Frequency-domain design of pid controllers for stable and unstable systems with time delay

An approach for tuning PID-type controllers is developed for single input single-output, linear time-invariant systems, based on an extension to the method of D-partition. This method permits design for simultaneous minimum gain and phase margin requirements. It also allows design for specified maximum gain and phase cross-over frequencies of the controlled system. The technique can be applied to systems with stable or unstable plants as well as to irrational systems with significant time delay. Another advantage of the method is that it can be used for various controller configurations including derivative in the feedback path. Three examples illustrate the tuning method.