Abstract

The availability of predictions of future system inputs has motivated research into preview control to improve set-point tracking and disturbance rejection beyond that achievable via conventional feedback control. The design of preview controllers, typically based upon model predictive control (MPC) for its constraint handling properties, is often performed in a monolithic nature, coupling the feedback and feed-forward problems. This can create problems, such as: (i) an additional feedback loop is introduced by MPC, which alters the closed-loop dynamics of the existing feedback compensator, potentially resulting in a deterioration of the nominal sensitivities and robustness properties of an existing closed-loop and (ii) the default preview action from MPC can be poor, degrading the original feedback control performance. In our previous work, the former problem is addressed by presenting a modular MPC design on top of a given output-feedback controller, which retains the nominal closed-loop robustness and frequency-domain properties of the latter, despite the addition of the preview design. In this paper, we address the second problem; the preview compensator design in the modular MPC formulation. Specifically, we derive the key conditions that ensure, under a given closed-loop tuning, the preview compensator within the modular MPC formulation is systematic and well-designed in a sense that the preview control actions complement the existing feedback control law rather than opposing it. In addition, we also derive some important results, showing that the modular MPC can be implemented in a cascade over any given linear controllers and the proposed conditions hold, regardless of the observer design for the modular MPC. The key benefit of the modular MPC is that the preview control with constraint handling can be implemented without replacing the existing feedback controller. This is illustrated through some numerical examples.

Highlights

  • In many control applications, preview knowledge is available for improving tracking quality and disturbance rejection

  • Model predictive control (MPC) is a popular method for incorporating both preview knowledge and constraints, because, in principle [1], the information is incorporated in a systematic fashion

  • This paper has first revisited the modular MPC design where the preview measurements and constraint handling capability are retrofitted into a known output-feedback controller, together with the conditions to ensure the former does not interfere with the closed-loop dynamics provided by the latter

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Summary

Introduction

Preview knowledge is available for improving tracking quality and disturbance rejection. MPC upon a given feedback controller, if the preview compensator is not carefully designed in a sense that it only handles the transient of the existing closed-loop, the preview action is mistakenly corrected by the pre-determined feedback control law, resulting in a deterioration in the performance We addressed the former problem in our earlier work [14] by presenting a preview modular MPC layer that is based on a known feedback controller. The novelty of this paper starts, where we derive a set of conditions that proves the preview compensator within the modular MPC formulation is well-designed and systematic in a sense that the preview compensator only handles the transient of the closed-loop based on the future reference signals. Let λ(V ) ∈ C denote the eigenvalues of the matrix V

System and the Existing Controller Models
Design of the Modular MPC
Cost Function and Optimisation Problem
Autonomous Prediction Model to Simplify the Optimisation Problem
Constraint Formulations in Terms of Perturbations
Analysis of the MPC Design upon an Existing Controller
Interactions between the Modular MPC and Existing Controller
Preview Compensator in the Modular MPC Formulation
Tuning of the Modular MPC
Discussions on Stability and Feasibility when Constraints Are Active
Illustrative Examples
Example 1
Example 2
Optimality and Consistency in Predictions
Findings
Conclusions
Full Text
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