A discrete-time fuzzy disturbance observer and its application to control

In this paper, a discrete-time fuzzy disturbance observer (FDO) is developed and its application to the control of a nonlinear system in the presence of the internal and external disturbances is presented. To construct the discrete-time FDO, a novel tuning method is proposed and shown to be useful in adjusting the parameters of the FDO. The tuning method uses the augmented error to guarantee that the FDO monitors the disturbance and the control objective is achieved. The design parameters such as a learning rate used in constructing the discrete-time FDO are determined in a numerical manner by solving a linear matrix inequality. It is shown in a rigorous manner that both the disturbance observation error and the control error converge to a compact set of which size can be kept arbitrarily small. In addition, the relationships between the suggested FDO-based control and the conventional adaptive fuzzy controls reported in the previous literatures are discussed. Finally, some examples and computer simulation results are presented to illustrate the effectiveness and the applicability of the FDO.