Step Response Improvement by Pole Placement with Observer

Abstract

attaining the performance criteria. A review of this AbstractE This paper presents simulation results method of pole placement [1, 2, 11] follows.for improving the performance of a single-input, single-output state-space system by the method of Consider a single-input, single-output state-space pole placement using an estimate of the state system with vector generated by a full-order observer. The particular performance criteria under x = Ax + Bu (1) consideration are percent overshoot, 2% settling y = Cx time, and zero steady-state error of the unit step response of the state-space system. It is observedAssuming that the state vector x is available, the input that if the initial conditions of the observer are not equation with full state feedback is close to those of the original system, the use of the observer state in place of the actual state for pole u = r -Kxc (2) placement will result in significant deviation of the performance criteria from the desired criteria. IfThe gain vector K is chosen in a way that the the initial conditions of the observer are very close eigenvalues ofA-BK are placed at the desired pole to that of the state-space system, the use of the locations that meet the performance criteria. An observer state can yield results close to that of example is given below to illustrate the procedure of using the actual state. For the case that the initial this method. The assumption of no finite zero in the conditions of the observer are not close to those of closed-loop transfer function is necessary. It is the state-space system, there is no improvement of because finite zeros will contribute to the dynamics the performance criteria by pushing the observer of the step response just like the poles but in a poles deep into the left half plane even though this different manner. will make the state of the observer converge rapidly to the state of the original system. Example 1. Consider the state-space model from [3]

Effect of observer poles on step responses

“…A discussion of the influence on the step response due to the observer initial conditions was discussed in [3]. Also discussed very briefly in [3] was the effect of the observer poles on the step response. To investigate further the effect of the observer pole locations on the step response, more simulation experiments were conducted.…”

Shaping of Dynamic Responses by Observers

“…However, there is an issue which was briefly reported in [1,7]. The issue was that the locations of the observer poles could increase or decrease the settling time.…”

“…The issue was that the locations of the observer poles could increase or decrease the settling time. The references [1,7] did not provide extensive investigations. In this paper, results of extensive investigations are provided.…”

Improving step responses by pole placement using reduced-order observers

“…A study of improving step response using full-order observers was covered in [3]. In this paper, it is intended to extend the study to reduced-order observers.…”

“…These estimates can be used for placing the poles at the desired locations. The effect of the estimates on the step response was discussed in [3].…”