Adaptive robust motion control of linear motors for precision manufacturing

Linear motors offer several advantages over their rotary counterparts in many precision manufacturing applications requiring linear motion; linear motors can achieve a much higher speed and have the potential of gaining a higher load positioning accuracy due to the elimination of mechanical transmission mechanisms. However, these advantages are obtained at the expense of added difficulties in controlling such a system. Specifically, linear motors are more sensitive to disturbances and parameter variations. Furthermore, certain types of linear motors such as the iron core are subject to significant nonlinear effects due to periodic cogging force and force ripple. To address all these issues, the recently proposed adaptive robust control (ARC) strategy is applied and a discontinuous projection-based ARC controller is constructed. In particular, based on the special structures of various periodic nonlinear forces, design models consisting of known basis functions with unknown weights are used to approximate those unknown nonlinear forces. On-line parameter adaptation is then utilized to reduce the effect of various parametric uncertainties such as unknown weights, inertia, and motor parameters while certain robust control laws are used to handle the uncompensated uncertain nonlinearities effectively for high performance. The resulting ARC controller achieves a guaranteed transient performance and a guaranteed final tracking accuracy in the presence of both parametric uncertainties and uncertain nonlinearities. In addition, in the presence of parametric uncertainties, the controller achieves asymptotic output tracking. Extensive simulation results are shown to illustrate the effectiveness of the proposed algorithm.     

Particle swarm optimization based feedforward controller for a XY PZT positioning stage

Compensations for cross-axis coupling effect and hysteretic nonlinearity of a novel XY piezo-actuated positioning stage are presented in this study. The piezo-actuated stage utilizes a monolithic flexure-based mechanism (FBM) to achieve translations in X- and Y-axes instead of using stacked mechanisms. A hysteresis model with crossover term is proposed to alleviate the cross coupling effect between X- and Y-stages during precision positioning tasks. System identifications using real-coded genetic algorithm (RGA) and clonal selection algorithm (CSA) are compared with particle swarm optimization (PSO). The results show that PSO provides better performance than the others. Therefore, a feedforward controller with cross-axis coupling compensation is studied and the used for the piezo-actuated FBM to enhance the precision of the coarse positioning stage. The experimental results confirm that the proposed controller can achieve precision tracking tasks with submicron precision.     

Adaptive Approach to Motion Controller of Linear Induction Motor with Friction Compensation

In this paper, we propose a nonlinear adaptive controller and an adaptive backstepping controller for linear induction motors to achieve position tracking. A nonlinear transformation is proposed to facilitate controller design. In addition, the very unique end effect of the linear induction motor is also considered and is well taken care of in our controller design. We also consider the effect of friction dynamics and employ observer-based compensation to cope with the friction force. A stability analysis based on Lyapunov theory is also performed to guarantee that the controller design here can stabilize the system. Also, the computer simulations and experiments are conducted to demonstrate the performance of our various controller design.     

PID-type sliding mode-based adaptive motion control of a 2-DOF piezoelectric ultrasonic motor driven stage

This paper presents a new scheme of adaptive sliding mode control (ASMC) for a piezoelectric ultrasonic motor driven X–Y stage to meet the demand of precision motion tracking while addressing the problems of unknown nonlinear friction and model uncertainties. The system model with Coulomb friction and unilateral coupling effect is first investigated. Then the controller is designed with adaptive laws synthesized to obtain the unknown model parameters for handling parametric uncertainties and offsetting friction force. The robust control term acts as a high gain feedback control to make the output track the desired trajectory fast for guaranteed robust performance. Based on a PID-type sliding mode, the control scheme has a simple structure to be implemented and the control parameters can be easily tuned. Theoretical stability analysis of the proposed novel ASMC is accomplished using a Lyapunov framework. Furthermore, the proposed control scheme is applied to an X–Y stage and the results prove that the proposed control method is effective in achieving excellent tracking performance.     

Nonlinear observer-based adaptive tracking control for inductionmotors with unknown load

In this paper, we propose a nonlinear observer-based adaptive controller for induction motors with unknown load. With the use of the skew-symmetric property of induction motors, a two-stage design technique is applied to construct an observer-based controller for velocity tracking control. To demonstrate the effectiveness of the proposed scheme, a voltage-control type of drive system is set up to perform the task of velocity tracking. The main computing facility consists of two personal computers, PC 486 and PC 286, of which one is to perform the calculation of the control law and the other is to provide the function of pulse width modulation (PWM) and to generate the gating pulses. Satisfactory experimental results are shown in the paper     

Robust adaptive control of sawyer motors without current measurements

We address nonlinear robust adaptive dynamic output feedback of voltage-fed dual-axis linear stepper (Sawyer) motors using a detailed motor model with electrical dynamics and significant uncertainties and disturbances. A coordinate transformation is proposed to decouple the model into three third-order subsystems along with an appended fifth-order subsystem. The controller utilizes only position and velocity measurements in each axis and achieves practical stabilization of position tracking errors. Adaptations are utilized so as not to require any knowledge of electromechanical system parameters. The controller is robust to load torques, friction, cogging forces, and other disturbances satisfying certain bounds. The controller corrects for the yaw rotation to achieve synchrony of motor and platen teeth.     

Nonlinear adaptive control of direct-drive brushless DC motors andapplications to robotic manipulators

Robust adaptive nonlinear control of brushless DC (BLDC) motors is considered. A controller is designed for the plant that is robust to parametric and dynamic uncertainties in the entire electromechanical system. These uncertainties are shown to be bounded by polynomials in the states. In addition, the controller can reject any bounded unmeasurable disturbances entering the system. A model for the motor incorporating magnetic saturation is used to design voltage-level control inputs for the motor. The design methodology is based on our earlier work on adaptive control of nonlinear systems. The overall stability of the system is shown using Lyapunov techniques. The tracking error is shown to be globally uniformly bounded. The design procedure is shown to be also applicable to multilink manipulators actuated by BLDC motors. The performance of the controller is verified through simulations and comparisons with a proportional-integral-derivative-type controller are made     

Adaptive Control of Two-Axis Motion Control System Using Interval Type-2 Fuzzy Neural Network

An interval type-2 fuzzy neural network (IT2FNN) control system is proposed for the precision control of a two-axis motion control system in this paper. The adopted two-axis motion control system is composed of two permanent-magnet linear synchronous motors. In the proposed IT2FNN control system, an IT2FNN, which combines the merits of an interval type-2 fuzzy logic system and a neural network, is developed to approximate an unknown dynamic function. Moreover, adaptive learning algorithms that can train the parameters of the IT2FNN online are derived using the Lyapunov stability theorem. Furthermore, a robust compensator is proposed to confront the uncertainties, including a minimum reconstructed error, optimal parameter vectors, and higher order terms in Taylor series. To relax the requirement for the value of the lumped uncertainty in the robust controller, an adaptive lumped uncertainty estimation law is also investigated. Last, the proposed control algorithms are implemented in a TMS320C32 digital-signal-processor-based control computer. From the simulated and experimental results, the contour tracking performance of the two-axis motion control system is significantly improved, and the robustness can be obtained as well using the proposed IT2FNN control system.     

基于跟踪微分器的模型参考自适应控制

为了处理二阶系统模型参数的大范围不确定性,提出了基于跟踪微分器的模型参考自适应控制,利用两个非线性跟踪微分器分别得到系统输出的微分信号和误差的微分信号,同时抑制了高频噪声放大效应。根据被控对象的数学模型,自适应调节律能自动实时调节控制律中的参数。实验结果表明,当雷达伺服系统被控对象模型的参数在较大范围内变化时,该新型控制器有效补偿了二阶系统参数的不确定性,提高了伺服系统稳态和动态跟踪精度,保证了系统的全局渐近稳定。     

Precision tracking control of a biaxial piezo stage using repetitive control and double-feedforward compensation

This article presents precision tracking control of an XY piezo stage using repetitive control and double-feedforward compensation. The XY piezo stage is composed of two piezoelectric actuators within a leaf spring mechanism. The study applies two feedback controllers, a Proportional-Integral-Derivative controller and a repetitive controller, to achieve precision trajectory tracking and evaluate performance against benchmarks. Moreover, the investigation applies a double-feedforward compensation approach that integrates a Zero-Phase-Error-Tracking-Controller and an adaptive plant inversion compensator adapted by a Least-Mean-Square algorithm, based on an inverse Prandtl-Ishlinskii model, to improve tracking control performance further. Performance analysis and comparison of the experimental results demonstrate that the proposed control structure improves dynamic tracking accuracy of the XY piezo stage.     

基于神经网络仿射非线性系统滑模自适应控制

研究了一类单输入单输出仿射非线性系统的自适应控制问题.采用反馈线性化方法设计控制器,用神经网络逼近系统中的未知非线性函数,并在神经网络权值的自适应律中引入权值误差的概念,以改善系统的动态性能.同时采用滑模控制方法设计补偿器,提高了系统的鲁棒性.理论分析及仿真结果表明,所设计的控制器,不仅能解决该系统的轨迹跟踪控制问题,...     

Nonlinear control of mechatronic systems with permanent-magnet DC motors

The current trends in development and deployment of advanced electromechanical systems have facilitated the unified activities in the analysis and design of state-of-the-art motion devices, electric motors, power electronics, and digital controllers. This paper attacks the motion control problem (stabilization, tracking, and disturbance attenuation) for mechatronic systems which include permanent-magnet DC motors, power circuity, and motion controllers. By using an explicit representation of nonlinear dynamics of motors and switching converters, we approach and solve analysis and control problems to ensure a spectrum of performance objectives imposed on advanced mechatronic systems. The maximum allowable magnitude of the applied armature voltage is rated, the currents are limited, and there exist the lower and upper limits of the duty ratio of converters. To approach design tradeoffs and analyze performance (accuracy, settling time, overshoot, stability margins, and other quantities), the imposed constraints, model nonlinearities, and parameter variations are thoroughly studied in this paper. Our goal is to attain the specified characteristics and avoid deficiencies associated with linear formulation. To solve these problems, an innovative controller is synthesized to ensure performance improvements, robust tracking, and disturbance rejection. One cannot neglect constraints, and a bounded control law is designed to improve performance and guarantee robust stability. The offered approach uses a complete nonlinear mechatronic system dynamics with parameter variations, and this avenue allows one to avoid the conservative results associated with linear concept when mechatronic system dynamics is mapped by a linear constant-coefficient differential equation. To illustrate the reported framework and to validate the controller, analytical and experimental results are presented and discussed. In particular, comprehensive analysis and design with experimental verification are performed for an electric drive. A nonlinear bounded controller is designed, implemented, and experimentally tested.     

H ∞ Output Tracking Control for Discrete-Time Switched Systems Based on Switching Method

This paper addresses the H _∞ output tracking control problem for a class of discrete-time switched linear systems. We do not require that the H _∞ output tracking control problem for each individual subsystem to be solvable. Based on the multiple Lyapunov functions approach, a switching law depending on the system state is designed, which, together with the designed controllers, can guarantee that the output tracking error dynamics converges H _∞ asymptotically to zero. In sufficient conditions, we introduce an additional scalar matrix variable to realize the decoupling between the system matrices and Lyapunov matrices. The controller gains can be obtained by solving linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the feasibility of the proposed design method.     

Chaos synchronization using higher-order adaptive PID controller

This paper is devoted to designing higher-order adaptive PID controllers as a new generation of PID controllers for chaos synchronization, in which second order integration and second-order derivative terms to the PID controller (PII²DD²) are employed. The five PII²DD² control gains are updated online with a stable adaptation law driven by Lyapunov’s stability theory. This is the unique advantage of the proposed approach. Furthermore, it is equipped with a novel robust control term to improve controller robustness against system uncertainties and unknown disturbances. An important feature of the proposed approach is that it is a model-free controller. In addition, to determine the control design parameters and avoid trial and error, the Teaching–learning-based optimization algorithm (TLBO) is employed to regulate these parameters and enhance the performance of the proposed controller. Based on the Lyapunov stability theory, it is proven that the proposed control scheme can guarantee the synchronization and the stability of closed-loop control system. The case study is the Duffing–Holmes oscillator. Comparative simulation results are presented which confirm the superiority of the proposed approach.     

Adaptive incremental sliding mode control for a robot manipulator

An adaptive incremental sliding mode control (AISMC) scheme for a robot manipulator is presented in this paper. Firstly, an incremental backstepping (IBS) controller is designed using time-delay estimation (TDE) to reduce dependence on the mathematical model. After substituting IBS controller into the nonlinear system, a linear system w.r.t. tracking errors is obtained while TDE error is the disturbance. Then, the AISMC scheme, including a nominal controller and an SMC, is developed for the resulted linear system to improve control performance. According to the equivalent control method, the SMC in the AISMC scheme is to handle TDE error. To receive optimal control performance at the sliding manifold, an LQR controller is selected as the nominal controller. The SMC is designed based on positive semi-definite barrier function (PSDBF) since it prevents switching gains from being over/under-estimated, and two practical problems are addressed in this paper: A new PSDBF is designed and conservative (large) setting bounds affecting tracking precision and/or system stability are avoided; An improved PSDBF based SMC is developed where the PSDBF and an adaptive parameter are used simultaneously to regulate switching gains, and the system is still stable when sliding variable occasionally exceeds the predefined vicinity. Moreover, finite-time convergence property of the sliding variable is strictly analyzed. Finally, real-time experiments are conducted to verify the effectiveness of the proposed control method.     

Exponential H ∞ Output Tracking Control for Switched Neutral System with Time-Varying Delay and Nonlinear Perturbations

In this paper, the problem of exponential H _∞ output tracking control is addressed for a class of switched neutral system with time-varying delay and nonlinear perturbations. The considered system consists of different neutral and discrete delays. By resorting to the average dwell time approach, a new Lyapunov–Krasovskii functional is proposed to establish sufficient conditions for the exponential stability and H _∞ performance of switched neutral systems. Then, the problem of exponential H _∞ output tracking control is investigated, an explicit expression for the desired exponential tracking controller is also given. Finally, a numerical example is provided to demonstrate the potential effectiveness of the proposed method.     

Dynamic triangular neural controller for stepper motor trajectorytracking

We present a novel neural controller for a stepper motor. This controller is developed as follows. Modifying published results for nonlinear identification using dynamic neural networks (NNs), an NN identifier of triangular form is implemented. Then, based on this mode, a control law using sliding modes is derived. This neural identifier and the proposed control law allow trajectory tracking for stepping motors. Applicability of the approach is tested via simulations     

Implementation of LLCC-resonant driving circuit and adaptive CMAC neural network control for linear piezoelectric ceramic motor

In this paper, an adaptive cerebellar-model articulation computer (CMAC) neural network (NN) control system is developed for a linear piezoelectric ceramic motor (LPCM) that is driven by an LLCC-resonant inverter. The motor structure and LLCC-resonant driving circuit of an LPCM are introduced initially. The LLCC-resonant driving circuit is designed to operate at an optimal switching frequency such that the output voltage will not be influenced by the variation of quality factor. Since the dynamic characteristics and motor parameters of the LPCM are highly nonlinear and time varying, an adaptive CMAC NN control system is designed without mathematical dynamic model to control the position of the moving table of the LPCM drive system to achieve high-precision position control with robustness. In the proposed control scheme, the dynamic backpropagation algorithm is adopted to train the CMAC NN online. Moreover, to guarantee the convergence of output tracking error for periodic commands tracking, analytical methods based on a discrete-type Lyapunov function are utilized to determine the optimal learning-rate parameters of the CMAC NN. The effectiveness of the proposed driving circuit and control system is verified by experimental results in the presence of uncertainties, and the advantages of the proposed control system are indicated in comparison with a traditional integral-proportional position control system. Accurate tracking response and superior dynamic performance can be obtained due to the powerful online learning capability of the CMAC NN with optimal learning-rate parameters.     

自适应模糊奇异摄动控制在航天器中的应用

带挠性附件航天器可以用含小摄动参数的多时标非线性系统进行描述,而目前的控制方法大多针对多时标线性系统,要求模型精确已知.为解决存在不确定性的带挠性附件航天器的跟踪问题,提出一种基于模糊奇异摄动模型的自适应控制器,采用鲁棒控制和自适应控制理论相结合的方法进行设计,由反馈项、自适应项和鲁棒控制项组成,反馈项的增益采用线性矩阵不等式(LMI)方法求解,自适应项用于减小系统的跟踪误差,鲁棒项用于保证系统的闭环稳定性.稳定性证明采用Lyapunov合成方法完成.该控制器适用于模型带有不确定性的多时标非线性系统的跟踪控制.由于采用了自适应方法消除系统不确定性,能够减少鲁棒控制方法带来的保守性.在带挠性附件航天器的跟踪控制中的应用验证了其有效性.     

Sensing of the time-varying angular rate for MEMS Z-axis gyroscopes

In this paper, a nonlinear estimation strategy for sensing the time-varying angular rate of a Z-axis MEMS gyroscope is presented. An off-line adaptive least-squares estimation strategy is first developed to accurately estimate the unknown model parameters. Both axes of a Z-axis MEMS gyroscope are then actively controlled utilizing an on-line controller/observer to facilitate time-varying angular rate sensing. The proposed nonlinear estimation strategy is developed based on a Lyapunov-based analysis, which proves that the time-varying angular rate experienced by the device can be estimated accurately. Two cases for angular rate are investigated which are time-varying and constant magnitudes. An adaptive controller/observer was also utilized for sensing the angular rate to investigate the performance of the proposed controller/observer. Representative numerical results are discussed to demonstrate the performance of the proposed nonlinear strategy in accurately sensing the applied angular rate. Overall, the proposed nonlinear controller/observer improves sensing the constant angular rate by 50% and the time-varying angular rate by 90% when compared with an adaptive controller/observer.