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This brief proposes a method for designing a disturbance observer (DOB) to decouple joint interactions in robot dynamics with nonlinearity. The traditional DOB based on filter design theory has limited performance since the cut-off frequency of its Q-filter is the only tunable parameter to deal with disturbance suppression and model uncertainty. In this brief, a robust optimal design method is developed for the DOB, which can achieve optimal performance of suppressing disturbance by systematically shaping its Q-filter. Simulation results of application to a two-link manipulator with flexible joints show the improvements in disturbance suppression, which illustrates the validity of the proposed method. IndexTerms-Disturbance observer (DOB), H ∞ standard control problem, low-pass filter, robust motion control, two degrees-of-freedom. I. INTRODUCTION I T IS ESSENTIAL to improve the robustness of a motion control system to external disturbance and parameter variations. Disturbance observer (DOB)-based control is one of the most popular methods to attain this purpose [1]. Recent results in experiments and applications have shown the effectiveness of DOB based control [2]-[6]. Especially, it is widely used to decouple the interactive model of robot manipulator, compensate its nonlinearity, and improve the speed and accuracy of control [7]. The DOB for this purpose is often designed by traditional filter models such as binomial model and Butterworth model [8]-[10], but these model have cutoff frequency as the only tunable parameter. In these models, To improve the performance of suppressing disturbance, the cutoff frequency should be increased. However, because of the existence of high frequency model uncertainty caused by flexibility of joint shafts and change of load etc., the cutoff frequency is restricted to guarantee robust stability. This is a substantial disadvantage of using conventional filter model.Recently, several design methods of DOB using H ∞ control scheme have been reported, which can provide optimal performances of rejecting disturbance and sensor noise on the condition of guaranteeing robust stability to parameter uncertainty. However, most of the methods employ numerical computation algorithms to obtain optimal Q-filter [11]-[13]. A systematic and straightforward method is proposed in [14],

The disturbance observer (DOB)-based controller is widely used to estimate and suppress disturbance in motion control system. Because the low-pass filter (Q-filter) in DOB decides the performances of disturbance suppression, noise rejection, and robust stability against system uncertainties, design of Q-filter is the principal task in DOB construction. This paper presents a systematic scheme for Q-filter design based on H 1 norm optimization. Cost function for optimization is proposed by considering performance and relative order condition of the Q-filter. The norm minimization problem is then transformed to a standard H 1 control problem. Furthermore, the relationship between performance and frequency weighting functions is investigated based on which selection of weighting functions is presented. Simulation results validate the global optimality and systematicness of the proposed method. Recently, several methods for designing DOB with H 1 robust control technique have been reported [15][16][17]. It was shown that H 1 norms of sensitivity functions of the system with DOB can When ! 0, the solution of standard problem goes to real solution Q K .s; 0 C / D lim !0 C < 1: