A Pole Placing PID Type Controller

The problem of designing a pole placing PID type (ppPIDt) controller is considered, motivated by educational considerations. Effectively the number of controller zeros, integrators and filtering poles can be extended to aid in the response shaping and stabilizing of the closed loop, while simultaneously avoiding spikes in the control signal. In contrast to the state feedback observer-controller, we do not emphasize maintaining the original systems order, rather we utilize the increased order of the closed loop to shape its response by a suitable choice of poles in the closed loop. This is similar to the classical PID which typically increases the order of the original system by two in the closed loop. We also propose a prefilter to cancel stable system zeros and ppPIDt zeros and replace them by new zeros if desirable. This results in a new overall transfer function of the controlled system, with full pole placement including good input tracking and disturbance rejection properties and guaranteed closed loop stability. The material is presented in a tutorial way suitable for basic undergraduate control courses and has been used successfully by the first author in such a course.