Disturbance observer (DOB) has been one of the most widely used robust control tools since it was proposed by Ohnishi in 1983. This paper introduces the origins of DOB and presents a survey of the major results on DOB-based robust control in the last 35 years. Furthermore, it explains DOB's analysis and synthesis techniques for linear and nonlinear systems by using a unified framework. In final section, this paper presents concluding remarks on DOB-based robust control and its engineering applications.

Disturbance Observer-Based Robust Control and Its Applications: 35th Anniversary Overview

This paper deals with the problem of reliable and robust $\mathscr {H}_{\infty }$ static output feedback (SOF) controller synthesis for continuous-time nonlinear stochastic systems with actuator faults. The nonlinear stochastic plant is expressed by an Ito-type Takagi–Sugeno fuzzy-affine model with parametric uncertainties, and a Markov process is employed to model the occurrence of actuator fault. The purpose is to design an admissible piecewise SOF controller, such that the resulting closed-loop system is stochastically stable with a prescribed disturbance attenuation level in an $\mathscr {H}_{\infty }$ sense. Specifically, based on a Markovian Lyapunov function combined with Ito differential formula, S-procedure, and some matrix inequality convexification procedures, two new approaches to the reliable SOF controller analysis and synthesis are proposed for the underlying stochastic fuzzy-affine systems. It is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness and advantages of the developed methods.

Approaches to T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control for Nonlinear Itô Stochastic Systems

The Active Disturbance Rejection Control (ADRC) prefers the cascaded integral system for a convenient design or better control effect and takes it as a typical form. However, the state variables of practical system do not necessarily have a cascaded integral relationship. Therefore, this paper proposes an algebraic substitution method and its structure, which can convert a noncascaded integral system of PID control into a cascaded integral form. The adjusting parameters of the ADRC controller are also demonstrated. Meanwhile, a numerical example and the oscillation control of a flexible arm are demonstrated to show the conversion, controller design, and control effect. The converted system is proved to be more suitable for a direct ADRC control. In addition, for the numerical example, its control effect for the converted system is compared with a PID controller under different disturbances. The result shows that the converted system can achieve a better control effect under the ADRC than that of a PID. The theory is a guide before practice. This converting method not only solves the ADRC control problem of some noncascaded integral systems in theory and simulation but also expands the application scope of the ADRC method.

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An ADRC Method for Noncascaded Integral Systems Based on Algebraic Substitution Method and Its Structure

In this research, a robust feedback linearization technique is studied for nonlinear processes control. The main contributions are described as follows: 1) Theory says that if a linearized controlled process is stable, then nonlinear process states are asymptotically stable, it is not satisfied in applications because some states converge to small values; therefore, a theorem based on Lyapunov theory is proposed to prove that if a linearized controlled process is stable, then nonlinear process states are uniformly stable. 2) Theory says that all the main and crossed states feedbacks should be considered for the nonlinear processes regulation, it makes more difficult to find the controller gains; consequently, only the main states feedbacks are utilized to obtain a satisfactory result in applications. This introduced strategy is applied in a fuel cell and a manipulator.

Robust feedback linearization for nonlinear processes control

This paper generalizes recent results on multi-instant observer design for discrete-time Takagi–Sugeno fuzzy systems through a valid ranking-based switching approach. The approach hereby develops a concentrated subdivision of spanning space composed of normalized fuzzy weighting functions and then substantially produces a new ranking-based switching mechanism. By taking advantage of this ranking-based switching mechanism, a class of new fuzzy multi-instant observers are achieved and more relaxed design conditions with respect to the recent work can be obtained for ensuring the asymptotically stability of the developed state estimation error system. Two illustrative examples are provided to validate the effectiveness of the result given in this study.

Multi-Instant Observer Design of Discrete-Time Fuzzy Systems: A Ranking-Based Switching Approach

In this work, we study the structure regulator for the perturbations attenuation which is based on the infinite structure regulator. The structure regulator is able to attenuate the perturbations if the transfer function of the departures and perturbations has a numerical value almost equal to zero, and it does not require the perturbations to attenuate them. We apply the structure regulator and the infinite structure regulator to a quadrotor which maintains the horizontal position with respect to the earth for the step and sine perturbations.

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Structure Regulator for the Perturbations Attenuation in a Quadrotor

In previous investigations, the nonlinear hypothesis use the linear bounded maps. Nonlinear hypothesis are described as the combination of the first order terms, and after of the mentioned combination, one bounded map is applied to alter the result. This document proposes two nonlinear hypothesis which use different structures instead of using the linear bounded maps. They are termed as novel nonlinear hypothesis and second order nonlinear hypothesis and their goal is to improve the second order processes modeling. The proposed nonlinear hypothesis are described as the combination of the first order and second order terms. Since the delta parallel robot is a second order process, it is an excellent platform to prove the effectiveness of the two proposed hypothesis.

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Novel Nonlinear Hypothesis for the Delta Parallel Robot Modeling

Adapting H-infinity controller for the desired reference tracking of the sphere position in the maglev process

In this study, an observer for the states and disturbance estimation in two renewable energy systems is introduced. The restrictions of the gains in the proposed observer are found to guarantee its stability and the convergence of its error; furthermore, these results are utilized to obtain a good estimation. The introduced technique is applied for the states and disturbance estimation in a wind turbine and an electric vehicle. The wind turbine has a rotatory tower to catch the incoming air to be transformed in electricity and the electric vehicle has generators connected with its wheels to catch the vehicle movement to be transformed in electricity.

Uniform stable observer for the disturbance estimation in two renewable energy systems.

Actuators nonlinearities are unknown external perturbations in robots, which are unwanted because they can severely limit their performance. This research is focused on the stabilization of robots subject to actuators nonlinearities with a regulator containing the sigmoid mapping. Our regulator has the following three main characteristics: a) a sigmoid mapping is used to ensure boundedness of the regulator law terms, b) the chattering is reduced by the usage of the saturation mapping instead of the signum mapping, and c) the stabilization is ensured by the Lyapunov analysis. Finally, we evaluate our regulator for the stabilization of two robots.

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Genaro Ochoa

Papers

Structure Regulator for the Perturbations Attenuation in a Quadrotor

Novel Nonlinear Hypothesis for the Delta Parallel Robot Modeling

Adapting H-infinity controller for the desired reference tracking of the sphere position in the maglev process

Uniform stable observer for the disturbance estimation in two renewable energy systems.

Stabilization of Robots With a Regulator Containing the Sigmoid Mapping