Comparison Of Steady-state Errors In Open-loop Control System And Closed Loop Control System
Comparison of steady-state errors in open-loop control system and closed loop control system:
If Go(0), the dc gain of the open-loop control system, is equal to unity, then the steady state error is zero. Due to environmental changes and aging of components, however, the dc gain Go(0) will drift from unity as time elapses, and the steady-state error will no longer be equal to zero. Such steady-state error in an open-loop control system will remain until the system is recalibrated.
For the closed-loop control system, the error signal is
The steady-state error in the unit-step response is
In the closed-loop control system, gain Kp is set at a large value compared with 1/K. Thus the steady-state error can be made small, although not exactly zero. Let us assume the following variation in the transfer function of the plant, assuming Kc and Kp constant:
For simplicity, let us assume that K = 10, ΔK = 1, or ΔK/K = 0.1. Then the steady-state error in the unit-step response for the open-loop control system becomes
For the closed-loop control system, if Kp is set at 100/K, then the steady-state error in the unit-step response becomes
Thus, the closed-loop control system is superior to the open-loop control system in the presence of environmental changes, aging of components, and the like, which definitely affect the steady-state performance.