In many industrial applications, the existing constraints mandate the use of controllers of low and fixed order while typically, modern methods of optimal control produce high-order controllers. The authors seek to start to bridge the resultant gap and present a novel methodology for the design of low-order controllers such as those of the P, PI and PID types. Written in a self-contained and tutorial fashion, this book first develops a fundamental result, generalizing a classical stability theorem – the Hermite–Biehler Theorem – and then applies it to designing controllers that are widely used in industry. It contains material on:

• current techniques for PID controller design;

• stabilization of linear time-invariant plants using PID controllers;

• optimal design with PID controllers;

• robust and non-fragile PID controller design;

• stabilization of first-order systems with time delay;

• constant-gain stabilization with desired damping

• constant-gain stabilization of discrete-time plants.