Suitability of PID controllers for unstable processes: An issue to be tackled in undergraduate control education

PID control is presented in undergraduate control textbooks as a universal control method while often neglecting their limitations regarding unstable processes. A major limitation is due to the introduction of a close-to-the-origin zero that undermines the damping and causes excessive overshoot. This paper illustrates the problem through examples and proposes a simple alternative configuration where the PD part is placed in parallel to the process (inner loop) while the I part is left in cascade (outer loop). It is shown that this I-PD configuration stabilizes the process and achieves desired transient response without introducing unwanted zeros. Results from tracking and disturbance rejection control for MIMO systems in state space are used to prove that I-PD control guaranties full controllability, robustness, and asymptotic tracking and disturbance rejection for second-order processes whether they are stable, integral, or unstable.