Limit Cycle Synchronization of Nonlinear Systems with Matched and Unmatched Uncertainties Based on Finite-Time Disturbance Observer

Hakimi, Ali Reza; Binazadeh, Tahereh

doi:10.1007/s00034-019-01134-w

Cited by 12 publications

(9 citation statements)

References 31 publications

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“…This method was developed by Hakimi and Binazadeh to design a robust limit cycle controller in the presence of both matched and unmatched uncertainties in nonlinear SISO systems. Similar studies has been done by Gómez‐Estern et al, Aguilar‐Ibañez et al, and Hakimi and Binazadeh . For discrete‐time systems, Kai proposed a numerical algorithm for creating limit cycle‐like behaviors in a class of second‐order discrete‐time systems.…”

Section: Introductionmentioning

confidence: 56%

“…In this section, the main contributions of this paper are presented. For this purpose, the general form of Equations (19) is studied in two different structures.…”

Section: Stable Limit Cycle Shaping In the Mimo Nonlinear Systemsmentioning

confidence: 99%

“…where (i) = ( (i) 1 , … , (i) ) and in comparison with (19), f i,j,l = 0. As seen, each block, in this case, is a SISO system in the strict feedback form with the control input u i and output i = (i) 1 for i = 1,2, … ,m. The nonlinear functions (i) n i (.)…”

Section: The First Structurementioning

confidence: 99%

“…In this regard, it is assumed that the functions f i,j,l ( ) are nonzero for some i, j and l. This adds further complexity to the design problem. Hence, the nonlinear MIMO system (19) can be described in general as follows:…”

Section: The Second Structurementioning

confidence: 99%

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Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

Hakimi

Binazadeh

2019

Intl J Robust & Nonlinear

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Summary This paper studies on generating periodic behaviors through shaping stable limit cycles in multiple‐input‐multiple‐output nonlinear systems. For this purpose, first, limit cycles are shaped with respect to the desired sustained oscillations of the system's outputs. Then, the Lyapunov analyses, which are appropriate for stability analysis of invariant sets, are employed to design the control law and conclude the asymptotic convergence toward the predefined limit cycles. The problem is studied in two cases. In the first case, some assumptions in the mathematical model are assumed that leads to simplification in the design procedure. In the second case, the design procedure is discussed in more general cases. Finally, the validity and performance of the proposed method for shaping limit cycles with different geometric shapes are illustrated by computer simulations for practical and numerical examples.

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Section: Introductionmentioning

confidence: 56%

“…In this section, the main contributions of this paper are presented. For this purpose, the general form of Equations (19) is studied in two different structures.…”

Section: Stable Limit Cycle Shaping In the Mimo Nonlinear Systemsmentioning

confidence: 99%

Section: The First Structurementioning

confidence: 99%

Section: The Second Structurementioning

confidence: 99%

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Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

Hakimi

Binazadeh

2019

Intl J Robust & Nonlinear

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“…8 Then, the Lyapunov function is shaped according to the desired limit cycle equation and limit cycle controller is designed for shaping this stable limit cycle in the phase trajectories of the controlled system. Backstepping control, 16 synchronization approach, 17 feedback linearization, 18 and state feedback control 5,19 are some of the designing methods employed by the second approach to generate stable oscillations in dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Robust Stable Limit Cycle Generation in Multi-Input Mechanical Systems

Binazadeh

Karimi

2021

Robotica

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SUMMARY This paper proposes a robust controller for the generation of stable limit cycles in multi-input mechanical systems subjected to model uncertainties. The proposed idea is based on Port-Controlled Hamiltonian (PCH) model and energy-based control by considering the Hamiltonian function as the Lyapunov function. For this purpose, first, a nominal controller is designed by shaping the energy function of the system according to the structure of the desired limit cycle. Then, an additional robustifying control term is designed based on the integral sliding mode method with the selection of an appropriate sliding surface. Finally, computer simulations for two practical case studies are provided to confirm the effectiveness of the proposed controller in the generation of stable limit cycles in the presence of uncertainties.

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