IMMPC: An Internal Model Based MPC for Rejecting Unknown Disturbances

TL;DR

Problem: Unknown disturbances can cause constraint violations and degrade MPC performance. Approach: An internal-model-based MPC is proposed, incorporating a known disturbance generator into the prediction model to achieve output regulation under unknown disturbances. Contributions: stability-based reformulation of the output regulation problem, recursive feasibility and constraint satisfaction guarantees, and validation on a four-tank benchmark via simulation and real experiments. Significance: enables robust disturbance rejection in constrained MPC for complex, coupled systems and provides practical guidelines for filtering transient effects.

Abstract

Model predictive control (MPC) is a powerful control method that allows to directly include state and input constraints into the controller design. However, errors in the model, e.g., caused by unknown disturbances, can lead to constraint violation, loss of feasibility and deteriorate closed-loop performance. In this paper, we propose a new MPC scheme based on the internal model principle. This enables the MPC to reject unknown disturbances provided that the dynamics of the linear signal generator are known. We reformulate the output regulation problem as a stability problem, to ensure feasibility, constraint satisfaction, and convergence to the optimal reachable setpoint. The controller is validated on a real fourtank system.

Figures (3)

• Figure 2: Four tank simulation results.
• Figure 3: Four tank system.
• Figure 4: Four tank experiment with constant references.