Design of a Robust Discrete Time Sliding Mode Repetitive Controller 1 Maria Mitrevska, 2 Zhenwei Cao, 3 Jinchuan Zheng, and 4 Edi Kurniawan 1,2,3 Faculty of Science, Engineering and Technology 1,2,3 Swinburne University of Technology, Hawthorn, VIC 3122, Australia 4 Research Center for Informatics 4 Indonesian Institutes of Sciences, Bandung 40135, Indonesia Email: 1 mmitrevska@swin.edu.au, 2 zcao@swin.edu.au, 3 jzheng@swin.edu.au, 4 edi.kurniawan@lipi.go.id Abstract—This paper presents the design of a robust discrete-time sliding mode repetitive controller (DSMRC) which combines the features of repetitive control (RC) and sliding mode control (SMC) to achieve fast transient response, improved robustness to various matched uncertainties, and improved steady state performance. The new control structure consists of a repetitive control component and a sliding mode control part. The task of the sliding mode component is to provide a fast dynamic response and improve the robustness of the system against various uncertainties. The repetitive control part is added to the system to reduce the periodic error and improve the steady state performance of the system. A small pure phase lead component is added to the RC structure to ensure system stability and achieve high bandwidth tracking performance in the presence of bounded uncertainties. The proposed control structure is applied to a linear actuator (LA) system subjected to payload variations. A detailed analysis of the new control structure is presented in this paper to show the significance of the proposed scheme. Simulation results verify the effectiveness of the proposed method. Index terms—Repetitive control, sliding mode control, robust control, describing function, linear actuator. I. INTRODUCTION Repetitive control (RC) is a learning control technique which is used in many dynamic systems to eliminate periodic error [1]. RC is based on the internal model principle (IMP) and can be seen as a periodic signal generator which is added to a stable closed loop system to ensure asymptotic tracking or rejection of repetitive signals [1, 2]. The high precision and simple implementation of RC is why this control structure has been extensively used in many applications of repetitive nature. So far RC has been successfully applied and used in many systems such as memory storage devices [3], robot manipulators [4], machining tools [5], power converters [6-8]. Different RC configurations are typically adopted in different practical RC applications. The standard RC structure consists of a pure internal model which usually results in a limited closed loop bandwidth [9]. This causes a sluggish system response and degraded tracking performance at the transient stage of the system response. Unmodelled system dynamics, disturbances, nonlinearities, and other structured and unstructured uncertainties commonly found in many systems are some other factors which can limit the tracking performance of RC systems. A variety of different RC structures which aim to improve the robust performance and stability of RC systems are proposed in [10-17]. In order to achieve fast transient response and improved robustness to various matched uncertainties, RC is usually combined with nonlinear control structures such as the sliding mode control (SMC) methodology. SMC is a widely used nonlinear robust control approach that is well known for its robustness characteristics and fast transient response [18, 19]. Due to its discontinuous control action, SMC allows infinitely fast switching between two different structures. This ensures fast transient response, and great system performance against bounded and matched uncertainties. Unlike continuous SMC, where switching can be applied at any instant as the state trajectory crosses the sliding surface, the switching frequency in discrete sliding mode control (DSMC) is limited by the sampling frequency [19, 20]. The finite switching time in DSMC constrains the system trajectories to stay in a close band around the sliding surface which is known as the quasi-sliding mode band, instead of allowing them to slide on the sliding surface. As a result, DSMC structures may not exhibit the desirable invariance and robustness properties of continuous SMC. Although DSMC structures can be designed to achieve the desired invariance and robustness properties [21-23], achieving good tracking performance is also a very important design aspect which needs to be considered in the design of DSMC structures for high precision applications. Various uncertainties present in a system can reduce the tracking bandwidth and hence limit the tracking accuracy of DSMC systems. It is well known that feedforward controllers such as the repetitive controller can be added to improve the tracking accuracy of the system at steady state. A number of discrete sliding mode repetitive control (DSMRC) structures which have the merits of both RC and SMC have been proposed in recent literature. A discrete time variable structure repetitive control structure for rejection of periodic disturbances and for tracking periodic inputs is proposed in [24]. The design of the robust control law and the selection of parameters in this structure are based on the reaching condition. Similarly, a discrete time sliding mode repetitive control structure with a disturbance estimator is proposed for eliminating periodic disturbances in optical disk drives in [25]. In [26], a discrete multivariable sliding mode repetitive control structure is proposed for rejecting periodic and multi-periodic signals. While, a discrete repetitive sliding mode control structure for dealing with periodic disturbances in nondecouplable multivariable systems is proposed in [27]. 2015 23rd Mediterranean Conference on Control and Automation (MED) June 16-19, 2015. Torremolinos, Spain 978-1-4799-9936-1/15/$31.00 ©2015 IEEE 656