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Robust IMMPC: An Offset-free MPC for Rejecting Unknown Disturbances

Felix Brändle, Frank Allgöwer

Abstract

Output regulation is the problem of finding a control input to asymptotically track reference trajectories and reject disturbances. This can be addressed by using the internal model principle to embed a model of the disturbance in the controller. In this work, we present a Model Predictive Control scheme to achieve offset-free control. To do so, we extend Internal Model MPC to general bounded disturbances that must not be generated by the disturbance model. We show recursive feasibility, constraint satisfaction, and provide convergence conditions for the optimal reachable output. The proposed controller is validated on a four-tank system.

Robust IMMPC: An Offset-free MPC for Rejecting Unknown Disturbances

Abstract

Output regulation is the problem of finding a control input to asymptotically track reference trajectories and reject disturbances. This can be addressed by using the internal model principle to embed a model of the disturbance in the controller. In this work, we present a Model Predictive Control scheme to achieve offset-free control. To do so, we extend Internal Model MPC to general bounded disturbances that must not be generated by the disturbance model. We show recursive feasibility, constraint satisfaction, and provide convergence conditions for the optimal reachable output. The proposed controller is validated on a four-tank system.

Paper Structure

This paper contains 9 sections, 2 theorems, 34 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Setup
  3. MPC
  4. Model
  5. Stabilizing Controller
  6. RPI-set
  7. Robust MPC
  8. Experiment
  9. Conclusion

Key Result

Lemma 1

Suppose $x([0,-n_p])$, $u([-1,-n_p])$ and $e([0,1-n_p])$ are generated according to eq:Setup:Dynamic, eq:Setup:Output, and eq:Setup:DynamicDisturbance, then hold for all $t\in\mathbb{N}^0$ with $\Delta x(t) = \sum_{i=0}^{n_p} p_i x(t-i)$, $\Delta w_x(t) \!= \!\sum_{i=0}^{n_p} p_i w_x(t-i)$, and $\Delta w_e(t) \!=\! \sum_{i=0}^{n_p} p_i w_e(t-i)$. $\blacktriangleleft$$\blacktriangleleft$

Figures (2)

  • Figure 3: Four-tank system consisting of two Quanser Coupled Tanks.
  • Figure 4: Four-tank experiment with piecewise constant references.

Theorems & Definitions (5)

  • Definition 1
  • Lemma 1: braendle2025, Theorem 1
  • proof
  • Theorem 2
  • proof