Smooth Second Order Sliding Mode Control of a Class of Underactuated Mechanical Systems

Shah, Ibrahim; Rehman, Fazal ur

doi:10.1109/access.2018.2806568

Cited by 31 publications

(27 citation statements)

References 47 publications

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“…The selected coefficients are used to compute the solution, P, of the Algebraic Riccati Equation (ARE) shown in (10).…”

Section: Primary State-feedback Controllermentioning

confidence: 99%

“…The fuzzy controllers, despite their flexibility, require elaborate qualitative logical rules and offline tuning of a multitude of parameters to deliver robust control effort [9]. The sliding mode controllers, despite their robustness, unavoidably inject chattering in the system's response [10], [11]. The ubiquitous Linear-Quadratic-Regulator (LQR) is a state-feedback controller that yields stable and optimal control decisions by minimizing a quadratic performance criterion that captures the state and control-input variations [12].…”

Section: Introductionmentioning

confidence: 99%

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Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

Saleem

Mahmood-ul-Hasan

2020

IEEE Access

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This paper presents the development of an indirect adaptive state-feedback controller to improve the disturbance-rejection capability of under-actuated multivariable systems. The ubiquitous Linear-Quadratic-Regulator (LQR) is employed as the baseline state-feedback controller. Despite its optimality, the LQR lacks robustness against parametric uncertainties. Hence, the main contribution of this paper is to devise and retrofit the LQR with a stable online gain-adjustment mechanism that dynamically adjusts the state weighting-coefficients of LQR's quadratic cost-function via state-error dependent nonlinear-scaling functions. An original self-mutating phase-based adaptive modulation scheme is systematically formulated in this paper to self-adjust the state weighting-coefficients. The scheme employs pre-calibrated secanthyperbolic-functions whose waveforms are dynamically reconfigured online based on the variations in magnitude and polarity of state-error variables. This augmentation dynamically alters the solution of the Riccati-Equation which modifies the state-feedback gains online. The proposed adaptation flexibly manipulates the system's control effort as the response converges to or diverges from the reference. The efficacy of proposed adaptive controller is validated by conducting hardware-in-the-loop experiments to vertically stabilize the QNET 2.0 Rotary Pendulum system. As compared to the standard LQR, the proposed adaptive controller renders rapid transits in system's response with improved damping against oscillations, while maintaining its asymptotic-stability, under bounded exogenous disturbances. INDEX TERMS Hyperbolic functions, linear quadratic regulator, cost-function, rotary inverted pendulum, self-tuning control, state weighting-coefficients.

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“…The selected coefficients are used to compute the solution, P, of the Algebraic Riccati Equation (ARE) shown in (10).…”

Section: Primary State-feedback Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

Saleem

Mahmood-ul-Hasan

2020

IEEE Access

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“…To design SOSM, a number of algorithms have been proposed in recent years in which twisting, super twisting, sub-optimal, and drift are commonly used. Due to not requiring time derivatives of sliding variables and having insensitivity to sampling time, Super Twisting (STW) algorithm has been gained much attention from the research community, and this algorithm is used for the systems having relative degree one [11], [16][17][18]. The algorithm guarantees that system trajectories twist around the origin within finite time.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Smooth Super-Twisting Sliding Mode Control of Nonlinear Systems With Unmatched Uncertainty

et al. 2020

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This article presents a novel strategy regarding the stabilization control problem for plants with unmatched uncertainties. The methodology is based on Adaptive Smooth Super Twisting Sliding Mode Control. At first, as an initial step, the plant with unmatched uncertainty is transformed into a plant with matched uncertainty. At the second step, the plant with matched uncertainty is decomposed into a unique framework containing the nominal part and some unknown terms (where these unknown terms are computed adaptively). The nominal system is stabilized by using Smooth Super Twisting Sliding Mode Control. The stabilizing controller for the plant with matched uncertainty is designed in a way; it contains some nominal control plus some compensator term. The stability of the said technique is presented impressively. The compensator controller and the adapted laws are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. The proposed method is tested on a fourthorder plant. The simulation results show the effectiveness and validity of the proposed controller. INDEX TERMS Sliding mode control, higher-order sliding mode control, adaptive smooth super-twisting algorithm, Lyapunov function, unmatched uncertainty.

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“…The capability to control complex nonlinear systems and the robustness to uncertainties and external disturbance are the two main reasons making SMC the first choice to control of nonlinear uncertain systems. Fast response, simple design, and order reduction are extra desirable features [21]. Although great efforts have made on the sliding mode control of IWP, the corresponding research still has a long way to go.…”

Section: Introductionmentioning

confidence: 99%

Sliding Mode Observe and Control for the Underactuated Inertia Wheel Pendulum System

Guo

Liu

2019

IEEE Access

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The inertia wheel pendulum (IWP) is a widely studied nonlinear benchmark underactuated system and its control problem is a challenging task for its underactuated nature. This paper considers the IWP stabilization problem with the classic sliding mode method. The nonlinear canonical model of the underactuated IWP is obtained through a collocated partial feedback linearization and two global changes of coordinates. In order to obtain the unmeasurable states of the newly derived model, two classic sliding mode observers are designed and it is ensured that the observing errors are convergent in finite time to meet the separation principle. In order to reduce the high frequency component of the observing output, the first-order filters are introduced from the view of practical applications. A simple sliding mode controller is proposed with the output of the first-order filters. It is proved that the proposed approach can guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system and the convergence speed can be improved by appropriately choosing design parameters. The simulation results demonstrate the effectiveness of the proposed approach. INDEX TERMS Underactuated mechanical systems, inertia wheel pendulum (IWP), sliding mode observe, sliding mode control.

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Smooth Second Order Sliding Mode Control of a Class of Underactuated Mechanical Systems

Cited by 31 publications

References 47 publications

Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

Adaptive Smooth Super-Twisting Sliding Mode Control of Nonlinear Systems With Unmatched Uncertainty

Sliding Mode Observe and Control for the Underactuated Inertia Wheel Pendulum System

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