New Super-Twisting Zeroing Neural-Dynamics Model for Tracking Control of Parallel Robots: A Finite-Time and Robust Solution.

Parallel robots are usually required to perform real-time tracking control tasks in the presence of external disturbances in the complex environment. Conventional zeroing neural-dynamics (ZNDs) provide an alternative solution for the real-time tracking control of parallel robots due to its capacity of parallel processing and nonlinearity handling. However, it is still a challenge for the solution in a unified framework of the ZND to deal with the external disturbances, and simultaneously possess a finite-time convergence property. In this paper, a novel ZND model by exploring the super-twisting (ST) algorithm, named ST-ZND model, is proposed. The theoretical analyses on the global stability, finite-time convergence, as well as the robustness against the external disturbances are rigorously presented. Finally, the effectiveness and superiority of the ST-ZND model for the real-time tracking control of parallel robots are demonstrated by two illustrative examples, comparisons, and convergence tests.

Intelligent nonsingular terminal sliding-mode control using MIMO Elman neural network for piezo-flexural nanopositioning stage.

The objective of this study is to develop an intelligent nonsingular terminal sliding-mode control (INTSMC) system using an Elman neural network (ENN) for the threedimensional motion control of a piezo-flexural nanopositioning stage (PFNS). First, the dynamic model of the PFNS is derived in detail. Then, to achieve robust, accurate trajectory-tracking performance, a nonsingular terminal sliding-mode control (NTSMC) system is proposed for the tracking of the reference contours. The steady-state response of the control system can be improved effectively because of the addition of the nonsingularity in the NTSMC. Moreover, to relax the requirements of the bounds and discard the switching function in NTSMC, an INTSMC system using a multi-input-multioutput (MIMO) ENN estimator is proposed to improve the control performance and robustness of the PFNS. The ENN estimator is proposed to estimate the hysteresis phenomenon and lumped uncertainty, including the system parameters and external disturbance of the PFNS online. Furthermore, the adaptive learning algorithms for the training of the parameters of the ENN online are derived using the Lyapunov stability theorem. In addition, two robust compensators are proposed to confront the minimum reconstructed errors in INTSMC. Finally, some experimental results for the tracking of various contours are given to demonstrate the validity of the proposed INTSMC system for PFNS.

Intelligent complementary sliding-mode control for LUSMS-based X-Y-theta motion control stage.

An intelligent complementary sliding-mode control (ICSMC) system using a recurrent wavelet-based Elman neural network (RWENN) estimator is proposed in this study to control the mover position of a linear ultrasonic motors (LUSMs)-based X-Y-theta motion control stage for the tracking of various contours. By the addition of a complementary generalized error transformation, the complementary sliding-mode control (CSMC) can efficiently reduce the guaranteed ultimate bound of the tracking error by half compared with the slidingmode control (SMC) while using the saturation function. To estimate a lumped uncertainty on-line and replace the hitting control of the CSMC directly, the RWENN estimator is adopted in the proposed ICSMC system. In the RWENN, each hidden neuron employs a different wavelet function as an activation function to improve both the convergent precision and the convergent time compared with the conventional Elman neural network (ENN). The estimation laws of the RWENN are derived using the Lyapunov stability theorem to train the network parameters on-line. A robust compensator is also proposed to confront the uncertainties including approximation error, optimal parameter vectors, and higher-order terms in Taylor series. Finally, some experimental results of various contours tracking show that the tracking performance of the ICSMC system is significantly improved compared with the SMC and CSMC systems.

Robust dynamic sliding-mode control using adaptive RENN for magnetic levitation system.

In this paper, a robust dynamic sliding mode control system (RDSMC) using a recurrent Elman neural network (RENN) is proposed to control the position of a levitated object of a magnetic levitation system considering the uncertainties. First, a dynamic model of the magnetic levitation system is derived. Then, a proportional-integral-derivative (PID)-type sliding-mode control system (SMC) is adopted for tracking of the reference trajectories. Moreover, a new PID-type dynamic sliding-mode control system (DSMC) is proposed to reduce the chattering phenomenon. However, due to the hardware being limited and the uncertainty bound being unknown of the switching function for the DSMC, an RDSMC is proposed to improve the control performance and further increase the robustness of the magnetic levitation system. In the RDSMC, an RENN estimator is used to estimate an unknown nonlinear function of lumped uncertainty online and replace the switching function in the hitting control of the DSMC directly. The adaptive learning algorithms that trained the parameters of the RENN online are derived using Lyapunov stability theorem. Furthermore, a robust compensator is proposed to confront the uncertainties including approximation error, optimal parameter vectors, and higher order terms in Taylor series. Finally, some experimental results of tracking the various periodic trajectories demonstrate the validity of the proposed RDSMC for practical applications.

FPGA-based Elman neural network control system for linear ultrasonic motor.

A field-programmable gate array (FPGA)-based Elman neural network (ENN) control system is proposed to control the mover position of a linear ultrasonic motor (LUSM) in this study. First, the structure and operating principle of the LUSM are introduced. Because the dynamic characteristics and motor parameters of the LUSM are nonlinear and time-varying, an ENN control system is designed to achieve precision position control. The network structure and online learning algorithm using delta adaptation law of the ENN are described in detail. Then, a piecewise continuous function is adopted to replace the sigmoid function in the hidden layer of the ENN to facilitate hardware implementation. In addition, an FPGA chip is adopted to implement the developed control algorithm for possible low-cost and high-performance industrial applications. The effectiveness of the proposed control scheme is verified by some experimental results.

An adaptive recurrent radial basis function network tracking controller for a two-dimensional piezo-positioning stage.

An adaptive recurrent radial basis function network (ARRBFN) tracking controller for a two-dimensional piezo-positioning stage is proposed in this study. First, a mathematical model that represents the dynamics of the two-dimensional piezo-positioning stage is proposed. In this model, a hysteresis friction force that describes the hysteresis behavior of one-dimensional motion is used; and a nonconstant stiffness with the cross-coupling dynamic due to the effect of bending of a lever mechanism in x and y axes also is included. Then, according to the proposed mathematical model, an ARRBFN tracking controller is proposed. In the proposed ARRBFN control system, a recurrent radial basis function network (RRBFN) with accurate approximation capability is used to approximate an unknown dynamic function. The adaptive learning algorithms that can learn the parameters of the RRBFN on line are derived using Lyapunov stability theorem. Moreover, a robust compensator is proposed to confront the uncertainties, including approximation error, optimal parameter vectors, higher-order terms in Taylor series. To relax the requirement of the value of the lumped uncertainty in the robust compensator, an adaptive law is investigated to estimate the lumped uncertainty. Using the proposed control scheme, the position tracking performance is substantially improved and the robustness to uncertainties, including hysteresis friction force and cross-coupling stiffness, can be obtained as well. The tracking performance and the robustness to external load of the proposed ARRBFN control system are illustrated by some experimental results.

Recurrent RBFN-based fuzzy neural network control for X-Y-theta motion control stage using linear ultrasonic motors.

A recurrent radial basis function network (RBFN) based fuzzy neural network (FNN) control system is proposed to control the position of an X-Y-theta motion control stage using linear ultrasonic motors (LUSMs) to track various contours in this study. The proposed recurrent RBFN-based FNN combines the merits of self-constructing fuzzy neural network (SCFNN), recurrent neural network (RNN), and RBFN. Moreover, the structure and the parameter learning phases of the recurrent RBFN-based FNN are performed concurrently and on line. The structure learning is based on the partition of input space, and the parameter learning is based on the supervised gradient decent method using a delta adaptation law. The experimental results due to various contours show that the dynamic behaviors of the proposed recurrent RBFN-based FNN control system are robust with regard to uncertainties.

Adaptive control with hysteresis estimation and compensation using RFNN for piezo-actuator.

Because the control performance of a piezoactuator is always severely deteriorated due to hysteresis effect, an adaptive control with hysteresis estimation and compensation using recurrent fuzzy neural network (RFNN) is proposed in this study to improve the control performance of the piezo-actuator. A new hysteresis model by modifying and parameterizing the hysteresis friction model is proposed. Then, the overall dynamics of the piezo-actuator is completed by integrating the parameterized hysteresis model into a mechanical motion dynamics. Based on this developed dynamics, an adaptive control with hysteresis estimation and compensation is proposed. However, in the designed adaptive controller, the lumped uncertainty E is difficult to obtain in practical application. Therefore, a RFNN is adopted as an uncertainty observer in order to adapt the value of the lumped uncertainty E on line. And, some experimental results show that the proposed controller provides high-performance dynamic characteristics and is robust to the variations of system parameters and external load.

An adaptive recurrent-neural-network motion controller for X-Y table in CNC machine.

In this paper, an adaptive recurrent-neural-network (ARNN) motion control system for a biaxial motion mechanism driven by two field-oriented control permanent magnet synchronous motors (PMSMs) in the computer numerical control (CNC) machine is proposed. In the proposed ARNN control system, a RNN with accurate approximation capability is employed to approximate an unknown dynamic function, and the adaptive learning algorithms that can learn the parameters of the RNN on line are derived using Lyapunov stability theorem. Moreover, a robust controller is proposed to confront the uncertainties including approximation error, optimal parameter vectors, higher-order terms in Taylor series, external disturbances, cross-coupled interference and friction torque of the system. To relax the requirement for the value of lumped uncertainty in the robust controller, an adaptive lumped uncertainty estimation law is investigated. Using the proposed control, the position tracking performance is substantially improved and the robustness to uncertainties including cross-coupled interference and friction torque can be obtained as well. Finally, some experimental results of the tracking of various reference contours demonstrate the validity of the proposed design for practical applications.

Adaptive wavelet neural network control with hysteresis estimation for piezo-positioning mechanism.

An adaptive wavelet neural network (AWNN) control with hysteresis estimation is proposed in this study to improve the control performance of a piezo-positioning mechanism, which is always severely deteriorated due to hysteresis effect. First, the control system configuration of the piezo-positioning mechanism is introduced. Then, a new hysteretic model by integrating a modified hysteresis friction force function is proposed to represent the dynamics of the overall piezo-positioning mechanism. According to this developed dynamics, an AWNN controller with hysteresis estimation is proposed. In the proposed AWNN controller, a wavelet neural network (WNN) with accurate approximation capability is employed to approximate the part of the unknown function in the proposed dynamics of the piezo-positioning mechanism, and a robust compensator is proposed to confront the lumped uncertainty that comprises the inevitable approximation errors due to finite number of wavelet basis functions and disturbances, optimal parameter vectors, and higher order terms in Taylor series. Moreover, adaptive learning algorithms for the online learning of the parameters of the WNN are derived based on the Lyapunov stability theorem. Finally, the command tracking performance and the robustness to external load disturbance of the proposed AWNN control system are illustrated by some experimental results.

Wavelet neural network control for linear ultrasonic motor drive via adaptive sliding-mode technique.

A wavelet neural network (WNN) control system is proposed to control the moving table of a linear ultrasonic motor (LUSM) drive system to track periodic reference trajectories in this study. The design of the WNN control system is based on an adaptive sliding-mode control technique. The structure and operating principle of the LUSM are introduced, and the driving circuit of the LUSM, which is a voltage source inverter using two-inductance two capacitance (LLCC) resonant technique, is introduced. Because the dynamic characteristics and motor parameters of the LUSM are nonlinear and time varying, a WNN control system is designed based on adaptive sliding-mode control technique to achieve precision position control. In the WNN control system, a WNN is used to learn the ideal equivalent control law, and a robust controller is designed to meet the sliding condition. Moreover, the adaptive learning algorithms of the WNN and the bound estimation algorithm of the robust controller are derived from the sense of Lyapunov stability analysis. The effectiveness of the proposed WNN control system is verified by some experimental results in the presence of uncertainties.