A backstepping procedure for a class of underactuated system with tree structure

Choukchou-Braham, Amal; Cherki, Brahim; Djemaï, Mohamed

doi:10.1109/ccca.2011.6031527

Cited by 9 publications

(8 citation statements)

References 26 publications

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“…In the literature on the continuous-time control, in order to facilitate backstepping control design, coordinate transformations are utilized. Being inspired by the study (Choukchou-Braham et al, 2011) in continuous-time literature, a discrete-time coordinate transformation can be given as…”

Section: Controller Designmentioning

confidence: 99%

“…The Inverted-Pendulum is a nonlinear mechanical system which has been studied by many researchers since the system can be used to investigate the performances of different control approaches considered for the various systems that depict similar dynamical properties but have higher orders such as flexible joint robots, mobile robots and underwater vehicles. In order to control nonlinear mechanical systems, there are several control strategies in the literature such as passivity based control (Ortega and Garcia-Canseco, 2004; Romero et al, 2017), the backstepping control (Choukchou-Braham et al, 2011; Man and Lin, 2010; Rudra et al, 2014), adaptive control (Huang et al, 2015), sliding mode control (Wang et al, 2004), adaptive fuzzy sliding mode control (Kung et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

“…The Inverted-Pendulum system is a nonlinear mechanical system, as mentioned before, which is normally not in strict-feedback form that backstepping design can be applied on it. In continuous-time domain some coordinate transformations are used to facilitate backstepping design for underactuated nonlinear mechanical systems (Choukchou-Braham et al, 2011). To the best of the authors’ knowledge, there is not any study on discrete-time backstepping control for nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Adıgüzel

Yalçın

2019

Transactions of the Institute of Measurement and Control

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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.

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Section: Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

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2019

Transactions of the Institute of Measurement and Control

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“…Underactuated systems have been studied for more than two decades now. Energy and passivity based control [107][108][109], energy shaping [110], and Controlled Lagrangians and Hamiltonians [111][112][113][114][115][116] are just a few methods among others proposed [117][118][119][120].…”

Section: Underactuated Systemsmentioning

confidence: 99%

Adaptive Systems: History, Techniques, Problems, and Perspectives

Black

Haghi²,

Ariyur

2014

Systems

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We survey some of the rich history of control over the past century with a focus on the major milestones in adaptive systems. We review classic methods and examples in adaptive linear systems for both control and observation/identification. The focus is on linear plants to facilitate understanding, but we also provide the tools necessary for many classes of nonlinear systems. We discuss practical issues encountered in making these systems stable and robust with respect to additive and multiplicative uncertainties. We discuss various perspectives on adaptive systems and their role in various fields. Finally, we present some of the ongoing research and expose problems in the field of adaptive control.

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“…In the recent two decades, a lot of advanced control approaches are considered for stabilization problem of underactuated systems such as the backstepping control, 5–9 passivity based control, 10,11 adaptive control, 12–14 sliding-mode control, 15,16 and adaptive fuzzy sliding-mode control. 17 The backstepping control method among the above-mentioned nonlinear control methods is the one that comes into prominence since it is possible to bring the mathematical model of many underactuated mechanical systems into the strict-feedback form making use of several mathematical techniques; for example, partial feedback linearization 18 and state transformation.…”

Section: Introductionmentioning

confidence: 99%

Backstepping control for a class of underactuated nonlinear mechanical systems with a novel coordinate transformation in the discrete-time setting

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2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this technical note, a combined discrete-time controller, consisting of a partial feedback linearization controller and a backstepping controller, is proposed to manage the stabilization for a class of underactuated nonlinear mechanical systems. The traditional backstepping control method is impracticable to directly apply it to underactuated systems since they are generally not in the lower triangular form. First, a feedback controller that partially linearizes the underactuated mechanical systems is derived to facilitate the backstepping controller design. In the design, discrete-time system dynamics obtained utilizing the Euler approximation are considered. Afterward, a novel coordinate transformation is introduced for a class of underactuated systems that transform the mathematical model of the partially linearized underactuated mechanical systems into the strict-feedback form. After these steps, the conventional backstepping approach is structured in discrete-time setting. The stability of the closed-loop system dynamics with the proposed combined discrete-time controller is shown utilizing Lyapunov theory. Several computer-based simulations are executed to depict the performance and the applicability of the proposed method on the Cart–Pole system and the Inertia Wheel Pendulum. Moreover, the effectiveness of the proposed nonlinear controller is verified by numerical simulation results in comparison with a discrete-time chattering-free sliding-mode controller.

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A backstepping procedure for a class of underactuated system with tree structure

Cited by 9 publications

References 26 publications

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

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

Adaptive Systems: History, Techniques, Problems, and Perspectives

Backstepping control for a class of underactuated nonlinear mechanical systems with a novel coordinate transformation in the discrete-time setting

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