Abstract
The performance characteristics of a dynamic control system are evaluated according to the transient and steady-state responses. The transient performance is the controllability of the output for the tracking of the reference or the ability to reduce or reject the effects of unwanted disturbances; alternatively, the steady-state performance is represented by the magnitude of the control error at the steady state. As the effects of the two performances on each other are reciprocal, a controller design that shows a zero steady-state error for the ramp input is uncommon because of the challenge regarding the achievement of an acceptable transient response. This paper proposes a PI+double-integral controller for the elimination of the steady-state error for the ramp input while a sound transient performance is maintained. The control-gain design procedure is described by the second-order response for the step input and the response of the error dynamics for the ramp input. The PI+double-integral controller is designed for the first-order transfer function that is derived from a system identification with the open-loop experiment data of the dc-motor. The simple structure of the proposed controller enables the adoption of a low-end microcontroller for the implementation of a real-time control. The experiment results show that the control performance is as effective as that of the simulation analysis for the operating point of linear system; furthermore, the PI+double-integral controller can be conveniently applied to the control system, which is desirable for the improvement of the steady-state error.