Complex hysteresis nonlinearities

Krasnosel’skii, M. A.; Pokrovskiǐ, Aleksei V.

doi:10.1007/978-3-642-61302-9_7

Cited by 5 publications

(7 citation statements)

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“…3. Detailed description of this converter is given in [15]. The parameter ε can be considered as an uncertainty in the measurement of the value Bφ+ω.…”

Section: Non-ideal Relay In Feedbackmentioning

confidence: 99%

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State-feedback Control Principles for Inverted Pendulum with Hysteresis in Suspension

Abbas¹,

Kanishcheva²,

Семенов³

et al. 2016

J. Sib. Fed. Univ., Math. phys.

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In this paper we consider the mathematical model of the inverted pendulum with the hysteretic nonlinearity (in the form of a backlash) under state feedback control. The analytic results for the stability criteria as well as for the solution of the linearized equation are observed and analyzed. The theorems that determine the stabilization of the considered system are formulated and discussed. The question on the optimal control of the system under consideration is also discussed and the corresponding theorem is considered.

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“…3. Detailed description of this converter is given in [15]. The parameter ε can be considered as an uncertainty in the measurement of the value Bφ+ω.…”

Section: Non-ideal Relay In Feedbackmentioning

confidence: 99%

“…[14]. The mathematical models of such nonlinearities according to the classical patterns of Krasnosel'skii and Pokrovskii [15], reduce to operators that are treated as converters in an appropriate function spaces. The dynamics of such converters are described by the relation of "input-state" and "stateoutput".…”

Section: Introductionmentioning

confidence: 99%

State-feedback Control Principles for Inverted Pendulum with Hysteresis in Suspension

Abbas¹,

Kanishcheva²,

Семенов³

et al. 2016

J. Sib. Fed. Univ., Math. phys.

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“…To deal with such a control problem, modeling the hysteresis nonlinearity is the first step of controller design. Until now, there have been five kinds of models for hysteresis: Preisach model, 35 Ishlinskii hysteresis operator, 36 Krasnoskl’skii-Pokrovskii hysteron, 36 Duhem hysteresis, 37 and backlash-like hysteresis. 38 Thereinto, the backlash-like hysteresis has been most widely investigated because of its accurate representation and facilitation for controller design.…”

Section: Introductionmentioning

confidence: 99%

Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

Wang,

Wei,

Wang

2024

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this article, a fractional-order adaptive iterative learning control scheme is proposed for a class of parameterized fractional-order systems with unknown control gain and backlash-like hysteresis nonlinearity under disturbance. Based on the sufficient condition for the stability of linear fractional-order systems, a sliding mode surface of tracking errors is constructed to facilitate the controller design and stability analysis. A new boundary layer function is designed by using Mittag-Leffler function to relax the restriction of the identical initial condition of iterative learning control design. The fractional-order differential-type adaptive laws and difference-type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. To deal with the influence of backlash-like hysteresis nonlinearity reminder term and unknown bounded external disturbance, a robust control term is designed by employing the hyperbolic tangent function with a convergent series sequence which can guarantee the learning convergence along iteration axis. By constructing Lyapunov-like composite energy function, the stability analysis is presented to prove the convergence of the system output to a small neighborhood of the desired trajectory and the boundedness of all the closed-loop signals. Finally, a simulation example of second-order nonlinear fractional-order system is presented, which demonstrates the effectiveness of the proposed fractional-order adaptive iterative learning control scheme.

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“…In the first class of solutions, the hysteresis is mathematically modeled and the inverse model is applied as compensation; consequently, a linear input-output relation is recovered, and existing linear control techniques can be applied. In particular, the Prandtl-Ishlinskii (P-I) model [9], Preisach model [10], Krasnosel'skii-Pokrovkii (K-P) model [11], Duhem model [12], and Bouc-Wen model [13] have been widely adopted in the literature. However, model-based compensation is impeded by a trade-off between model accuracy and control performance; higher order models provide accuracy at the cost of lower sampling speed and control performance at high frequencies.…”

Section: Introductionmentioning

confidence: 99%

Model-Free Output-Feedback Sliding-Mode Control Design for Piezo-Actuated Stage

2023

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Hysteresis in a piezoelectric actuator must be compensated for, and this compensation constitutes the main challenge in the high-precision motion control of piezo-actuated stages. This paper presents an output-feedback sliding-mode control (SMC) scheme to suppress unknown nonlinearity; in this scheme, hysteresis behavior is considered an external disturbance, and complex hysteresis models are thus not required. The scheme functions in the absence of transfer function of system state information, and a robust loop-transfer recovery observer is employed as a noise-free differentiator to estimate the required signal derivatives when the relevant system is in a noisy environment.

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Complex hysteresis nonlinearities

Cited by 5 publications

References 0 publications

State-feedback Control Principles for Inverted Pendulum with Hysteresis in Suspension

State-feedback Control Principles for Inverted Pendulum with Hysteresis in Suspension

Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

Model-Free Output-Feedback Sliding-Mode Control Design for Piezo-Actuated Stage

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