Inverse optimal control formulation for guaranteed dominant pole placement with PI/PID controllers

This paper presents an analytical approach of guaranteed dominant pole placement tuning for PID controllers to handle second order systems. Analytical expression of PID controller gains are reported in terms of the system´s open loop characteristics and desired closed loop damping ratio, natural frequency and relative dominance of pole placement. Inverse optimal control formulation has been done, considering that the PID controller gains are equivalent to optimal state feedback gains of a quadratic regulator and a brief comparison of the achievable cost of control for various specified open loop and closed loop conditions are reported. The idea has been extended for pole placement tuning of PI controllers as well to handle first order systems along with discussion about the corresponding inverse optimality.