Unknown Hysteresis Nonlinearities Research Articles

Neural Networks Based Learning Control for a Piezoelectric Nanopositioning System

In this article, approximation model-based control and neural networks-based adaptive control are investigated for obtaining the solution to the motion tracking of a piezoelectric nanopositioning system, respectively. In order to reduce the effect of unknown hysteresis nonlinearity, a disturbance observer is introduced to estimate it. By considering nominal parts of an unknown piezoelectric nanopositioning system, approximation model-based control is obtained. The unknown parts corresponding to nominal parts are dealt with by the online learning ability of neural networks, and an adaptive neural network control is proposed to improve control accuracy. Compared with existing works, a great benefit of the proposed control method is that the neural networks-based learning algorithm is developed to deal with uncertainty of a piezoelectric nanopositioning system in an online way such that the closed-loop system can be governed automatically, obtaining satisfactory motion tracking. With Lyapunov stability theory, it is proved that all error signals are semiglobally uniformly ultimately bounded. Experiment is carried out to verify the effectiveness of the proposed control.

Echo State Network for Extended State Observer and Sliding Mode Control of Vehicle Drive Motor with Unknown Hysteresis Nonlinearity

An echo state network (ESN) for extended state observer (ESO) and sliding mode control (SMC) of permanent magnet synchronous motor (PMSM) in an electric vehicle system is investigated in this paper. For the PMSM model, most researches neglect the hysteresis loss and other nonlinear factors, which reduces the accuracy of the PMSM model. We present a modified PMSM model considering the hysteresis loss and then transform the new PMSM model to a canonical form to simplify the controller design. In order to deal with the hysteresis loss, an ESN is utilized to estimate the nonlinearity. Considering that some states cannot be directly obtained, an ESO with ESN is proposed to estimate unknown system states of the electric vehicle PMSM system. Afterwards, an SMC is adopted to control the closed-loop system based on the ESO with ESN, and a double hyperbolic function instead of the sign function is used to suppress the chattering of the SMC. The stabilities of the observer and the controller are all guaranteed by Lyapunov functions. Finally, simulations are presented to verify the validity of the echo state network for extended state observer and the neural network sliding mode control.

Modelling and control of flexible guided lifting system with output constraints and unknown input hysteresis

Modelling and control vibration is studied for the flexible guided lifting system in the presence of output constraints, input hysteresis, guided rope fault, etc. Flexible guided lifting system, subjected to external disturbances from the boundary disturbance or fluid interaction, is an inherent distributed parameter system with time-varying length and infinite dimensions. According to extended Hamilton’s principle, the governing equation in the form of hybrid partial differential equations and ordinary differential equations is derived to reflect the dynamic response of such multiple ropes under the boundary disturbances and multiple constraints. Adaptive neural network control combining with backstepping technique is subsequently designed to suppress undesirable vibration and stabilise the system, where the neural network is provided as a feedforward compensator for the unknown hysteresis nonlinearities in the control input. Asymptotic stability and uniform boundedness of the system are guaranteed through the Lyapunov theorem, which indicates that all states are uniformly convergent by LaSalle’s invariance principle. The original governing equation is solved numerically by using the finite difference method, where simulation results are illustrated to validate the efficiency of the hybrid partial differential equation and ordinary differential equation model and the adaptive stabilisation design.

Adaptive robust image-based visual servoing control of robot with unknown actuator hysteresis

This paper investigates the image-based visual servoing (IBVS) manipulator system with unknown hysteresis nonlinearity by utilizing the uncalibrated eye-to-hand configuration. Compared with the conventional IBVS system, the unknown actuator hysteresis nonlinearity, which widely exists in the real physical mechanical systems and significantly limits the performances of the robotic system, is fully considered. The problem of unknown actuator nonlinearity prevents direct input of existing controllers and will result in some challenging difficulties in control design. In this paper, an adaptive IBVS control scheme, which takes the unknown actuator hysteresis into account, is presented. Without the prior knowledge of both the intervals of hysteresis parameters and the bound of the dynamic disturbance term, a novel adaptive algorithm is developed to estimate the unknown parameters on-line. The image tracking errors are guaranteed to converge to a small neighborhood of the origin. Simulations and comparative experiments are carried out to test the performance of the proposed scheme.

Adaptive control of piezoelectric fast steering mirror for high precision tracking application

A piezoelectric fast steering mirror (PFSM) is a complex, strong coupling nonlinear system that integrates optics, mechanics, electrics, and control. Due to the existence of hysteresis nonlinearity, mechanical resonance, and all kinds of disturbances, precise tracking control of a PFSM is a challenging task. This paper presents a comprehensive study of modeling, controller design, and simulation evaluation for a PFSM system. First a general model of a PFSM system integrating mechanical dynamics, electrical dynamics, and hysteresis nonlinearity is proposed, and then a robust adaptive controller is developed under both unknown hysteresis nonlinearities and parameter uncertainties. The parameters needed directly in the formulation of the controller are adaptively estimated. The proposed control law ensures the uniform boundedness of all signals in the closed-loop system. Furthermore, a stability analysis of the control system is performed to guarantee that the output tracking error converges to zero asymptotically. Finally, simulation tests with different motion trajectories are conducted to verify the effectiveness of the proposed method.

Development of a Recurrent Fuzzy CMAC With Adjustable Input Space Quantization and Self-Tuning Learning Rate for Control of a Dual-Axis Piezoelectric Actuated Micromotion Stage

This paper proposes a recurrent fuzzy cerebellar model articulation controller (RFCMAC) for a dual-axis micromotion stage powered by piezoelectric actuators. The proposed RFCMAC employs an adjustable input space quantization method with a learning rate capable of self-tuning. The proposed RFCMAC is aimed at dealing with the adverse effects due to unknown hysteresis nonlinearity, modeling uncertainty, and external disturbance that are commonly found in the piezoelectric actuator systems. The proposed RFCMAC mainly focuses on overcoming the drawbacks of the conventional CMAC control scheme when used to control a piezoelectric actuator system. In particular, the adjustable input space quantization method uses a simple repartitioning decision function to determine an appropriate input space quantization. In addition, the self-tuning law for the learning rate of the proposed RFCMAC is derived based on the discrete-time Lyapunov function so that convergence and faster learning can be guaranteed. Finally, in order to validate the effectiveness of the proposed control methodology, several contour-following experiments were conducted on a dual-axis piezoelectric actuated micromotion stage. Experimental results show that the proposed control scheme is feasible, and its performance is superior to that of the conventional CMAC control scheme.

Motion Control of Piezoelectric Positioning Stages: Modeling, Controller Design, and Experimental Evaluation

In this paper, a general skeleton on modeling, controller design, and applications of the piezoelectric positioning stages is presented. Toward this framework, a general model is first proposed to characterize dynamic behaviors of the stage, including frequency response of the stage, voltage-charge hysteresis and nonlinear electric behavior. To illustrate the validity of the proposed general model, a dynamic backlash-like model is adopted as one of hysteresis models to describe the hysteresis effect, which is confirmed by experimental tests. Thus, the developed model provides a general frame for controller design. As an illustration to this aspect, a robust adaptive controller is developed based on a reduced dynamic model under both unknown hysteresis nonlinearities and parameter uncertainties. The proposed control law ensures the boundedness of the closed-loop signals and desired tracking precision. Finally, experimental tests with different motion trajectories are conducted to verify the proposed general model and the robust control law. Experimental results demonstrate the excellent tracking performance, which validates the feasibility and effectiveness of the proposed approach.

Adaptive tracking of stochastic nonlinear systems with Prandtl–Ishlinskii hysteresis

SUMMARYThis paper deals with adaptive tracking problems for a class of stochastic nonlinear systems with unknown hysteresis nonlinearities. The system considered is in a strict‐feedback form driven by unknown Prandtl–Ishlinskii hysteresis and Wiener noises of unknown covariance. By employing backstepping design techniques and stochastic Lyapunov design method, parameter adaptive laws and control laws are obtained, which ensure that the tracking error can converge to a small residual set around the origin in the sense of mean quartic value. Copyright © 2011 John Wiley & Sons, Ltd.

Robust adaptive control for a class of perturbed strict-feedback non-linear systems with unknown Prandtl-Ishlinskii hysteresis

This paper deals with robust adaptive control for a class of perturbed strict-feedback non-linear systems preceded by unknown hysteresis non-linearities. By using the Prandtl-Ishlinskii model with play and stop operators and the properties of this model, a robust adaptive control scheme is proposed to mitigate effects of the preceded hysteresis. The global uniform ultimate boundedness of the closed-loop system is achieved, and the effectiveness of the proposed control approach is demonstrated through simulation examples.

Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl–Ishlinskii presentations

This paper deals with robust adaptive control of a class of nonlinear systems preceded by unknown hysteresis nonlinearities. By using a Prandtl–Ishlinskii model with play and stop operators, we attempt to fuse the model of hysteresis with the available control techniques without necessarily constructing a hysteresis inverse. A robust adaptive control scheme is therefore proposed. The global stability of the adaptive system and tracking a desired trajectory to a certain precision are achieved. Simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach.

Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl-Ishlinskii hysteresis

Control of nonlinear systems preceded by unknown hysteresis nonlinearities is a challenging task and has received increasing attention in recent years due to growing industrial demands involving varied applications. In the literature, many mathematical models have been proposed to describe the hysteresis nonlinearities. The challenge addressed here is how to fuse those hysteresis models with available robust control techniques to have the basic requirement of stability of the system. The purpose of the note is to show such a possibility by using the Prandtl-Ishlinskii (PI) hysteresis model. An adaptive variable structure control approach, serving as an illustration, is fused with the PI model without necessarily constructing a hysteresis inverse. The global stability of the system and tracking a desired trajectory to a certain precision are achieved. Simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach.

Adaptive Output Feedback Control of Systems Preceded by the Preisach-Type Hysteresis

An adaptive output feedback controller is presented for a class of single-input-single-output (SISO) nonlinear systems preceded by an unknown hysteresis nonlinearity represented by the Preisach model. First, a novel model is developed to represent the hysteresis characteristic in order to handle the case where the hysteresis output is not directly measured. The model is motivated by the Preisach model but implemented by the neural networks (NN). Therefore, it is easily used for controller design. Then, a radius-basis-functional-neural-networks (RBF NN) adaptive controller based on the model estimation is presented by combining the high-gain state observer. The updated laws and control laws of the controller are derived from Lyapunov stability theorem, so that the ultimate boundedness of the closed-loop system is guaranteed. At last, an example is used to verify the effectiveness of the controller.

BACKSTEPPING CONTROL OF A CLASS OF NONLINEAR SYSTEMS PRECEDED BY HYSTERESIS WITH PRANDTL-ISHLINSKII PRESENTATIONS

Control of nonlinear systems preceded by unknown hysteresis nonlinearities is a challenging task. In the literature, many mathematical models have been proposed to describe the hysteresis. The challenge addressed here is how to fuse those hysteresis models with available robust control techniques to have the basic requirement of stability of the system. The purpose of the paper is to show such a possibility by using the Prandtl-Ishlinskii (PI) hysteresis model. A backstepping based robust control approach, serving as an illustration, is fused with the PI model without necessarily constructing a hysteresis inverse. The global stability of the system and tracking a desired trajectory to a certain precision are achieved. Simulations performed on a nonlinear system illustrate and further validate the effectiveness of the proposed approach.