An MPC-based reference governor approach for offset-free control of constrained linear systems

Abstract

This paper presents a model predictive control (MPC) based reference governor approach for control of constrained linear systems. A nominal closed-loop system is first designed to guarantee that, in the unconstrained case, asymptotic zero-error regulation for (piecewise) constant reference signals is achieved. Then, a couple of exogenous signals are added to the reference signal and to the control variable and their value is determined by formulating a MPC problem in order to guarantee that (i) when the state and control constraints are not active, the nominal closed-loop system is recovered, (ii) in transient conditions the constraints are always satisfied and the difference of the performances between the real and the nominal closed-loop systems is minimised, and (iii) when the reference signal is infeasible, the output is brought to the nearest feasible value. A simulation example is reported to witness the potentialities of the approach

Reference and command governors for systems with constraints: A survey on theory and applications

“…As demonstrated in Section 2, effective RG/CG design techniques are available when the system model is linear, as in (1) or (18). However, many systems in real world applications are nonlinear.…”

The impact of the input parameterisation on the feasibility of MPC and its parametric solution

“…In consequence, due to the implied closed-loop form of (6), the predictions must include information such as the future target, measured disturbance and current input. A convenient means of combining (1,6) is with an autonomous model formulation [10]. In this case, the formulation must be extended to capture the evolution of r k+1 − d k , x k , u k , ∆u k as these values appear in the constraints (2).…”

“…(ii) Secondly, in this case, adding a d.o.f. c ∞ as opposed to c k+1 as given significant enlargements in the feasible region (all figures (1,2) and (3,4) have the same number of d.o.f. but clearly the latter of each pair has larger volumes.…”

“…It is of interest to consider the extent to which infeasible MPC optimisations can occur and also, what mitigating action might be appropriate. This issue was recognised early on in the literature and the simplest solutions provided were so called reference governors [7], [1]. In these, a tacit assumption is made that infeasibility is often caused by a fast change of the set point and thus, feasibility can be retained by slowing down set point changes.…”

Systematic and effective embedding of feedforward of target information into MPC

“…Remark 3 : Reference governor approaches (Gilbert et al 1994, Aghaei et al 2013) have analogies to both the above in that a governor deploys a transient change in the target to maintain feasibility. However these will be discussed no further as their focus is on simplicity so they often lead to a loss in performance.…”