Analysis and Synthesis of Feedback Control Systems in the Parameter Plane I-Linear Continuous Systems

A general and unique approach to the analysis and synthesis of control systems in the parameter plane is presented which may be advantageously applied to the design of linear continuous systems, sampled-data systems, nonlinear systems, and systems with distributed parameters. This paper is concerned with the application of the method to linear continuous systems. As a simple and rapid procedure for factoring characteristic polynomials in the parameter plane, the proposed method permits the designer to maintain control over salient characteristics of both transient and frequency responses. The introduction of the Chebyshev functions greatly facilitates the procedure and makes it suitable for simulation on either analog or digital computers. In the design procedure, all graphical and analytical operations are performed in the real domain.