Proportional–integral–derivative stabilization of complex conjugate-order systems

Proportional–integral–derivative (PID) stabilization is an important control design strategy that provides the designer with all PID controller set which results control system stability absolutely. In this way, the designer has a wide range of freedom to obtain the controller that meets the desired criteria. This process is particularly advantageous in situations where it is difficult to clearly define the design criteria at the beginning of the design or to make a balanced decision among the design criteria. The main objective of this paper is to present for the first time a PID stabilization method for complex conjugate-order systems, which is a new type of system for the control community and has been little studied on. The method is based on obtaining of stability/instability regions using the D-decomposition method in the controller parameter space graphically. These regions are formed by stability boundaries that are defined as real root, infinite root and complex root boundaries. The stability of the regions is determined using generalized modified Mikhailov stability criterion that is a powerful stability tool of the system theory. The simulation results indicate that the presented stabilization method is effective and practically useful in the analysis and control of the complex conjugate-order systems.