Jonas Öhr

PhD Thesis, Uppsala University, ISBN 91-506-1691-9 Aug. 2003, 217 pp.

The thesis available in Pdf.

Paper copies of the thesis can be obtained from Ylva Johansson, Signals and Systems Group, Uppsala University, Box 534, SE-75121 Uppsala, Sweden.

Outline:

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". Examples 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 normal operation.

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 the controller. Actuator nonlinearities, such as amplitude- and rate limiters, appearing at 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.

Abstract:

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

1. linear quadratic (LQ) optimization techniques and
2. heuristic design using Nyquist-like techniques and pole-placement techniques.

A root-locus like technique that can, approximately, foretell possible 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.

Keywords:

Anti-windup compensator, saturating actuator, amplitude limiter, rate limiter, path anti-windup, double integrator, time-optimal control, container crane, spreader, hydraulic cylinder.

Related publications:

Swedish Control Meeting 96
ECC 97
SIAM 98