Predictive Functional Control for Unstable First-Order Dynamic Systems

Abstract

Predictive functional control (PFC) has emerged as a popular industrial choice owing to its simplicity and cost-effectiveness. Nevertheless, its efficacy diminishes when dealing with challenging dynamics because of prediction mismatch in such scenarios. This paper presents a proposal for reducing prediction mismatch and thus improving behaviour for simple unstable processes; a two-stage design methodology pre-stabilises predictions via proportional compensation before introducing the PFC component. It is demonstrated that pre-stabilisation reduces the dependency of the closed-loop pole on the coincidence point and also improves robustness to uncertainty. Simulation results verify the improved performance as compared to conventional PFC.

A Comparison of Tuning Methods for Predictive Functional Control

“…The most recent suggestion for modifying PFC builds on some ideas with the case by case modifications for the original algorithm [6] but implements this in a more systematic and effective manner. The basic idea is to recognise that where a system has poor openloop dynamics, a simple feedback loop, often based solely on simple proportional control, can improve those dynamics [11,16,17]. As the efficacy of PFC is strongly linked to the nominal dynamics having a shape somewhat close to a well-damped system, this initial prestabilisation can be hugely effective in enabling PFC.…”

“…• CLPFC clearly demonstrates a much stronger link between the actual and the desired closed-loop performance, even with longer coincidence horizons. This is important since long horizons may be necessary for better loop shaping against external perturbations, as pointed out in [17]. Furthermore, the control effort with CLPFC is smooth and the least aggressive as opposed to both CPFC and LPFC, which is crucial for constraint adherence in practice.…”

“…Consequently, in recent years, many authors have proposed a number of more systematic modifications to improve tuning for specific cases, e.g., [9,10,[13][14][15][16][17]. Nevertheless, there is overlap in the application and benefits of these approaches alongside an undesirable multiplicity of options.…”

Recent Developments in Tuning Methods for Predictive Functional Control

“…Nevertheless, as highlighted in the recent review paper [1], simplicity and computational efficiency come at a cost, that is, the tuning of PFC is often not as straightforward or effective as one would like [12]; thus, recent research efforts, such as the development of closed-loop PFC [13,14], Laguerre PFC [15], PFC with an improved feedforward component [16], and designs based on model decomposition [17,18], have focussed improving tuning efficacy. This paper will not repeat the review of those methods (see [1] for details), but will rather develop and extend them.…”

“…All of the recently developed proposals have used the same defining principle and have focussed on how the input degrees of freedom are parameterised; changing the input predictions has a significant impact on the efficacy of the overall design.Indeed, this latter point will be preserved in the proposal of this paper, as it is well known in the MPC field [20,21] that consistency between open-loop predictions and closed-loop behaviour is a solid foundation for sensible MPC design. Recent work has shown that there are two input parameterisations that, in general, seem to be more effective in ensuring this consistency: (i) Laguerre-based parameterisations [15] and (ii) parameterisations that exploit an inner feedback loop [13,14,22]. Consequently, this paper will mainly focus on those two input parameterisations.…”