Design of LMI‐based sliding mode controller with an exponential policy for a class of underactuated systems

Mobayen, Saleh

doi:10.1002/cplx.21636

Cited by 101 publications

(81 citation statements)

References 50 publications

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“…The stabilization and tracking control of nonlinear and time-varying systems have important applications in electronics, mechanics and robotic systems [2][3][4][5][6]. Conventional feedback control methods do not obtain robustness and high performance when facing with the nonlinearities, uncertainties and external disturbances [7][8][9][10].…”

Section: Background and Motivationsmentioning

confidence: 99%

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

Mobayen

2015

Nonlinear Dyn

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100

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In this paper, an adaptive fast terminal sliding mode control technique combined with a global sliding mode control scheme is investigated for the tracking problem of uncertain nonlinear third-order systems. The proposed robust tracking controller is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Under the uncertainty and nonlinearity effects, the reaching phase is removed and the chattering phenomenon is eliminated. This scheme guarantees robustness against nonlinear functions, parameter uncertainties and external disturbances. The derivative of the state variable is replaced by a delay term in the form of an Euler approximation of the derivative function. Furthermore, the knowledge of upper bounds of the system uncertainties is not required, which is more flexible in the real implementations. Simulation results are presented to show the effectiveness of the suggested method.

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Section: Background and Motivationsmentioning

confidence: 99%

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

Mobayen

2015

Nonlinear Dyn

Self Cite

100

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“…They estimated the friction parameters in order to calculate the friction compensation term. Some other works were realized on the control of inverted pendulums [17,[37][38][39][40].…”

Section: Literature Reviewmentioning

confidence: 99%

“…Using quadratic representation of each term in (38) and applying the S-procedure (Lemma 4), (38a) and (38b) are equivalent to the existence of positive scalar variables µ 1 , µ 2 , µ 3 , η 1 , η 2 and η 3 , and a positive matrix M such that the two matrix inequalities in (29) hold. This ends the proof of Theorem 1.…”

Section: Asymptotic Stabilization Of the Tracking Errormentioning

confidence: 99%

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

et al. 2017

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This paper deals with the tracking approach of a self-generated stable limit cycle for an underactuated mechanical system: The Inertia Wheel Inverted Pendulum (IWIP). Such system is subject to unilateral constraints limiting its swing motion. It is known that an Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) can be employed to control such pendulum to its upright position. In this work, we briefly show first that the IWIP can generate a stable period-1 limit cycle through a Hopf bifurcation by varying some gain parameter of the IDA-PBC. Thus, such self-generated limit cycle is used as a reference trajectory, which is chosen to be tracked by the IWIP. To achieve the tracking problem, a supplementary control input is added. Such tracking problem is reformulated as an asymptotic stabilization of the tracking error. Our fundamental approach hinges mainly on the use of the S-procedure to introduce the unilateral constraints, and the Schur complement and the matrix inversion lemma to transform Bilinear Matrix Inequalities (BMI) into Linear Matrix Inequalities (LMI). Several simulations have been presented to corroborate the mathematical results and to show the efficiency of the proposed tracking scheme of the self-generated stable limit cycle of the controlled IWIP, even if it is subject to external disturbances, or in the presence of uncertainties in the friction parameters.

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“…Similarly, since the inequation (26) holds and V 30 to be the initial value of V 3 (at the instant T o1 + T o2 when sliding motion is attained on e 1 = e 1 = 0 and e 2 =̇e 2 = 0) and T o3 to be the time taken for V 3 to converge to zero. Integrating both sides, yields…”

Section: Stability Analysismentioning

confidence: 99%

FTESO‐Based Finite Time Control for Underactuated System Within a Bounded Input

Wang¹,

Zhou²,

Chen³

et al. 2017

Asian Journal of Control

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Finite time control problem is investigated for a class of underactuated systems with uncertainties and external disturbances. For the sake of expanding control region furthest within a bound input, finite time extended state observer (FTESO) and a novel adaptive terminal sliding mode (ATSM) controller are applied to improve the stability performance of system. Compared to the general extended state observer (ESO), FTESO makes use of fractional powers to reduce the estimation errors to zero in finite time. The coordinate transformation is made for more degrees of design freedom. Rigorous analysis of finite time convergence results has been performed through Lyapunov theory and sufficient conditions are provided for the observer/controller-design. Finally, simulation results on the Rotating Inverted Pendulum are given to demonstrate the effectiveness of the proposed controller and observer.

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Design of LMI‐based sliding mode controller with an exponential policy for a class of underactuated systems

Cited by 101 publications

References 50 publications

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC

FTESO‐Based Finite Time Control for Underactuated System Within a Bounded Input

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