Initial-value compensation of a proportional-integral-derivative controller for non-overshooting motion

This article presents a proportional-integral-derivative controller design for monotonic, non-overshooting output responses of a class of second-order plants that do not need to be initially at rest. The proposed scheme is applicable to twice-differentiable reference commands, and monotonic, non-overshooting responses are achieved by compensating for the initial value of integral state. That is, the integral state is initially set to a certain value so that the subsequent response has no overshoot. In the proposed scheme, the initial value that should be assigned to the integral feedback is found to be a nonlinear function of the plant's initial state. This result differs from those in previous schemes that constrain the controller's initial state to be a linear function of the plant's initial state. The proposed scheme is practically applied to layer-jump control and single-track jump control of an optical disk drive. Experimental results confirm the effectiveness of the proposed scheme and its applicability to mode-switching control systems.