A Comparison of Tuning Methods for Predictive Functional Control

Abstract

Predictive functional control (PFC) is a fast and effective controller that is widely used in preference to PID for single-input single-output processes. Nevertheless, the core advantages of simplicity and low cost come alongside weaknesses in tuning efficacy. This paper summarises and consolidates the work of the past decade, which has focused on proposing more effective tuning approaches while retaining the core attributes of simplicity and low cost. The paper finishes with conclusions on the more effective approaches and links to context.

Recent Developments in Tuning Methods for Predictive Functional Control

“…A number of proposals [1,16] have appeared in the literature to improve the tuning efficacy of PFC because of the poor correspondence between the chosen λ and the resulting closed-loop pole, thus undermining a core selling point of PFC, that is, the ease of tuning. This issue was exacerbated for systems with more challenging dynamics, such as unstable open-loop poles, significant underdamping, or integrating dynamics; hence, modifications to the basic PFC algorithm are essential.…”

“…Predictive functional control (PFC) is a popular control technique-especially for single-input single-output (SISO) applications [1][2][3][4][5][6][7]-because it typically outperforms PID while being of similar cost and implementation complexity. PFC exploits model information explicitly and, thus, in principle, can deal with more challenging dynamics than PID can.…”

“…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. We note that a priori stability guarantees [18,19] are rarely considered with PFC, as they are considered unrealistic with such low computational complexity.…”

“…The parameterisation of the future inputs is too simplistic for many cases and is inconsistent with the desirable closed-loop input trajectory [1].…”

“…The recent review [1] concluded that, of the various options that had been considered, input shaping [26][27][28][29] would not be pursued for the time being. Apart from the algebra being somewhat awkward, these approaches can be quite sensitive to parameter uncertainty, which is difficult-or, rather, systematic guidance for deciding the precise shaping needed does not yet exist, and moreover, they do not deal with the first and third fundamental weaknesses listed above.…”