Discrete-Time Dynamic Disturbance Rejection for the Modified Linear Extended State Observer

In this paper, a time discretization of the Modified Linear Extended State Observer (MLESO) is proposed to improve performance for large sample times. Stemming from Model Reference Adaptive Control (MRAC) and L1-adaptive control schemes, the goal of MLESO control is to approximately track a reference model. This is achieved by interpreting all deviations from the reference model as an effect of disturbances, estimating the disturbances, and rejecting the estimates by using a suitable control law. Fast sampling, which is favorable for accurate estimation and compensation, is often limited by hardware. To reduce the required sample time, the continuous-time MLESO is discretized in this paper. After discretizing the plant, state-space dead-beat methods are used to derive a discrete-time control law. Parts of the method can be used for general discrete-time dynamic disturbance rejection. The effectiveness of the proposed discretization scheme is demonstrated in simulation on a hydraulic system.