A design of disturbance observer in standard H_∞ control framework

Abstract

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:

Robust Current Control of Voice Coil Motor in Tip-Tilt Mirror Based on Disturbance Observer Framework

“…Condition 2) indicates that the Q-filter design is limited by the upper bound of the uncertainties. Similar conditions are also given in the previous works [26]- [30]. However, such kind of condition is not clear enough for the application in the practical system.…”

“…Moreover, new sufficient conditions for the robust stability based on H ∞ algorithm are presented, which is suitable for the DOBbased robust current control of induction motors. Compared with traditional H ∞ algorithm [26]- [30], the upper bound of the uncertainty is calculated directly, so that the ranges of different electrical parameters of the VCM are very clear for the robust stability. Experiment results show that as the environment temperature changes, the robustness of the current control is highly improved by the proposed methodology comparing with the traditional PID control.…”

Robust DOBC for Stabilization Loop of a Two-Axes Gimbal System

“…According to given Theorem 1 in [22], the optimized loop function L is independent of the choice ofP and is uniquely determined whenP does not have any unstable poles and zeros except infinite zeros. Therefore, the selectedP will not have any effect on the norm minimization of the problem as long as it meets the requirements.…”

“…Further, [21] proposed a graphical DOBC design method using frequency response analysis. In [22], [23], DOBC filter design under the performance constraints is implemented by the H ∞ method. Moreover, an extended H ∞ control based on disturbance observation is proposed [24].…”

Performance analysis of 2‐DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbances

“…To tackle external disturbances, several significant control methods with the idea of estimating and compensating for external disturbance have been developed, such as the disturbance accommodation control and the disturbance observer–based control. () On the other hand, since many physical plants contain both internal and external uncertainties, dealing with the mixed uncertainties is of great engineering necessity and is becoming a very attractive field.…”