Direct synthesis of first order controllers from frequency response measurements

This paper gives a constructive algorithm to obtain the entire set of stabilizing first order controllers for a given single-input single-output linear time invariant system. Unlike earlier results, a mathematical model such as the transfer function or a state space model is not required. Instead, only the frequency response (Nyquist-Bode data) and knowledge of the number of RHP poles of the plant are utilized to solve the problem. The method is of practical importance especially when mathematical models are not available or identification is not desirable. We also show that the method can be extended to include various performance requirements such as guaranteed gain and phase margins, and guaranteed H_∞ margin. An example is given for illustration.