Nonlinear stabilizing control of a rotary double inverted pendulum: a modified backstepping approach

Jabbar, Abdul; Malik, Fahad Mumtaz; Sheikh, Shahzad Amin

doi:10.1177/0142331216645174

Cited by 16 publications

(8 citation statements)

References 17 publications

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“…The proposed method stabilize the RDIP system regardless of certain parametric uncertainties and input disturbances. Back stepping control for the under-actuated RDIP system is described by Jabbar et al (2017), where in the first stage, the controller is implemented for individual active and passive links, and in the second stage, a Lyapunov-based compensator is designed to cater uncertain terms for individual link. The design and implementation of fractional order controller (FOC) investigated by Mehedi et al (2019) for controlling RDIP system is a promising research domain.…”

Section: Introductionmentioning

confidence: 99%

Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

Mehedi

Ansari

Al‐Saggaf

2020

Journal of Vibration and Control

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The aim of this article was to determine control strategy for balance control of rotary double inverted pendulum system, which is highly nonlinear and unstable under-actuated system. The complexities involved in rotary double inverted pendulum dynamics make this system a useful engineering test bed to test and verify newly designed controllers. In this article, a constraint-based control approach titled robust generalized dynamic inversion is designed and implemented for robust stabilization of rotary double inverted pendulum system. The robust generalized dynamic inversion control is designed in two stages; in the first stage, constraint differential equations of the controlled state variables are prescribed, which encompasses the control objectives. To enforce the constraint dynamics, the equivalent control is realized by means of Moore–Penrose generalized inversion. To enhance robustness, the switching (discontinuous) control is introduced in second stage, whose design principle is based on classical sliding mode control theory. Finally, the controllers obtained in two stages are augmented to form the resultant robust generalized dynamic inversion control law. The proposed controller ensures robustness along with improved time domain performance regardless of system nonlinearities, uncertainties, and unwanted disturbances. The stability analysis is presented for guaranteeing semi-global asymptotically stable closed loop performance via Lyapunov stability criteria. Numerical simulation and experimental investigations are carried out along with comparative analysis, to demonstrate the effectiveness of robust generalized dynamic inversion control algorithm over other conventional control methods.

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Section: Introductionmentioning

confidence: 99%

Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

Mehedi

Ansari

Al‐Saggaf

2020

Journal of Vibration and Control

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“…Underactuated systems have less available control inputs than degrees of freedom and this characteristic brings a great challenge for the controller development and stability analysis. Therefore, the control issues of different kinds of underactuated systems have attracted much attention in academia and many meaningful results have been reported in the literature (Dehghani and Abedi, 2018; Huang et al, 2015; Jabbar et al, 2017; Li and Huang, 2020; Li et al, 2017; Liang et al, 2019a, b; Liu, 2018; Sun et al, 2017, 2018; Tabataba’i-Nasab et al, 2019; Wu and He, 2017; Wu et al, 2020; Xu et al, 2014; Zhang et al, 2018). The translational oscillation with a rotational actuator (TORA) is a kind of underactuated systems.…”

Section: Introductionmentioning

confidence: 99%

Energy-based output feedback control of the underactuated 2DTORA system with saturated inputs

et al. 2020

Transactions of the Institute of Measurement and Control

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In this paper, we consider the control issues of the two-dimensional translational oscillator with rotational actuator (2DTORA) system, which has two translational carts and one rotational rotor. An output feedback controller for the 2DTORA system is proposed, which can prevent the unwinding behaviour. In addition, the velocity signal unavailability and actuator saturation are taken into account, simultaneously. In particular, the dynamics of the 2DTORA system are given first. On the basis of the passivity and control objectives of the 2DTORA system, an elaborate Lyapunov function is constructed. Then, based on the introduced Lyapunov function, a novel output feedback control method is proposed straightforwardly for the 2DTORA system. Lyapunov theory and LaSalle’s invariance principle are utilized to analyse the stability of the closed-loop system and the convergence of the states. Finally, simulation results are provided to illustrate the excellent control performance of the proposed controller in comparison with the existing method.

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“…On the other hand, the use of a linearized system model may cause instability and poor closed-loop system behavior. Nonlinear control techniques such as feedback linearization [9] and back stepping [10], output feedback stabilization [11], delayed feedback [12], H infinity [13], and sliding mode [6,14,15] techniques have been developed for the control of IP systems. Although the nonlinear control techniques have shown desirable performance in tracking and stabilization problems of nonlinear systems, they are the most difficult and complicated control techniques in implementation.…”

Section: Introductionmentioning

confidence: 99%

Performance comparison of optimization algorithms in LQR controller design fora nonlinear system

Önen¹,

Çakan²,

İlhan³

2019

Turk J Elec Eng & Comp Sci

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The development and improvement of control techniques has attracted many researchers for many years.Especially in the controller design of complex and nonlinear systems, various methods have been proposed to determine the ideal control parameters. One of the most common and effective of these methods is determining the controller parameters with optimization algorithms.In this study, LQR controller design was implemented for position control of the double inverted pendulum system on a cart. First of all, the equations of motion of the inverted pendulum system were obtained by using Lagrange formulation. These equations were linearized by Taylor series expansion around the equilibrium position to obtain the state-space model of the system. The LQR controller parameters required to control the inverted pendulum system were determined by using a trial and error method. The determined parameters were optimized by using five different configurations of three different optimization algorithms (GA, PSO, and ABC). The LQR controller parameters obtained as a result of the optimization study with five different configurations of each algorithm were applied to the system and the obtained results were compared with each other. In addition, the configurations that yielded the best control results for each algorithm were compared with each other and the control results were evaluated in terms of response speed and response smoothness.

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Nonlinear stabilizing control of a rotary double inverted pendulum: a modified backstepping approach

Cited by 16 publications

References 17 publications

Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

Energy-based output feedback control of the underactuated 2DTORA system with saturated inputs

Performance comparison of optimization algorithms in LQR controller design fora nonlinear system

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