Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra.

This paper presents the new algorithm of PP-PFC (Pole-placement Predictive Functional Control) for stable, linear under-damped higher-order processes. It is shown that while conventional PFC aims to get first-order exponential behavior, this is not always straightforward with significant under-damped modes and hence a pole-placement PFC algorithm is proposed which can be tuned more precisely to achieve the desired dynamics, but exploits complex number algebra and linear combinations in order to deliver guarantees of stability and performance. Nevertheless, practical implementation is easier by avoiding complex number algebra and hence a modified formulation of the PP-PFC algorithm is also presented which utilises just real numbers while retaining the key attributes of simple algebra, coding and tuning. The potential advantages are demonstrated with numerical examples and real-time control of a laboratory plant.

Pole-placement Predictive Functional Control for over-damped systems with real poles.

This paper gives new insight and design proposals for Predictive Functional Control (PFC) algorithms. Common practice and indeed a requirement of PFC is to select a coincidence horizon greater than one for high-order systems and for the link between the design parameters and the desired dynamic to be weak. Here the proposal is to use parallel first-order models to form an independent prediction model and show that with these it is possible both to use a coincidence horizon of one and moreover to obtain precisely the desired closed-loop dynamics. It is shown through analysis that the use of a coincidence horizon of one greatly simplifies coding, tuning, constraint handling and implementation. The paper derives the key results for high-order and non-minimum phase processes and also demonstrates the flexibility and potential industrial utility of the proposal.