Textbook in PDF format 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. Overview of Control Systems Some Current Techniques for PID Controller Design The Hermite-Biehler Theorem and Its Generalization Stabilization of Linear Time-invariant Plants Using PID Controllers Optimal Design Using 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