Linear Control System Design

In this chapter a review of the design of multivariable feedback controllers for linear systems will be considered. This review treats mainly deterministic control objects with deterministic disturbances. After giving an overview of the type of linear sys

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Linear Control System Design

Abstract In this chapter a review of the design of multivariable feedback controllers for linear systems will be considered. This review treats mainly deterministic control objects with deterministic disturbances. After giving an overview of the type of linear systems to be treated, this chapter will handle the basic control system design method known as pole or eigenvalue placement. First systems where measurements of all the states are available will be treated. For cases when such complete state measurements are not available the concept of deterministic observers to estimate the states which are not measured directly will be introduced. It will also be shown that it is often possible to design reduced order observers where only the unmeasured states are estimated.

4.1 Control System Design Before going into the specific task of designing linear control systems it is necessary to set the ground rules for the treatment. This can be done by presenting an overall picture of the components and configuration of the system which is to be considered. A control system is a dynamic system which is designed to operate in a prescribed manner without external interference, in spite of unavoidable effects (disturbances) which impede its proper operation. The main purpose of this book is to present methods to analyze and synthesize such systems. A second purpose is to present methods to model disturbances and design control systems for minimum disturbance sensitivity. This requires a tabulation of the main elements of such systems and a presentation of their general configuration. The main components of a control system are 1. 2. 3. 4.

The plant or control object. The actuators or drivers for the plant. The sensors which measure the current operating point of the plant. The controller which drives the plant in accordance with the overall control objective given the sensor measurements.

E. Hendricks et al., Linear Systems Control, DOI: 10.1007/978-3-540-78486-9_4, Ó Springer-Verlag Berlin Heidelberg 2008

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194 Fig. 4.1 Block diagram of a typical control system. The plant or control object is shown in the upper part of the figure while the controller and feedback loop is shown at the bottom

4 Linear Control System Design Plant disturbances

Control object (Plant)

Actuators

Control signals

Sensor disturbances

Sensors Plant outputs

Plant inputs

Sensor outputs

Feedback loop

Controller Reference inputs

A block diagram of a typical control system is presented on Fig. 4.1. Note, that the actuators and sensors are usually considered to be external to the control object itself. However it is often necessary that the dynamics of these components are taken into account in the design of the overall feedback control system. The plants or control objects which may be controlled in this way can be of many different types: mechanical, electrical, fluid dynamic, economic, biological, etc. or combinations of such plants. The only limitation to the nature of the plant (as far as this book is concer