PROOF COPY 013302ISA
PROOF COPY 013302ISA
Comparison of several well-known controllers used
in process control
Weidong Zhang,* Xing He, Xiaoming Xu
Department of Automation, Shanghai Jiaotong University, Shanghai 200030, People’s Republic of China
Received 10 July 2001; accepted 29 April 2002
Abstract
In this paper, several well-known design methods, PID control, Smith predictor, inferential control, internal model
control, Dahlin controller, deadbeat control, and predictive control, are studied. A suboptimal Smith predictor is
derived. The relationship among these methods is investigated. It is shown that these methods are equivalent to each
other on certain premises. This explains why they are widely used in process control and provides insight into the work
of bringing these techniques together to control system design. Examples are given to illustrate the result. © 2003
ISA—The Instrumentation, Systems, and Automation Society.
Keywords: Linear system; Time delay; PID controller; Smith predictor; Dahlin controller; Deadbeat control; Inferential control; Predictive
control
1. Introduction
The control of processes involving time delay
presents a continuing challenge to the control
theorists. The nature of the time delay and the sig-
nificant amounts of lag which can be introduced
into the system response frequently make the use
of conventional control algorithms a poor pros-
pect. As early as 1953, Cohen and Coon 1 ad-
dressed the problem of controller design for sys-
tem with time delay by correlating PID settings
with model gain, time constant, and time delay.
Low loop gain was required to avoid instability
when time constant was small compared to the
time delay, leading to poor system performance.
Smith 2 suggested a time delay compensation
scheme for single input/single output systems,
now referred to as Smith predictor. Smith
predictor is a simple and powerful control tech-
nique for processes with time delay. Its attractive-
ness comes from the fact that the design can be
performed by using techniques applied to pro-
cesses with rational transfer functions. However, it
is sensitive to model mismatch and has poor dis-
turbance rejection capability. How to overcome
these shortcomings is the subject of numerous
studies 3–6. Other well-known techniques used
in process control include continuous frequency
domain i.e., s domain design methods, such as
inferential control 7 and internal model control
IMC8, and discrete domain methods such as
the Dahlin controller 9, deadbeat control 10,
and predictive control 11. All of these methods
have been applied to physical systems and
achieved good response. Then, an interesting
problem is what relationship exists among these
methods? This problem was first presented by
Zhang 12 and this paper will give a detailed dis-
cussion.
*Corresponding author. Tel: +86.21.62933329;
fax: +86.21.62826946. E-mail address:
wdzhang@mail.sjtu.edu.cn; URL: http://iic.sjtu.edu.cn/
wdzhang, http://wdzsjtu.home.chinaren.net
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PROOF COPY 013302ISA