Active disturbance rejection controller design for
distributed parameter systems
Jing Xiao, Dazi Li
*
, Jinglin Zhou
College of Information Science and Technology
Beijing University of Chemical Technology
Beijing, China
lidz@mail.buct.edu.cn
Abstract—A control problem of dynamic processes described
by partial differential equations (PDE’s) is proposed and studied
in this paper. They are linear distributed parameter models. The
inputs of the models discussed are position-independent. As is
known to all, distributed parameter systems always demand high
tracking precision and good stability. However, it is difficult for
classical approaches to achieve a high performance in
disturbance rejection. Active disturbance rejection controller
(ADRC) has great ability of resisting disturbance and could meet
the demand of fast-track. In order to ensure the system output
converging to the reference value, ADRC controller is designed.
Extended state observer (ESO) is a key part of ADRC and a
reasonable designed ESO can improve the performance of
ADRC. In this study, the Gaussian approximation is used to
design a higher order ESO to eliminate the model uncertainty
and total disturbance. Simulation results indicate that ADRC
controller is superior to traditional PI controller both in terms of
set-point tracking and disturbance rejection.
Keywords—ADRC; distributed parameter system; heat
exchanger; non-isothermal plug flow reactor
I. INTRODUCTION
Numerous process control systems generally belong to
distributed parameter systems, namely the system state
variables and parameters which are not only functions of time
but also functions of space [1]. In recent years, due to the
higher demands of industrial systems, directly using the
distributed parameter control theory to study the control
strategy of the industrial object has become one of popular
topics [2-3]. Here are some studied of modern control theory
applications. In [4], a control problem of nonlinear distributed
systems was discussed, and an iterative learning controller was
designed under the condition that a direct channel existed
between input and output. In [5], a traditional PI controller was
designed for a tubular polymerization with temperature
distribution. In [6], sliding mode controller was designed for a
parabolic PDE’s. The controller overcame the parameter
variations and boundary uncertainties. However, they do not
mention the influence of parameters perturbation, such as
outside disturbance and many nonlinear actors. Therefore lots
of modern control theories are not realistic because they
demand an accurate model that cannot be obtained in the real
distributed parameter systems. Besides, the control objective of
distributed parameter systems is not only to obtain a curve, but
a curved surface, which makes the demand of controller
increase [18-19]. In a word, the methods mentioned above have
limitations respectively.
ADRC firstly proposed by J. Han in 1990s [7-10], is
independent of the model. In other words, ADRC achieves an
access to control without accurate mathematical model. In
addition, its ability to overcome all the disturbances is valuable
for the control of distributed parameter systems [11-13]. This
approach does not have been applied to solve the control
problem in the distributed parameter systems. However, in
some other industrial processes, it has been widely applied in
the existing literatures. In [14], ADRC controller was designed
for a ship main engine. The difficulty of the wave disturbances
could be solved under the controller designed. In [15], attitude
tracking was discussed for a spacecraft model with inertia
uncertainty. The model was nonlinear in dynamics. A
reasonable ESO was designed to achieve this nonlinear
dynamics model control problem. Actually, ADRC does not
depend on the accurate mathematical model, and it has good
ability to overcome many disturbances, for instance varied
parameters and indelible noises. It could eliminate the
disturbances to a certain extent in the whole working area. Both
of the two applications demonstrate that ADRC control
algorithm has an excellent disturbance rejection ability to
overcome the disturbance uncertainties. Therefore, ADRC is
used to control problem of distributed parameter systems in
this work.
As is known to all, distributed parameter systems are
usually represented by PDE’s. In this paper, the problem of
convection control dynamic processes with
position-independent inputs is proposed. These models usually
described by First Order PDE’s (FOPDE’s). This work tries to
design an efficient controller to solve the problems existing in
this field. Considering the influences of the model uncertainty
and input disturbances of the control system, a method of using
higher order Taylor polynomial is applied to approximate total
disturbance [16]. After that, high order ESO can be constructed
with the input and output data. Both system original state and
extended state can be refactored and sent back to the reference
input by ESO. Combining the virtual control signal and
estimated value of disturbances, the actual control law can be
achieved. The whole controlled system is equivalent to the
integral series type in the control system design. This approach
simplifies the controller design, and it has a high ability of
disturbance rejection through accurately estimating and
effectively eliminating of disturbance. The algorithm will be
This research was supported by the National Natural Science Foundation
of P.R. China (Grant No 61573052, 61473025)
978-1-4673-7189-6/15/$31.00©2015 IEEE