Augmenting MPC Block with Integral Action

I want to augment my standard MPC controller with an integral action, as an analogue of adapting an LQR controller to LQI for reference tracking. I am aware that MPC already requires a reference to track but research shows that disturbance rejection can improve with an added integral state. The paper below details the required augmentation of the state space model.

https://www.researchgate.net/publication/274586957_Model_Predictive_Control_with_Integral_Action_A_simple_MPC_algorithm

Is this possible within the Simulink MPC block and associated MATLAB MPC object or would it require a custom implementation? As a starting point I want to apply this to a position servomechanism for a DC motor and have additional integral action to remove steady state error when there is a model mismatch. I can easily derive the equivalent LQI controller with an augmented state space model but the Model Predictive Toolbox does not seem to like the augmented MPC state space model.

Answer 1

[Emmanouil Tzorakoleftherakis]

Hello,

Let me paste a couple of links here that show how we formulate the underlying QP problem in linear mpc in Model Predictive Control Toolbox:

https://www.mathworks.com/help/mpc/ug/controller-state-estimation.html

https://www.mathworks.com/help/mpc/ug/optimization-problem.html

Essentially, the augmentation that you mention is already handled under the hood so there is no need for you to do it again.

Take a look at the first image on the first link above. The built-in Kalman filter in the mpc object considers input and output disturbances, that when tuned properly can lead to zero-offset tracking.

Here is an example that shows how the disturbance models can help.

Hope this makes sense

[Joe Gibbs]

Amazing, thank you for your response! This will save me a bunch of time writing my own version.