Inverse Compensation of Hysteresis Using Krasnoselskii-Pokrovskii Model

Li, Zhi; Shan, Jinjun; Gabbert, Ulrich

doi:10.1109/tmech.2018.2805761

Cited by 113 publications

(49 citation statements)

References 34 publications

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“…A number of nonlinear models to represent hysteresis nonlinearity of piezoelectric actuator are investigated in the literature. Some of these models are differential based models, like Duhem model [10], Bouc-Wen model [11], Dahl model [12], and some models are operator based models, like Prandtl-Ishlinskii model [13], Preisach model [14], Maxwell model [15] and Krasnosel'skii-Pokrovskii model [16] etc. To compensate the hysteresis nonlinearity, two different control strategies are generally adopted in the literature.…”

Section: Introductionmentioning

confidence: 99%

Robust μ-Synthesis With Dahl Model Based Feedforward Compensator Design for Piezo-Actuated Micropositioning Stage

Ahmad

Ali

2020

IEEE Access

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In this paper, a combined feedback-feedforward control design scheme is presented to enhance the tracking performance of a piezo-actuated micropositioning stage by compensating the nonlinear hysteretic behavior of the piezoelectric actuator and model uncertainties of the system. Detailed investigation of the presented control scheme is performed not only in simulation by analyzing the robust stability and robust performance but also in real-time with motion trajectories of multiple frequencies. To design the presented control scheme, first of all, the dynamic model of the system is identified from the real-time experimental data by using the recursive least squares parameter adaptation algorithm. Then, Dahl hysteresis model is considered to represent the nonlinear hysteretic behavior of the piezoelectric actuator. To deal with this hysteresis nonlinearity, Dahl feedforward compensator is designed without involving inverse model calculations to avoid any computational complexity. This feedforward compensator is then combined with µ-synthesis robust feedback controller which is designed in the presence of model uncertainties of the system. The presented control scheme ensures the boundedness of the closed-loop signals and the desired tracking performance of the considered micropositioning stage. Finally, experimental tests are conducted with motion trajectories of multiple frequencies for the validation of the control scheme. An average improvement of 95% in compensating the hysteresis nonlinearity and 80% in reducing the tracking error is achieved which demonstrates the efficacy of the presented control scheme. INDEX TERMS Dahl feedforward compensator, hysteresis nonlinearity, micropositioning, model uncertainties, piezoelectric actuator, µ-synthesis robust feedback controller.

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Section: Introductionmentioning

confidence: 99%

Robust μ-Synthesis With Dahl Model Based Feedforward Compensator Design for Piezo-Actuated Micropositioning Stage

Ahmad

Ali

2020

IEEE Access

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“…Such models typically have a rate-independent hysteretic nature, which is their output variable does not depend on the first derivative of the input one [ 6 , 7 , 8 , 9 ]. Such as Duhem model [ 10 ], Bouc–Wen model [ 11 , 12 ], Prandtl–Ishlinskii (PI) model [ 13 , 14 ], Preisach model [ 15 ], and Krasnoselskii–Pokrovskii (KP) model [ 16 , 17 , 18 ]. The Duhem model and Bouc–Wen model are differential equation-based hysteresis models.…”

Section: Introductionmentioning

confidence: 99%

Rate Dependent Krasnoselskii-Pokrovskii Modeling and Inverse Compensation Control of Piezoceramic Actuated Stages

Nie

Liu

et al. 2020

Sensors

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The piezoceramic actuated stages have rate-dependent hysteresis nonlinearity, which is not simply related to the current and historical input, but also related to the frequency of the input signal, seriously affects its positioning accuracy. Consider the influence of frequency on hysteresis modeling, a rate-dependent hysteresis nonlinearity model that is based on Krasnoselskii–Pokrovskii (KP) operator is proposed in this paper. A hybrid optimization algorithm of improved particle swarm optimization and cuckoo search is employed in order to identify the density function of rate-dependent KP model, avoiding the blind search process caused by the high randomness of Levy’s flight in the cuckoo search algorithm, and improving the parameter identification performance. For the sake of eliminating the hysteresis characteristics, an inverse feed-forward compensation control that is based on recursive method is proposed without any additional conditions, and a feed-forward compensation controller is designed accordingly. The experimental results show that, under different frequency input signals, as compared with the classic KP model, the proposed rate-dependent KP model can accurately describe the rate-dependent hysteresis characteristics of the piezoceramic actuated stages, and the recursive inverse feed-forward compensation control method can effectively mitigate the hysteresis behaviors.

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“…The servo motor plays a role of actuator, its precision is mainly restrained by trigger deadzone and hysteresis, while the deadzone can be seen as external disturbance to eliminate. Many researchers have drawn a common conclusion that that hysteresis of motor will deteriorate its response characteristic and tracking precision [13,14]. Therefore, to promote the performance of GSP, hysteresis problem has to be solved.…”

Section: Introductionmentioning

confidence: 99%

Guaranteeing Prescribed Performance Control for Gyrostabilized Platform with Unknown Control Direction Preceded by Hysteresis

Wang

Lei

et al. 2019

International Journal of Aerospace Engineering

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This paper investigates the problem of precise and quick tracking for gyrostabilized platform (GSP) with unknown hysteresis, unknown control directions, and unknown compound disturbance. Firstly, the dynamic model of GSP is transformed into a strict feedback formulation by designed FD to facilitate the backstepping control system. Secondly, performance functions are constructed at each step of backstepping design to force tracking errors to fall within the prescribed boundaries. Besides, through ingenious transformation, radial basis function neural network (RBFNN) is applied to estimate the unknown control gains preceded by hysteresis. Hence, the problem of prescribed performance control with unknown compound disturbances, unknown hysteresis, and unknown control directions is creatively solved. Furthermore, the exploited controllers are accurate model independent, which guarantees satisfactory robustness of control laws against unknown uncertainties. Finally, the stability of the closed-loop control system is confirmed via Lyapunov stability theory, and numerical simulations are given for a GSP to validate the effectiveness of the proposed controller.

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Inverse Compensation of Hysteresis Using Krasnoselskii-Pokrovskii Model

Cited by 113 publications

References 34 publications

Robust μ-Synthesis With Dahl Model Based Feedforward Compensator Design for Piezo-Actuated Micropositioning Stage

Robust μ-Synthesis With Dahl Model Based Feedforward Compensator Design for Piezo-Actuated Micropositioning Stage

Rate Dependent Krasnoselskii-Pokrovskii Modeling and Inverse Compensation Control of Piezoceramic Actuated Stages

Guaranteeing Prescribed Performance Control for Gyrostabilized Platform with Unknown Control Direction Preceded by Hysteresis

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