On Anti-Windup and Control of Systems
with Multiple Input Saturations:
Tools, Solutions and Case Studies
PhD Thesis, Uppsala University,
Aug. 2003, 217 pp.
The thesis available in Postscript :
Paper copies of the thesis can be obtained from
Signals and Systems Group, Uppsala University,
Box 534, SE-75121 Uppsala, Sweden.
Control of a dynamic system requires manipulable
inputs. The manipulation is usually
transmitted (or transferred)
to the system via constrained actuators. In many technical
systems actuators are transducers which transforms a low
power signal, usually electric, into high power "action".
are valves for flow control and high power electronics for
electric power control. The latter can in a second step e.g. be
used for torque control of an electric motor. In most cases,
properly dimensioned actuators will saturate even under
What happens if, or when, actuators saturate depends
critically on the ability of control strategy (the controller) to
handle a saturation event as well as on the properties of
controlled system. Some systems are easier to control via
constrained actuators than others. Some controllers are better
suited to handle saturation events than others.
Many dynamic systems behave as "almost" linear, under
certain operating conditions, and therefore linear control theory
is widely applicable in reality. But quite often, e.g. when
operating a system on its limits, different kinds of
nonlinearities make themself known and
may degrade the stability
and performance properties to such an extent that they are no
longer acceptable. These nonlinearities must then be taken into
account when designing and implementing
nonlinearities, such as amplitude- and rate limiters,
the plant input, are examples of such nonlinearities. By
introducing amplitude- and/or rate limiters at the input of an
otherwise linear model, one will be able to describe a
significantly larger class of dynamic systems in such a way that
the controller design results in good performance.
Control of linear systems with saturating actuators
are considered and anti-windup compensators for
multiple-input multiple-output systems, and robust,
almost time-optimal controllers for double integrators
with input amplitude saturations, are proposed.
Windup effects are defined and anti-windup
compensators aiming at minimizing the windup
effects are proposed. The design is based on
- linear quadratic (LQ) optimization techniques and
- heuristic design using Nyquist-like techniques and
A root-locus like technique that can, approximately,
directional problems that may be
present in MIMO systems with input saturations,
and that can be used for design of anti-windup
compensators and for selection of appropriate
static directional compensators, is proposed.
The problem of control of double integrators via
saturating inputs is addressed and a ro-bust piece-wise
linear controller that gives almost time-optimal
performance is suggested. It is shown that time optimal
control of a double integrator via an input amplitude
limiter, is equivalent to time-optimal control of a single
integrator having a rate limiter at the in-put.
One such application, concerning control of hydraulic
cylinders in container crane systems, is presented.
An extension of the controller, allowing synchronous
control of two integrators with
input rate limitations, is proposed.
Anti-windup compensator, saturating actuator,
amplitude limiter, rate limiter, path anti-windup,
double integrator, time-optimal control,
container crane, spreader, hydraulic cylinder.
Swedish Control Meeting 96
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