Tuning of PID-type controllers for stable and unstable systems with time delay

A graphical technique for tuning PID-type controllers based on the method of D-partition is proposed for single-input-single-output linear time invariant systems. The tuning method shifts all the roots of the characteristic equation of the controlled system to a certain desirable region in the left half of the complex plane (LHP) to achieve a specified least absolute and least relative stability margin. The method can be used to tune a precompensator, in a two degree of freedom structure, so as to improve tracking behaviour. The method can be used for both stable and unstable systems, for systems with significant time delay and for various controller configurations, including derivative in the feedback path.