Preface

Summary

This book, Identification and Classical Control of LinearMultivariable Systems, has been structured for an elective course for undergraduate students and for a core course for post graduate students of Chemical Engineering, Instrumentation and Control Engineering, and Electrical Engineering.

Many systems are described byMulti Input and Multi Output (MIMO) systems. To design controllers for such systems, we require the identification of a transfer function matrix of the system. If the system is mildly interactive, then we can design decentralized Proportional and Integral (PI) controllers based on diagonal transfer functions with appropriate detuning of the PI controllers. If the interaction is significant, then a centralized PI control system is to be designed. The design of the controller becomes complicated if the system is unstable in nature.

Classical Control Theory studies the physical systems and the control design in the frequency domain, while Modern Control Theory studies it in the time domain. Systems in the frequency domain are expressed in transfer functions (via Laplace Transforms), while the time-domain systems are described in state-space representations (a set of differential equations). In Chapter 1, a basic reviewis given of the Classical Control Theory and the Modern Control Theory.

In Chapter 2, basics of open loop and closed loop identification of transfer function models of Single Input and Single Output (SISO) systems are reviewed. An open loop method for identifying First Order Plus Time Delay (FOPTD) model and Critically Damped Second Order Plus Time Delay (CSOPTD) transfer function model is proposed. The closed loop reaction curve method and optimization method are discussed. A review of the techniques available for design of PI controllers for transfer function models for SISO systems is brought out.

In Chapter 3, the concept of relative gain array for the measure of interactions in a multivariable system is given. The need to detune the diagonal controllers’ settings is brought out and also the method of tuning decentralized PI controllers by relay auto tune method. Simple methods of designing centralized PI controllers and the analyses of robust stability and robust performances are discussed.

In Chapter 4, a Closed Loop Reaction Curve (CRC) method for the identification of a stableMIMO system is discussed.