Discrete‐time design and applications of uncertainty and disturbance estimator

Abstract

This article proposes a discrete-time design for the robust control technique of uncertainty and disturbance estimator (UDE), with studies on applications to real-world systems. Despite the ease of implementation of discrete-time strategies, almost all prior work on UDE is for designing continuous-time control laws, with no general, complete research for discrete-time design. To design an appropriate discrete-time control law, a novel digital filter similar to the original analog filter for disturbance estimation is designed, a discrete-time error-based control law is derived, and a detailed stability analysis is provided. However, most real-world, physical systems are nonlinear and continuous-time in nature. Thus, the techniques of sampling and digital-analog (D/A) conversion are used, enabling the control of linear, time-invariant as well as a class of nonlinear, continuous-time systems using discrete-time UDE. The considered nonlinear system is for the phenomenon of wing-rock motion. Simulations are performed for the proposed techniques, and results indicate highly accurate stabilization and tracking performance, with excellent disturbance rejection. In particular, it is seen that the proposed control law is less sensitive to initial values of the error when compared to the original continuous-time UDE law.

Discrete Robust Control of Robot Manipulators using an Uncertainty and Disturbance Estimator

“…In the following section, a brief review of discrete-time UDE, or DT-UDE is provided. The multiple-input, multiple-output case, which was not dealt with in detail in [35], is considered here. The DT-UDE strategy, along with the design of a robust controller-observer structure in Section 4 enable the design of a control law that is robust to modeling uncertainties and any external disturbances, without requiring the measurement of link velocities.…”

“…One of the most important aspects to analyze in the closed-loop system described by the plant (10), reference model (11) and the control law ( 17) is stability. While not reproduced here, it has been shown in [35] that the condition on the filter parameter τ to ensure asymptotic stability of the system is:…”

“…The design of DT-UDE also enables implementation on a microcontroller or digital computer. A drawback of the design in [35] is the requirement of all states for feedback for control design. This is not realistic in common engineering systems, as mentioned earlier, and is addressed here.…”

“…The objective of this work is to present a discrete controller for robot manipulators based on the formulation of DT-UDE in [35]. The principal contributions are summarized as follows.…”

“…The tracking objective is also presented here. Section 3 reviews the theory of DT-UDE according to [35]. In Section 4.1, a discrete-time observer based on DT-UDE is designed, along with the control law, resulting in a robust controller-observer structure.…”