Design of UDE-based controllers from their two-degree-of-freedom nature

The control algorithm based on the uncertainty and disturbance estimator (UDE) is a robust control strategy and has received wide attention in recent years. In this paper, the two-degree-of-freedom nature of UDE-based controllers is revealed. The set-point tracking response is determined by the reference model, whereas the disturbance response and robustness are determined by the error feedback gain and the filter introduced to estimate the uncertainty and disturbances. It is also revealed that the error dynamics of the system is determined by two filters, of which one is determined by the error feedback gain and the other is determined by the filter introduced to estimate the uncertainty and disturbances. The design of these two filters are decoupled in the frequency domain. Moreover, after introducing the UDE-based control, the Laplace transform can be applied to some time-varying systems for analysis and design because all the time-varying parts are lumped into a signal. It has been shown that, in addition to the known advantages over the time-delay control, the UDE-based control also brings better performance than the time-delay control under the same conditions. Design examples and simulation results are given to demonstrate the findings.