A Reset‐Time Dependent Approach for Stability Analysis of Nonlinear Reset Control Systems

Ghaffari, Valiollah; Karimaghaee, Paknosh; Khayatian, Alireza

doi:10.1002/asjc.1274

Cited by 4 publications

(3 citation statements)

References 30 publications

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“…By giving a specific value of p r , the parameters of K P , K I , and 𝛼 can be solved by the equations of ( 35), (36), and (37). Sweeping all the values of p r ∈ [0, 1], we can get all the parameter sets that satisfy the constraints of ( 22), (23), and (24) for all different values of p r .…”

Section: The Optimal Robust Pi 𝛼 + CI 𝛼 Controller Design Methodsmentioning

confidence: 99%

“…The H

{}_{\beta }

‐condition developed based on Lyapunov stability can be used to prove the stability of the reset control system [1, 21,22]. The stability conditions dependent on the reset time were addressed in [23] for nonlinear reset control systems based on the Lyapunov stability concept. The sufficient stability conditions were given based on the frequency responses in [16].…”

Section: Introductionmentioning

confidence: 99%

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An optimal robust design method for fractional‐order reset controller

Wang

Sun

et al. 2022

Asian Journal of Control

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In this paper, a novel design method for the reset controller structure (i.e., fractional‐order proportional and integral plus Clegg integrator (PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$)), is proposed for a second‐order plus time delay plant. To this end, the designer can get an optimal fractional reset controller that gives the control system more phase margin over the base linear PI controller and robust to loop gain variation. The describing function method is used to investigate the capability of phase lead and the frequency domain properties of PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$. The gain crossover frequency and phase margin specifications ensure the stability of the control system, and the flat phase constraint makes the control system robust to loop gain variations. Meanwhile, the integral of time and absolute error (ITAE) value is applied to achieve the optimal dynamic performance as the cost function. PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$ is compared with its integer‐order counterpart (i.e., proportional and integral plus Clegg integrator (PI + CI) controller) and their base controllers (i.e., integer‐order PI and fractional‐order PI controllers) in terms of the step response and robustness to loop gain variations. The simulation results illustrate that the PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$ control system obtains lower overshoot and oscillation and better robustness to loop gain variations than others. The experiments are performed on the speed control of an air bearing stage. Experimental results show that the designed PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$ control system behaves better than others. The proposed PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$ design method can be applied to other general control plants easily.

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Section: The Optimal Robust Pi 𝛼 + CI 𝛼 Controller Design Methodsmentioning

confidence: 99%

“…The H

{}_{\beta }

Section: Introductionmentioning

confidence: 99%

An optimal robust design method for fractional‐order reset controller

Wang

Sun

et al. 2022

Asian Journal of Control

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“…where ∶ = ( 2 + 1). Consequently, by Lyapunov stability theory [27][28][29][30], the point (t) = 0 is a globally asymptotically stable equilibrium point of the NNN-L (7). By substituting (t) = || (t)|| 2 F ∕2 into (10), we havė(t) ≤ −2 (t), (t) ≤ (0) exp(−2 t) ( (0) = || (0)|| 2 F ∕2), which yields:…”

Section: Theoretical Analysismentioning

confidence: 99%

Improved recurrent neural networks for online solution of Moore‐Penrose inverse applied to redundant manipulator kinematic control

Tan

Chen

et al. 2018

Asian Journal of Control

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In this paper, two novel neural networks (NNNs), namely NNN-L and NNN-R neural models, are proposed to online left and right Moore-Penrose inversion. As compared to GNN (gradient neural network) and the recently proposed ZNN (Zhang neural network) for the left or right Moore-Penrose inverse solving, our models are theoretically proven to possess superior global convergence performance. More importantly, the proposed NNN-R model is successfully applied to path-tracking control of a three-link planar robot manipulator. Illustrative examples well validate the theoretical analyses as well as demonstrate the feasibility of the proposed models, which are adopted and verified their effectiveness in kinematic control of a redundant manipulator, for real-time Moore-Penrose inverse solving.

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