Decentralised Model Predictive Control of Time-Varying Splitting Parallel Systems

Abstract

This chapter is devoted to the development of a decentralised model predictive control (MPC) strategy for splitting parallel systems that have time-varying and unknown splitting ratios. The large-scale system in consideration consists of several dynamically-coupled modular subsystems. Each subsystem is regulated by a dedicated multivariable controller employing the open-loop MPC algorithms in conjunction with stability constraints. The connection topology of the large-scale systems includes serial, parallel and recirculated configurations. The solution to splitting parallel systems in this chapter is not only an alternative to the hybrid approach for duty-standby modes, but also a novel approach that accommodates the concurrent operations of splitting parallel systems. The effectiveness of this approach rests on the newly introduced asymptotically positive real constraint (APRC) which prescribes an approaching characteristic towards a positive real property of the system under control. The asymptotic attribute of APRC smooths out all significant wind-up actions in the control trajectories. The APRCs are developed into a one-time-step quadratic constraint on the local control vectors, which plays the role of a stability constraint for the decentralised MPC. The recursive feasibility is assured by characterizing the APRC with dynamic multiplier matrices. Numerical simulations for two typical modular systems in an alumina refinery are provided to illustrate the theoretical results.