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.

Periodic exogenous signals often exist in motion systems, especially those involving one or more rotating elements. These periodic exogenous signals deteriorate the performance of motion systems, and these adverse effects cannot be practically eliminated by straightforwardly increasing feedback control gains due to sensor noise, actuator saturation, and unmodeled plant dynamics. This paper describes a sliding repetitive controller for motion systems subject to periodic exogenous signals. Moreover, an adaptive law for bound estimation is devised to ensure the presence of a sliding motion for both repetitive learning and disturbance observation. The tracking motion system of a disk drive is considered in practice, and a traditional repetitive controller is also implemented for performance comparisons with the proposed scheme. Experimental results are reported in this paper, showing the efficacy of the proposed scheme.