Design of discrete-time adaptive repetitive controllers and application to feed drive systems

Abstract

Although repetitive control is well known to be useful for controlling systems required to perform periodic motions with high accuracy, the repetitive control system is generally a high-order system and has undesirable high-frequency characteristics. Hence, there has been much research on the robustness improvement of repetitive controllers. Although adaptive control is useful when the plant dynamics is unknown, little effort has been made to apply adaptive control to the repetitive control system. Since the repetitive control system is generally a high-order system, many controller parameters need to be estimated online, especially if adaptive pole-placement control, which enables arbitrary pole placement of the control system, is applied. This paper presents a discrete-time design of adaptive poleplacement repetitive controllers for plants with unknown transfer function coefficients (orders of the plants are assumed to be known) and disturbances by assuming that a non-minimum phase continuous-time plant is controlled with a small sampling period. From this assumption, plant unstable zeros appearing by discretization can be approximated by known ones (limiting zeros). By employing the idea of limiting zeros, the repetitive controller can be realized as a feedforward controller without knowing the plant transfer function coefficients. Since the repetitive controller is placed out of the feedback loop by this design, the adaptive pollplacement controller can be realized without updating a large number of controller parameters. Experimental results with the application of a feed drive system, which is often used in computer numerical control (CNC) machine tool systems with repetitive motion, demonstrate the effectiveness of the proposed method. Design methods with and without the limiting zeros are compared in the experiment. It is then shown that using the limiting zeros reduces the control input variance and improves the control performance.