Modified anti-windup scheme for PID controllers
A. Visioli
Abstract: An anti-windup scheme for proportional-integral-derivative controllers is presented.
The approach is based on the combined use of back-calculation and conditional integration anti-
windup techniques. In this way, the disadvantages that can hinder previously proposed strategies
are overcome. Specifically, the method can guarantee a satisfactor y performance for processes
with different normalised dead times, without the tuning of additional parameters being required.
Therefore, considering its simplicity, it is highly suitable for implementation in industrial
regulators.
1 Introduction
Despite the advent of many effective design methodologies
in the control field in recent years, propor tional-integral-
derivative (PID) controllers are undoubtedly still the most
adopted controllers in industrial settings, because they
provideacost=benefit ratio that is very difficult to amelio-
rate by other t ech niques. However, the performance of PID
controllers can be severely limited i n practical cases by the
presence of saturation of the actuators, which causes the
well-known phenomenon of integrator windup [1].
To deal with this problem, it is necessary, from a
theoretical point of view, to design the controller explicitly
taking into account the actuator c onstraints from the first
stage, e.g. refer ring to the nonlinear systems framework.
However, the overall design becomes mu ch more compli-
cated and therefore inappropriate in the PID control
context, where the ease of implementation has to be
preserved as a major feature. Therefore, the typical
method to deal with the integrator windup problem is to
tune the controller ignoring the actuator saturation and
subsequently to add an anti-windup compensator to
prevent the degradation of performance. In this context,
several techniques have been devised to de sign the
compensator [2, 3]. Basically, they b elong to two different
approaches, namely, conditional integration (in which the
value of the integrator is frozen when certain conditions
are verified) and back-calculation (in which the difference
between the controller output and the actual process input
is fed back to the integral terms) [4]. Note that the latter
case also includes the conditioning technique [5, 6] and
that a unified framework for the linear ti me-invariant anti-
windup schemes (including the use of an observer to
estimate the correct state of the controller [7, 8])has
been pre s en t ed in [9].
However, these techniq ues can s uffer from the presence
of a significant dead time in the process or, to deal with
processes with different normalised dead times, they might
require an extra tuning effort (see Section 2), which is
undesirable for industrial regulators. Therefore, it is
proposed to combine the different approaches (in a very
simple way) in order to overcome these problems.
2 Anti-windup strategies for PID controllers
2.1 Generalities
The int eg ra tor windu p is a phenom eno n that can oc cur in
the presence of a saturation of the process input. We refer
totheschemeofFig. 1,whereu is the controller output, u
s
is the actual process input, y is the process output, w is the
setpoint reference value and e i s the s ystem er ror. It is
assumed that a transition from the value y
0
to the value y
1
is
required for the system output and this determines the
amplitude of the step signal to be applied as input to
the closed-loop system. The PID controller is described by
the following expression (non-interacting form) in the
Laplace domain:
UðsÞ¼K
p
EðsÞþ
1
T
i
s
EðsÞ
sT
d
1 þ sðT
d
=NÞ
Y ðsÞ
ð1Þ
where K
p
, T
i
and T
d
are the proportional gain and the
integral and derivative time constants respectively, and N is
usually set between five and 20.
The integrator w indup occurs when a step change in w
causes the actuator to saturate. In this case the system error
decreases more slowly than in the ideal case (when there is
no input limitation) and therefore the value of the integral
term becom es large. Thus, even when the value of y attains
that of w, the controller still saturates due to the integral
term and this generally leads to large overshoots and
settling times.
It has to be noted that the integrator windup m ainly
occurs when a step is applied to the reference setpoint
signal rather than to the manipulated variable (i.e. in the
# IEE, 2003
IEE Proceedings online no. 20020769
DOI: 10.1049/ip-cta:20020769
Paper first received 22nd April and in revised form 20th September 2002
The author is with the Dipartimento di Elettronica per l’Automazione,
University of Brescia, Via Branze 38, 25123 Brescia, Italy
µ
s
min
µ
s
max
u
s
u
PID
wy
process
Fig. 1 General control scheme
IEE Proc.-Control Theory Appl., Vol. 150, No. 1, January 2003 49
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