A design of disturbance observer in frequency domain for robust control of time delay system

Abstract

The disturbance observer (DOB) based robust control is widely used to suppress the effect of model uncertainty and disturbances. Improvement of disturbance suppression performance in DOB based control (DOBC) is achieved by expansion of the Q-filter's bandwidth or equivalently increment of its cutoff frequency. However, if the system has time delay property, the bandwidth cannot be arbitrarily extended because of the stability demand of the closed loop system. Although the Q-filter's bandwidth is restricted, there is still room for improving disturbance suppression performance by elaborately designing the Q-filter's structure and coefficients. For the optimized design of Q-filter, at the beginning of this paper, based on the analysis of the model uncertainty due to time delay and its upper bound, a new robust stability condition of closed loop system is derived as a type of inequality on complementary sensitivity function of whole closed loop system with DOB. Then a mixed sensitivity optimization problem for optimizing disturbance suppression performance under this stability condition is formulated with structural constraint. Finally, in order to solve this optimization problem, pseudo loop factorization and shaping method is used to transform it into standard H ∞ $$ {H}_{\infty } $$ control problem without the structural constraint so that it can be solved systematically. The results of illustrative examples and simulations validate the effectiveness of the proposed method.