Model-free active input–output feedback linearization of a single-link flexible joint manipulator: An improved active disturbance rejection control approach

Wameedh Riyadh Abdul-Adheem,Ahmad Taher Azar,Amjad J Humaidi,Ibraheem Kasim Ibraheem

doi:10.1177/0020294020917171

Abstract

Traditional input–output feedback linearization requires full knowledge of system dynamics and assumes no disturbance at the input channel and no system’s uncertainties. In this paper, a model-free active input–output feedback linearization technique based on an improved active disturbance rejection control paradigm is proposed to design feedback linearization control law for a generalized nonlinear system with a known relative degree. The linearization control law is composed of a scaled generalized disturbance estimated by an improved nonlinear extended state observer with saturation-like behavior and the nominal control signal produced by an improved nonlinear state error feedback. The proposed active input–output feedback linearization cancels in real-time fashion the generalized disturbances which represent all the unwanted dynamics, exogenous disturbances, and system uncertainties and transforms the system into a chain of integrators up to the relative degree of the system, which is the only information required about the nonlinear system. Stability analysis has been conducted based on the Lyapunov functions and revealed the convergence of the improved nonlinear extended state observer and the asymptotic stability of the closed-loop system. Verification of the outcomes has been achieved by applying the proposed active input–output feedback linearization technique on the single-link flexible joint manipulator. The simulations results validated the effectiveness of the proposed active input–output feedback linearization tool based on improved active disturbance rejection control as compared to the conventional active disturbance rejection control–based active input–output feedback linearization and the traditional input–output feedback linearization techniques.

Highlights

There are numerous classes of nonlinear models, given the following one &x_ = fðxÞ + gðxÞu y = hðxÞ ð1Þ where x = (x1x2 . . . x2)T 2 Rn is the state vector, u 2 R is the control input, and y 2 R is the system output.The functions f, g, and h are sufficiently smooth in a domain D & Rn
This paper proposes a new robust method for Input–output feedback linearization (IOFL) in an active manner, namely, active input–output feedback linearization (AIOFL), in which the nonlinearities, model uncertainties, and external disturbance are excellently estimated and canceled using improved active disturbance rejection control (IADRC) paradigm, such that the resulting nonlinear system is reduced into a chain of integrators up to the relative degree of the system
The contribution of this paper lies in the following: 1. Proposing an AIOFL technique for a single-link flexible joint manipulator (SLFJM) which is a highly nonlinear uncertain system based on the IADRC with an improved nonlinear extended state observer (INLESO) of a saturation-like behavior developed in our previous work.29 where Lfh(x) = (∂h=∂x)f(x) is called the Lie derivative of h(x) with respect to f

Summary

Introduction

This paper proposes a new robust method for IOFL in an active manner, namely, active input–output feedback linearization (AIOFL), in which the nonlinearities, model uncertainties, and external disturbance are excellently estimated and canceled using improved active disturbance rejection control (IADRC) paradigm, such that the resulting nonlinear system is reduced into a chain of integrators up to the relative degree of the system. The advantage of this technique is that it transforms any nonlinear uncertain system with exogenous disturbances and uncertainties into a pure chain of integrators up to the relative degree of the system.

Background and problem statement

Findings

Conclusion