Pooya Rezaei, University of Vermont, USA.

Comments and Ratings (6)

Hi there,
If I have an already discrete system SS matrices, is it fine to just assign Ts = 1 and it works fine?
thanks in advance for your answer.

In file of run_mpc_siso.m value of prediction horizon is mentioned but value of control horizon is absent please tell me whats the solution and please tell me if we want solution without constraints then whats the modification in program ???

nice work :)


Khanh (view profile)

Thanks for your work!
But I got warning as:
"Warning: Trust-region-reflective algorithm does not solve this type of problem, using active-set
algorithm. You could also try the interior-point-convex algorithm: set the Algorithm option to
interior-point-convex and rerun. For more help, see Choosing the Algorithm in the documentation.
> In quadprog at 371
In MPC_calculation at 97
In MPC_simulation at 23
In run_MPC_old at 64
Optimization terminated."
Could you solve it?


Khanh (view profile)



delta_u formulation (page 24 of pdf) is added (*_delta_u). The new obj func to be minimized is: f = 1/2*(y-yref)'*Qy*(y-yref)+1/2*delta_u'*Qu*delta_u
Also, the capability of having a varied yref is added.
Run run_MPC_delta_u.m.

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