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Augmenting MPC Block with Integral Action

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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.
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.

Accepted Answer

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:
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
  1 Comment
Joe Gibbs
Joe Gibbs on 12 Feb 2024
Amazing, thank you for your response! This will save me a bunch of time writing my own version.

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