ABSTRACT
3.1 INTRODUCTION
The birth of control theory goes back to the period of World War II when the analysis and design of servo mechanisms play a key role in the development of feedback control. The evolution of control theory starts from simple frequency domain approach to linear control systems to mathematically enriched theory of linear/nonlinear systems based on the theory of differential equations for dynamical systems. Essentially, the advent of the space age in 1957 changes the basic spirit of control theory. The competition in space and the challenges posed by the complexity of control problems related to the guidance of space vehicles, attract a number of prominent mathematics, most notably L.S. Pontryagin in the USSR and R.E. Bellman in the United States towards control theory. As a result, the level of mathematical sophistication of the theory begins to grow very rapidly, swinging the pendulum all the way from the low-brow approaches of the forties and fifties to the high-brow mathematical formalism of the seventies, eighties, and nineties and till to date. Conventional controllers based on existing control theory techniques are designed either from the frequency domain model, that is the transfer function model, or from the time domain model, that is the state space model of the open loop system (process). The objective of the feedback controller is to guarantee a desired response of the output y. The process of keeping the output y close to the setpoint (reference input) y*, despite the presence of disturbances of the system parameters and noisy measurements, is called regulation. The output of the controller (which is the input of the system) is the control action u.
