Discrete-time backstepping control with nonlinear adaptive disturbance attenuation for the inverted-pendulum system


Adiguezel F., Yalçın Y.

TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, vol.43, no.5, pp.1068-1076, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1177/0142331219867775
  • Journal Name: TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, Metadex, DIALNET, Civil Engineering Abstracts
  • Page Numbers: pp.1068-1076
  • Keywords: Inverted-Pendulum, discrete-time backstepping control, disturbance estimation, immersion and invariance, partial feedback linearization, SLIDING-MODE CONTROLLER, STATE-FEEDBACK, IMMERSION, INVARIANCE, STABILIZATION, DESIGN
  • Istanbul Technical University Affiliated: Yes

Abstract

A discrete-time backstepping controller with an active disturbance attenuation property for the Inverted-Pendulum system is constructed in this paper. The main purpose of this study is to show that Immersion and Invariance (I & I) approach can be used to design a nonlinear observer for disturbance estimation and demonstrate its effectiveness considering a nonlinear system with an unstable equilibrium point, namely Inverted-Pendulum system, by utilizing the estimated values in backstepping control design. All designs are directly performed in discrete-time domain to obtain directly implementable observer and controller in discrete processors with superior performance compared to emulators. The Inverted-Pendulum system is not in strict feedback form therefore backstepping procedure cannot be directly applied. In order to enable backstepping construction, firstly a partial feedback linearization is performed and afterwards a novel discrete-time coordinate transformation is proposed. Prior to the construction of partial feedback linearizing and backstepping controller, a nonlinear disturbance estimator design is proposed with Immersion and Invariance approach. The estimated disturbance values used in the partial feedback linearization and construction of the backstepping controller. The global asymptotic stability of the estimator and local asymptotic stability of overall closed loop system are proved in the sense of Lyapunov. Performance of proposed direct discrete-time backstepping control with discrete I & I observer is compared with a backstepping sliding mode controller with another nonlinear disturbance observer (NDO) by simulations.