Unknown Prandtl-Ishlinskii Hysteresis Research Articles

Dynamic surface control based on observer for a class of nonlinear systems with Prandtl-Ishlinskii hysteresis

Unknown hysteresis characteristics can seriously affect control accuracy, resulting in system oscillation and instability. This study explored a dynamic surface control (DSC) method according to disturbance observer for a type of uncertain nonlinear system with unknown Prandtl-Ishlinskii hysteresis. First, DSC is adopted for the trajectory tracking control, which solves the “differential explosion” in the traditional backstepping control scheme and simplifies the structure of the controller. Then, an observer is introduced to monitor the hysteresis, effectively suppressing the effect of the hysteresis features on the system and achieving accurate tracking of the system. The scheme proposed in this study is confirmed to be effective based on the simulation results.

Event-Triggered Adaptive Fuzzy Tracking Control for Uncertain Nonlinear Systems Preceded by Unknown Prandtl-Ishlinskii Hysteresis.

In this article, the problem of event-triggered tracking control for a class of uncertain nonlinear systems with unknown Prandtl-Ishlinskii (PI) hysteresis is investigated. To solve this problem, two control schemes are proposed via synthesizing the techniques of the event-triggered strategy, fuzzy-logic systems (FLSs), and adaptive backstepping control. The first basic design scheme applies an effective method to keep a balance between communication constraints and system performance under the influence of actuator PI hysteresis, while the Zeno behavior can be avoided. Furthermore, the basic design scheme not only guarantees the tracking error asymptotically converges to zero but also establishes a preserved transient performance. Nevertheless, note that the inclusive sign functions of the basic design scheme will cause possible chattering phenomenon, an alternative event-triggered adaptive control approach is then proposed. Unlike the previous control scheme, the second chattering-avoidance design approach ensures asymptotic convergence of the tracking error within a prescribed boundary δ , and finally the [Formula: see text]-norm transient performance of the tracking error is constructed. Simulations verify the established theoretical results that the proposed schemes successfully overcome the communication constraints and compensate the actuator PI hysteresis, and also present different tracking performances between two control schemes for comparison.

Force feedback control for bilateral teleoperation system with unknown Prandtl-Ishlinskii hysteresis

Hysteresis nonlinearity is a common phenomenon in mechanical actuators. Specially, it appears when the direction of motion of mechanical actuated joint is reversed in robotic manipulator. This paper focuses on the force feedback control problem for bilateral teleoperation system with unknown Prandtl-Ishlinskii (PI) hysteresis. First, an improved sliding mode observer with adaptive gains is provided for estimating the external force signals acting on the manipulators. This removes the need for force sensors and reduces hardware-cost. Next, to improve transparency and guarantee the passivity of the communication network, a four-channel wave variable transformation scheme including force information is introduced. Then, an adaptive switching-based control framework is proposed to deal with Prandtl-Ishlinskii hysteresis dynamics. Finally, the theoretical findings are supported by simulation and experiment results.

Adaptive Sampled-Data Observer Design for a Class of Nonlinear Systems with Unknown Hysteresis

In this paper, a novel adaptive sampled-data observer design is studied for a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis and unknown unmatched disturbances based on radial basis function neural networks (RBFNNs). To begin with, we investigate a sampled-data nonlinear system and present sufficient conditions such that the sampled-data nonlinear system is ultimately uniformly bounded (UUB). Then, an adaptive sampled-data observer is designed to estimate the unknown states of the nonlinear system. The unknown hysteresis and the unknown disturbances are approximated by RBFNNs. We also give the learning laws of the weights of RBFNNs, and prove that the estimation errors of the states and the weights are UUB, based on the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

Output feedback prescribed performance control for interconnected time-delay systems with unknown Prandtl–Ishlinskii hysteresis

In this paper, output feedback prescribed performance control problem is investigated for interconnected time-delay systems with unknown Prandtl–Ishlinskii hysteresis. Decentralized reduced-order observer independent of time delay is first designed. Then, by using a novel state transformation, the prescribed performance control problem is transformed to stabilization problem. An adaptive variable structure control approach is proposed to address the Prandtl–Ishlinskii hysteresis model without necessarily constructing a hysteresis inverse. Subsequently, via backstepping method, the output feedback controller is designed. Based on Lyapunov stability theory, the constructed controllers are proved to guarantee the stability of the closed-loop system with the prescribed performance. Finally, a simulation example is given and the results verify the effectiveness of the proposed design technique.

Adaptive control of Hammerstein systems with unknown Prandtl–Ishlinskii hysteresis

We numerically investigate the sense in which an adaptive control law achieves internal model control of Hammerstein plants with Prandtl–Ishlinskii hysteresis. We apply retrospective cost adaptive control to a command-following problem for uncertain Hammerstein systems with hysteretic input nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. Describing functions are used to determine whether the adaptive controller inverts the plant at the exogenous frequencies.

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.

A robust adaptive dynamic surface control for a class of nonlinear systems with unknown Prandtl–Ishilinskii hysteresis

AbstractIn this paper, a robust adaptive dynamic surface control for a class of uncertain perturbed strict‐feedback nonlinear systems preceded by unknown Prandtl–Ishlinskii hysteresis is proposed. The main advantages of our scheme are that the explosion of complexity problem can be eliminated when the hysteresis is fused with backstepping design and, by introducing an initialization technique, the ℒ︁∞ performance of system tracking error can be achieved. It is proved that the new scheme can guarantee semi‐global uniform ultimate boundedness of all closed‐loop signals and make the convergence of the tracking error to an arbitrarily small residual set. Simulation results are presented to demonstrate the efficiency of the proposed scheme. Copyright © 2010 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.

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.