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