Effect of observer poles on step responses

Abstract

State feedback using an observer is a technique for placing the poles of a linear system at desired locations. An application of such technique is to stabilize an unstable system by placing the new system poles in the left half plane. When the desired system poles are achieved by using observer state feedback, the step response parameters such as peak time, settling time, and percent overshoot are no longer controlled by the desired dominant system poles. The observer poles can change these parameters. This paper intends to elucidate this effect through computer simulations. A set of experiments were conducted with observer poles gradually farther away from the desired system poles. With the observer poles being pushed deeper into the left half plane, the observer states can track the system state faster. It is expected that the step response parameters will be closer to those dictated by the dominant poles. But such improvement was only minimally observed in the simulation results.