On the Steady-State Behavior of Finite-Control-Set MPC with an Application to High-Precision Power Amplifiers

TL;DR

This paper proposes a new FCS-MPC design that improves steady-state behavior by penalizing deviations from a steady-state limit cycle, validated on high-precision power amplifiers.

Contribution

It introduces a novel cost function and terminal cost for FCS-MPC that guarantees convergence to a steady-state limit cycle, enhancing steady-state performance.

Findings

Significantly reduces output current ripple in power amplifiers

Ensures convergence to a steady-state limit cycle

Improves steady-state behavior in high-precision control applications

Abstract

Motivated by increasing precision requirements for switched power amplifiers, this paper addresses the problem of model predictive control (MPC) design for discrete-time linear systems with a finite control set (FCS). Typically, existing solutions for FCS-MPC penalize the output tracking error and the control input rate of change, which can lead to arbitrary switching among the available discrete control inputs and unpredictable steady-state behavior. To improve the steady-state behavior of FCS-MPC, in this paper we design a cost function that penalizes the tracking error with respect to a state and input steady-state limit cycle. We prove that if a suitable terminal cost is added to the FCS-MPC algorithm convergence to the limit cycle is ensured. The developed methodology is validated in direct switching control of a power amplifier for high-precision motion systems, where it significantly improves the steady-state output current ripple.