Systems analysis and design in classical control theory can be done in time domain or frequency domain using transform techniques. Most of these methods heavily rely on the transfer function model which can represent only a special subclass of systems, called time invariant systems. The time invariant systems can be described by constant parameter differential equations or transfer functions.

Acontrol system is constructed to maintain the output of a plant or process suitably related to the input. It can be a regulator in which the output remains constant or at the most varies slowly as the input remains constant. It can also be a servomechanism in which the output being controlled is a mechanical position.

Control systems can be broadly classified into continuous systems and discrete data systems based on the nature of the signals at one or more points within the system. Continuous systems, also called analogue systems, have signals which are continuous functions of the independent variable time.

The classical control theory essentially makes use of transform techniques for the analysis and design of control systems. The most commonly used method is by the use of transfer function which is essentially an input output model relating the Laplace transform of the output to the Laplace transform of the input for a system which does not contain any initial
energy. The major limitations of the ......

In an earlier chapter, it was brought out that the state variable method has definite advantages over transfer function approach. This is true both in the analysis and design of control systems. In classical control, design is based on a set of specifications in time domain or frequency domain and techniques used are basically graphical in nature (see Chapter 2).

The study of linear control systems is relatively simple and large number of methods is available for studying the performance of linear time invariant systems. However, the study of nonlinear systems is not that simple due to many reasons. The fact that the superposition principle does not apply to nonlinear systems makes generalisation difficult and study of many nonlinear systems has to be spec ......

As discussed in the beginning of chapter seven, there are several methods available for the study of nonlinear systems based on linearization. Local linearization method is restricted to the study of the behaviour of nonlinear systems in the immediate neighborhood of the
equilibrium point. Other linearization techniques have been developed which does not have such a restriction.

For linear time invariant systems, as reviewed in chapter 1, the concept of stability is simple and can be formalised into the definition of bounded input bounded output stability. Several techniques are available for the determination of stability of such systems. Routh Hurwitz criterion, Nyquist criterion and methods based on Bode plots are simple to apply for single input single output linear t ......

The resources available on the planet earth are being consumed at an alarming rate and in order to preserve whatever is left for the future generations, it is essential that consumption has to be reduced to the minimum possible. The situation applies to almost all resources, energy, fuel, food and so on. Any system that is designed in these years should confirm to stringent conditions on energy ef ......