Step Response Improvement by Pole Placement with Observer

This paper presents simulation results for improving the performance of a single-input, single-output state-space system by the method of pole placement using an estimate of the state vector generated by a full-order observer. The particular performance criteria under consideration are percent overshoot, 2% settling time, and zero steady-state error of the unit step response of the state-space system. It is observed that if the initial conditions of the observer are not close to those of the original system, the use of the observer state in place of the actual state for pole placement will result in significant deviation of the performance criteria from the desired criteria. If the initial conditions of the observer are very close to that of the state-space system, the use of the observer state can yield results close to that of using the actual state. For the case that the initial conditions of the observer are not close to those of the state-space system, there is no improvement of the performance criteria by pushing the observer poles deep into the left half plane even though this will make the state of the observer converge rapidly to the state of the original system.