Extension of First Order Predictive Functional Controllers to Handle Higher Order Internal Models

Abstract

Predictive Functional Control (PFC), belonging to the family of predictive control techniques, has been demonstrated as a powerful algorithm for controlling process plants. The input/output PFC formulation has been a particularly attractive paradigm for industrial processes, with a combination of simplicity and effectiveness. Though its use of a lag plus delay ARX/ARMAX model is justified in many applications, there exists a range of process types which may present difficulties, leading to chattering and/or instability. In this paper, instability of first order PFC is addressed, and solutions to handle higher order and difficult systems are proposed. The input/output PFC formulation is extended to cover the cases of internal models with zero and/or higher order pole dynamics in an ARX/ARMAX form, via a parallel and cascaded model decomposition. Finally, a generic form of PFC, based on elementary outputs, is proposed to handle a wider range of higher order oscillatory and non-minimum phase systems. The range of solutions presented are supported by appropriate examples.

Using Laguerre functions to improve the tuning and performance of predictive functional control

“…The computer can then do a quick search over diffferent choices of coincidence horizon n, displays the associated responses and then the user can determine which value n gives the most desireable closed-loop behaviour. However, herein lies two major weaknesses (Khadir & Ringwood, 2005Rossiter & Haber, 2015).…”

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

“…However, one cannot easily write down a simple expression for the n y step ahead prediction [13]. In order to maintain simple coding, PFC overcomes the complexity of prediction algebra by using partial fractions to express a model as a sum of first-order models [3,5,11] and hence:…”

Predictive functional control for active queue management in congested TCP/IP networks

“…The PFC technique has been developed by Richalet and complete details of the computations may be found in [18,19]. PFC operates based on the four principals: similar to other MPC variants a prediction model is used to predict the future system outputs; a desired trajectory, which is an exponential curve from the current output value to its desired one, is calculated to be followed by the closed-loop system response; auto-compensation of probable mismatches between the model and process is done by introducing a disturbance term equal to the process and model output difference in each sampling time; and finally the control law will be computed from equating the estimated outputs (prediction model output plus the considered disturbance component) and the reference trajectory in a few future points called coincident points [23]. With this idea, in PFC, instead of the optimization problem, just a few algebraic equations must be solved and therefore, the computational complexity is reduced considerably.…”