OUTPUT FEEDBACK CONTROLLER OF A MULTIVARIABLE PROCESS Abderraouf GAALOUL and Faouzi M’SAHLI Department of Electrical Engineering, National Engineering School of Monastir, 5019, Monastir, Tunisia abderraouf.gaaloul@enim.rnu.tn, faouzi.msahli@enim.rnu.tn ABSTRACT The incorporation of an observer into a state feedback controller results into the so-called output feedback controller. Due to its easiness of design and implementation, many control strategies were reformulated under output feedback. This paper deals with the control problem of a MIMO process represented by a quadruple tank process through the use of a recently proposed output feedback controller. Such one is based on the use of a high gain observer which we propose to substitute with a sliding mode observer. Numerical simulations are developed to show the effectiveness of the proposed observer when applied to estimate the water levels into two bottom tanks. Into the control law is incorporated a filtered integral action. The effectiveness of such component is showed when we evaluate the robustness of the whole process against step like disturbances and stochastic noises. Index Terms—Output feedback, High gain, Sliding mode, Quadruple tank process. 1. INTRODUCTION The control of nonlinear systems under output feedback design stills an open research axe that has attracted the attention of numerous researchers and the problem of global stabilization of output feedback controlled systems has received much attention. Due to the easiness of the control principle and its implementation, such control strategy has been widely used for the purpose of process monitoring. So, many control strategies were reformulated under an output feedback design [19], [20]. In [18], authors established an output feedback nonlinear model predictive control for, respectively, a continuous stirred tank reactor and a continuous mixed culture bioreactor. In [15], authors applied experimentally an observer based second order sliding mode control law to solve the problem of accurate trajectory tracking for the stepper motor position. In [17], a globally bounded output feedback variable structure controller is designed for a feedback linearizable field controlled DC motor. Most results using state feedback control assume full state feedback. However, this is not the case in many industrial processes. So, the presence of unknown state becomes a serious drawback when implementing a state feedback control law. Such difficulty can be overcome through the design of an appropriate observer to estimate the missing states of the system from the knowledge of its input/output. Over the last four decades, many techniques have been proposed in the literature to deal with the estimation of unknown states of nonlinear systems such as HGO [9], [4], [5], SMO [1], EKF [12], [16], UKF [14], etc. The main problem of the observer-based feedback controller is the so-called separation problem. It means that a controller and an observer can be designed separately, so that the combined observer-controller output feedback preserve the main features of the controller with the full state available. The separation principle was proved for asymptotic continuous-feedback stabilization of a class of nonlinear systems combined with high-gain observers [2]. In a previous work [7], we solved a regulation problem of an inverted pendulum on a cart using an output feedback sliding mode-like controller established recently by [6]. In [8], we extended the application of such technique to deal with a tracking problem of MIMO nonlinear systems represented by a quadruple tank process. Such process exhibits in an elegant and simple way complex dynamics. For this reason, it has been used to show the results of different control strategies [13], [11]. In this paper, our main goal is to control the level of the two lower tanks using output feedback controller [10]. The estimation of the two immeasurable bottom levels is accomplished using sliding mode and high gain observers. It’s shown that, besides the capability of tracking a variable signal reference, the robustness of the closed loop system against disturbances and noisy measurement is ensured. The rest of this paper is organized as follows. The quadruple tank process and the corresponding mathematical model is introduced in the following section. The problem statement is presented in section 3. In section 4, the adopted output feedback controller is briefly described. The application of the observer-based controller to solve a tracking problem of the considered process is treated in section 5. Finally, conclusions are presented in section 6. 2. QUADRUPLE TANK PROCESS The experimental setup considered in this work consists of four interconnected tanks as shown in figure (1). 978-1-4244-4346-8/09/$25.00 ©2009 IEEE 2009 6th International Multi-Conference on Systems, Signals and Devices