COMPARISON OF OPTIMAL CONTROL STRATEGIES FOR SUPERVISORY AND REGULATORY LEVEL Doris Sáez* & Andrzej Ordys** *Electrical Engineering Department, Universidad de Chile, Tupper 2007, Chile **Industrial Control Centre, Department of Electronic and Electrical Engineering, University of Strathclycle, 50 George Street, Glasgow, Scotland Abstract: In this paper, the conditions for the equivalence between the supervisory level and regulatory level control strategies based on the same objective function are established. Both controllers use the same general objective function with constraints. It is shown that the supervisory controller modifies the control action of the fixed regulatory controller in such a way that the solution of general objective function with constraints is generated at the regulatory level. In order to demonstrate the theoretical results, the proposed controllers are applied to a power plant boiler simulator. Keywords: Supervisory control, predictive control, optimisation, boiler simulator. 1. INTRODUCTION For the industrial process, the plant optimisation is an important issue that could be solves using supervisory control strategies. However, the supervisory controllers usually are based on the steady state of the costs, which provide the optimal static set points [1]. In the last years, there are some papers that deal with dynamic models. For example, de Prada [2] proposes a predictive control strategy based on the optimisation of an economic index. This strategy is applied to a chemical reactor. Katebi [3] describes a decentralised control strategy, based on the optimisation of a GPC objective function. The objective function has only regulatory objectives. The control strategy is applied to a thermal power plant simulator. Also, there are some industrial applications, for example a DMC supervisory controller for a petrochemical process (YHP) [4] that gives good economic results based on linear dynamic models. On the other hand, Bemporad [5] and Angeli [6] propose a reference governor at the supervisory level. The objective function is given by the minimization of the reference trajectory error. The main goal is to satisfy certain constraints. The algorithms are developed using a state-space representation. A different approach for a reference governor with the same objective is proposed by Gilbert [7]. In this case, the reference governor is given by a non-linear pre-filter. Tadeo et. al [8] proposes a constrained predictive supervisory controller that can deal with the retuning of the PID controllers at regulatory level. The typical MBPC objective function is considered. Recently, Uduedi & Ordys [9] presented the equivalence between supervisory control strategy based on GPC objective function and a regulatory GPC controller. The state space formulation is considered for multivariable systems. In this work, based on Lagrange theory with Kuhn Tucker conditions, we derive the equivalence between a supervisory control strategy and a regulatory controller, both with constraints, based on the same general objective function. This objective function may represent not just regulatory criterion (GPC), but also economic criterion or others. The control design is first described, including the supervisory optimal controller and the regulatory optimal controller derivations. The equivalence of the two strategies is demonstrated. The proposed supervisory and regulatory controllers are assessed using a boiler simulator. Finally, the conclusions are summarised.