Abstract
The control signal in position control systems is inherently constrained by some limited value, such as the current or voltage driving a servo motor is limited by a maximum current or maximum voltage. To design the controller for achieving the desired performances, a fast tracking of set point change and a robustness with respect to the parameter variation, of system, it is necessary to ensure that the control signal satisfies the constraint value. A well-known time optimal Bang-Bang controller yields a shortest time response of a nominal system, however, the response is sensitive to the parameter variation. The other one, high gain control can make the system be robust and track the set point quickly beneath the unconstraint of control signal. Because the existing of contraint of control signal, its performance will be poor such as the overshoot response.
In this paper, we introduce a state feedback control law associated with time scale. The feedback law based on this time scale can, assign the system to be the high gain mode if the time scale is sufficiently large. However, the large time scale causes the control signal over the limited value. This work proposes a control method which attempt to adjust the time scale suitably, in such a way that the control signal being the inner produce of state variable and feedback control law must satisfy the constraint condition at all time. Roughly mention, when the error is quite small, the time scale will be adjusted to the very large value and the system will be high gain nearly.
The study case of a position control system using proposed scheme is simulated by digital computer. The results show the fast tracking response of the control system and the robustness with respect to the parameter change. Finally, the comparison of proposed scheme and the Bang-Bang control, LQR control are shown also.
