Disturbance Observer Design for Nonlinear Systems Represented by Input–Output Models

Shihong Ding,Wen-Hua Chen,Keqi Mei,David J Murray-Smith

doi:10.1109/tie.2019.2898585

Abstract

A new approach to the design of nonlinear disturbance observers (DOBs) for a class of nonlinear systems described by input–output differential equations is presented in this paper. In contrast with established forms of nonlinear DOBs, the most important feature of this new type of DOB is that only measurement of the output variable is required, rather than the state variables. An inverse simulation model is first constructed based on knowledge of the structure and parameters of a conventional model of the system. The disturbance can then be estimated by comparing the output of the inverse model and the input of the original nonlinear system. Mathematical analysis demonstrates the convergence of this new form of nonlinear DOB. The approach has been applied to disturbance estimation for a linear system and a new form of linear DOB has been developed. The differences between the proposed linear DOB and the conventional form of frequency-domain DOB are discussed through a numerical example. Finally, the nonlinear DOB design method is illustrated through an application involving a simulation of a jacketed continuous stirred tank reactor system.

Highlights

Dealing with discrepancies between properties of the real plant and its mathematical description has become one of the main problems of modern control theory, and many nonlinear control techniques have been developed to reduce the adverse effects of external disturbances, unmodeled dynamics and parameter uncertainties
The systems considered in [25], [26] are characterized by some special structures and this restricts the application of this disturbance observer (DOB) design method. Motivated by these important observations, this paper aims to develop a nonlinear DOB design method that uses only the output of the nonlinear system
In the context of DOB design those results imply that the disturbance may be estimated by subtracting the control input in the DOB block diagram (Fig. 1) from the reconstructed input obtained from the inverse simulation model

Summary

INTRODUCTION

Dealing with discrepancies between properties of the real plant and its mathematical description has become one of the main problems of modern control theory, and many nonlinear control techniques have been developed to reduce the adverse effects of external disturbances, unmodeled dynamics and parameter uncertainties. In more recent years the method was developed further and applied to more general problems of inverse modelling and simulation, as described in [30], [31] and [32], [33] This approach has been adopted for the application considered in this paper, leading to development of a new form of nonlinear DOB which can be constructed for a class of nonlinear systems represented by input-output differential equations. In the context of DOB design those results imply that the disturbance may be estimated by subtracting the control input in the DOB block diagram (Fig. 1) from the reconstructed input obtained from the inverse simulation model This offers the possibility of extending the inverse simulation approach based on feedback to provide a new form of nonlinear DOB for system described by nonlinear input-output ordinary differential equations. The second contribution is that the basic idea of developing the proposed nonlinear DOB is to construct the inverse of the original system, which is analogous to the conventional frequency-domain DOB

PROBLEM FORMULATION

THE NEW DOB DESIGN FOR NONLINEAR SYSTEMS

PERFORMANCE ANALYSIS

NONLINEAR DOB DESIGN EXAMPLE

Findings

CONCLUSIONS