Model-Free Synthesis of Fixed Structure Stabilizing Controllers Using the Rate of Change of Phase ?

This technical note outlines an approach to the problem of synthesizing fixedstructure low-order controllers for systems whose mathematical models are unknown, but their frequency responses are available. Stability of the closed-loop system is guaranteed if the frequency response of the plant and the controller satisfy certain conditions at specific frequencies. It is shown that the relation between the rate of change of phase of the plant and the controller, at specific frequencies, characterizes the closed-loop system stability. We use this characterization in a systematic way to design fixed-structure low-order controllers such as PI and PID-controllers.