Nonlinear Control of Magnetic Bearings

In this paper, recent results controling nonlinear systems with output tracking error constraints are applied to the design of new tracking controllers for magnetic bearings. The proposed controllers can force the rotor to track a bounded and sufficiently smooth refer-ence trajectory asymptotically and guarantee non-contactedness be-tween the rotor and the stator of the magnetic bearings. Simulation results are included to illustrate the effectiveness of the proposed con-trollers.     

Adaptive time-varying formation tracking control of unmanned aerial vehicles with quantized input

This paper considers the adaptive time-varying formation tracking control of unmanned aerial vehicles (UAVs) with quantized input. Uncertainties and nonholonomic constraint are involved in the UAV model. With a novel transformation of the final control signal, a very coarse quantization can be achieved. Adaptive quantized controllers are proposed by employing backstepping technique. It is proved that, with our proposed strategy, all signals of the closed-loop system are globally uniformly bounded, and the formation tracking error converges to an arbitrarily small residual set. Simulation results are given to illustrate the effectiveness of the proposed strategy.     

Performance limitations of networked control systems with quantization and packet dropouts

This paper investigates the problem of optimal tracking performance of networked control systems (NCSs) with quantization and packet-dropouts. The system under consideration is linear time-invariant (LTI), multi-input multi-output (MIMO), where an H₂ norm of error signal between the reference input and the system output is used as the tracking performance index. The impacts of packet-dropouts in the communication channel and the quantized input and output are studied. The goal is to obtain the minimal error in tracking a random signal, by searching through all possible stabilizing two-parameter controllers. It is shown that, the minimum value of tracking error is closely related to the reference input signal direction, the non-minimum phase zeros and unstable poles of the given plant, including the locations and directions. We also demonstrated the quantization error and the packet-dropouts may degrade the tracking performance. A typical example is given to evaluate the theoretical results.     

快速反射镜姿态角的高精度解算

为了提高跟瞄转台出射激光的指向精度,研究了快速反射镜(FSM)姿态角与转台跟踪误差间的关系,提出了FSM姿态角的高精度解算方法。介绍了跟瞄转台出射激光的光路特点和FSM的工作原理;确定了坐标系中入射光与出射光的方向,依据坐标变换理论和光的反射定律,建立了FSM反射镜姿态角与转台跟踪误差间的函数关系。然后,推导出姿态角的解析表达式,描述了姿态角的空间分布规律,并从解析表达式中推出了近似表达式,确定了近似表达式引入的指向误差。最后,通过指向精度实验验证了姿态角解算方法的正确性。实验结果表明:在跟踪误差不超过(A 12.9′,E13.5′)时,应用姿态角解析表达式和近似表达式均能取得优于2.5″的指向精度;跟踪误差增大为(A38.6′,E37.8′)时,解析表达式对应的指向误差仍低于2.5″,而近似表达式对应的指向误差迅速增大为13.2″。得到的结果显示:FSM姿态角的解析表达式不存在原理误差,在任意跟踪误差下均能使出射激光具有高精度指向能力,且其形式简洁,满足伺服控制器快速运算的要求。     

Design of multiloop PI controllers based on quadratic optimal approach

The LQR methodology is extended to produce multiloop PI controllers in this study. With this method, a multivariable P controller is first obtained and then diagonalized using an iterative procedure. The resulting controller is further complemented with the integral action in a similar process. The proposed tuning process explores different values of the control weight matrix to balance the output error and control signal in both stages, and is refined through additional indices related with the error to reference tracking, disturbance rejection and the associated control use. In addition, the diagonalization procedure is generalized to obtain multiloop versions of existing multivariable PI controllers. The developed theory was applied to the design of multiloop controllers for a distillation column as well as the diagonalization of existing controllers for a nonlinear CSTR. The tuning procedure allowed the synthesis of multiloop PI controllers with performance indices comparable to those reported by other authors. Furthermore, diagonalized controllers exhibited a similar operation as the original multivariable ones.     

带补偿因子的双模糊控制在电液伺服阀控非对称缸系统上的应用研究

为解决电液伺服阀控非对称缸系统在进行对称运动时由于液压缸的非对称性带来的控制非对称问题,提出一种含补偿因子的双模糊控制算法。以电液伺服阀控非对称缸系统为对象,针对非对称液压缸在两个运动方向上动态特性的非对称性问题,采用含补偿因子的模糊控制器进行补偿。同时,针对负载力大范围变化的特点,采用模糊PID控制算法来适应负载的变化。模糊PID控制器及含补偿因子的模糊控制器以经过跟踪微分器处理的误差及误差的微分作为输入,模糊PID控制器输出为PID控制器各项系数,含补偿因子的模糊控制器输出为补偿因子,结合模糊PID控制器,形成有效解决非对称液压缸非对称性问题的控制方法。仿真和试验结果表明,提出的控制方法能够有效解决电液伺服阀控非对称缸系统的控制非对称性问题,并拥有良好的控制效果。     

具有迟滞和蠕变特性压电作动器的模糊自适应逆控制方法

针对具有迟滞和蠕变特性的压电作动器非线性模型,提出了一种前馈控制和反馈控制相结合的自适应模糊逆控制方案。在前馈控制器中压电作动器的迟滞和蠕变非线性特性的逆模型由自适应模糊逻辑系统近似;在反馈控制器中比例控制器用来调节压电作动器的输出误差。该方法可以实时补偿压电作动器的迟滞和蠕变特性,减少作动器跟踪误差。仿真计算结果表明了该方法的有效性。     

Robust friction compensation for submicrometer positioning and tracking for a ball-screw-driven slide system

Ball-screw-driven slide systems are largely used in industry for motion control applications. Their performance using standard proportional-integral-derivative (PID) control algorithm is unsatisfactory in submicrometer motion control because of nonlinear friction effects. In this article, controllers based on a bristle-type nonlinear contact model are developed and implemented for submicrometer motion. For submicrometer positioning, a proportional-derivative (PD) control scheme with a nonlinear friction estimate algorithm is developed, and its performance is compared with that of a PID controller. For tracking, a disturbance observer was added to reject external disturbances and to improve robustness. The experimental results indicate that the proposed controller has consistent performance in positioning with under 1.5% of steady-state error in the submicrometer range. For tracking performance, the proposed controller shows good and robust tracking with respect to parameter variation.     

Improving dynamic performances of PWM-driven servo-pneumatic systems via a novel pneumatic circuit

In this paper, the effect of pneumatic circuit design on the input–output behavior of PWM-driven servo-pneumatic systems is investigated and their control performances are improved using linear controllers instead of complex and costly nonlinear ones. Generally, servo-pneumatic systems are well known for their nonlinear behavior. However, PWM-driven servo-pneumatic systems have the advantage of flexibility in the design of pneumatic circuits which affects the input–output linearity of the whole system. A simple pneumatic circuit with only one fast switching valve is designed which leads to a quasi-linear input–output relation. The quasi-linear behavior of the proposed circuit is verified both experimentally and by simulations. Closed loop position control experiments are then carried out using linear P- and PD-controllers. Since the output position is noisy and cannot be directly differentiated, a Kalman filter is designed to estimate the velocity of the cylinder. Highly improved tracking performances are obtained using these linear controllers, compared to previous works with nonlinear controllers.     

基于误差反馈学习的永磁同步电机变负载有限时间速度控制

针对传统永磁同步电机调速系统面对变负载和大范围调速时,P、I参数需要频繁调整且速度跟踪不理想的问题,提出了一种基于误差反馈学习结构的永磁同步电机有限时间速度控制方法。在对永磁同步电机运动方程分析的基础上,使用非线性PI和径向基神经网络建立了速度环控制器模型。前者保证控制系统收敛和稳定,其输出作为神经网络的误差学习参数;后者基于终端滑模理论设计参数调整律,加快神经网络的参数收敛速度,使得神经网络的输出逐渐取代非线性PI成为控制系统的主要控制器。利用李雅普诺夫稳定判据分析了控制器的收敛性,并在永磁同步电机调速系统上进行了试验。研究结果表明,基于误差反馈学习结构的有限时间控制策略能够减小系统静态误差和抖振,具有一定的抗干扰能力。     

Performance limitations in the tracking and regulation problem for discrete-time systems

In this paper, the optimal tracking and regulation performance of discrete-time, multi-input multi-output, linear time-invariant systems is investigated. The control signal is influenced by the external disturbance, and the output feedback is subjected to an additive white Gaussian noise (AWGN) corruption. The tracking error with channel input power constraint and the output regulation with control energy constraint are adopted as the measure of tracking and regulation performance respectively, which can be obtained by searching through all stabilizing two-parameter controllers. Both results demonstrate that the performance is closely related to locations and directions of the nonminimum phase zeros, unstable poles of the plant and may be badly degraded by external disturbance and AWGN.     

Generalized predictor based active disturbance rejection control for non-minimum phase systems

In this paper, a generalized predictor based control scheme is proposed to improve system performance of set-point tracking and disturbance rejection for non-minimum phase (NMP) systems. By using a generalized predictor to estimate the system output without time delay, a model-based extended state observer (MESO) is designed to simultaneously estimate the system state and disturbance. Accordingly, an active disturbance rejection control design is developed which consists of a state feedback control and a feedforward control for the disturbance rejection. The MESO and feedback controllers are analytically derived by specifying the desired characteristic roots of MESO and closed-loop system poles, respectively. To improve the output tracking performance, a pre-filter is designed based on a desired closed-loop transfer function for the set-point tracking. A sufficient condition guaranteeing robust stability of the closed-loop system against time-varying uncertainties is established in terms of linear matrix inequalities (LMIs). Three illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control scheme.     

Asymmetric Fuzzy Control of a Positive and Negative Pneumatic Pressure Servo System

The pneumatic pressure control systems have been used in some fields. However, the researches on pneumatic pressure control mainly focus on constant pressure regulation. Poor dynamic characteristics and strong nonlinearity of such systems limit its application in the field of pressure tracking control. In order to meet the demand of generating dynamic pressure signal in the application of the hardware-in-the-loop simulation of aerospace engineering, a positive and negative pneumatic pressure servo system is provided to implement dynamic adjustment of sealed chamber pressure. A mathematical model is established with simulation and experiment being implemented afterwards to discuss the characteristics of the system, which shows serious asymmetry in the process of charging and discharging. Based on the analysis of the system dynamics, a fuzzy proportional integral derivative (PID) controller with asymmetric fuzzy compensator is proposed. Different from conventional adjusting mechanisms employing the error and change in error of the controlled variable as input parameters, the current chamber pressure and charging or discharging state are chosen as inputs of the compensator, which improves adaptability. To verify the effectiveness and performance of the proposed controller, the comparison experiments tracking sinusoidal and square wave commands are conducted. Experimental results show that the proposed controller can obtain better dynamic performance and relatively consistent control performance across the scope of work (2–140 kPa). The research proposes a fuzzy control method to overcome asymmetry and enhance adaptability for the positive and negative pneumatic pressure servo system.     

Controller designs for constant cutting force turning machine control

A simulation study of a constant cutting force metal turning process is investigated. The process is a challenging control problem due to its nonlinear and time varying dynamics. Simulated implementations of PID, adaptive and non-adaptive sliding mode and model reference adaptive controllers were developed. Tests of the closed loop systems were performed for a range of cutting conditions including specific machined part contours that are presented here to verify the force tracking capability and flexibility of each control scheme. Results indicate that careful design and use of a fixed-gain sliding mode controller with output feedback can give roughly equivalent performance to that of more complex adaptive controllers.     

State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities

This paper presents three fuzzy adaptive controllers for a class of uncertain multivariable nonlinear systems with both sector nonlinearities and dead zones: two first controllers are state feedbacks and the last controller is an output feedback. The design of the first controller concerns systems with symmetric and positive definite control–gain matrix, while the second control design is extended to the case of nonsymmetric control–gain matrix thanks to an appropriate decomposition, namely the product of a symmetric positive definite matrix, a diagonal matrix with diagonal entries +1 or ?1, and a unity upper triangular matrix. The third controller is an output feedback extension of the second controller. In this controller, a high-gain observer is incorporated to estimate the unmeasurable states. An appropriate adaptive fuzzy logic system is used to reasonably approximate the uncertain functions. A Lyapunov approach is adopted to derive the parameter adaptation laws and prove the stability of those control systems as well as the exponential convergence of their underlying tracking errors within an adjustable region. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.     

New hybrid adaptive neuro-fuzzy algorithms for manipulator control with uncertainties–Comparative study

Control of an industrial robot includes nonlinearities, uncertainties and external perturbations that should be considered in the design of control laws. In this paper, some new hybrid adaptive neuro-fuzzy control algorithms (ANFIS) have been proposed for manipulator control with uncertainties. These hybrid controllers consist of adaptive neuro-fuzzy controllers and conventional controllers. The outputs of these controllers are applied to produce the final actuation signal based on current position and velocity errors. Numerical simulation using the dynamic model of six DOF puma robot arm with uncertainties shows the effectiveness of the approach in trajectory tracking problems. Performance indices of RMS error, maximum error are used for comparison. It is observed that the hybrid adaptive neuro-fuzzy controllers perform better than only conventional/adaptive controllers and in particular hybrid controller structure consisting of adaptive neuro-fuzzy controller and critically damped inverse dynamics controller.     

Controller Parameter Tuning of Delta Robot Based on Servo Identification

High-speed pick-and-place parallel robot is a system where the inertia imposed on the motor shafts is real-time changing with the system configurations.High quality of computer control with proper controller parameters is conducive to overcoming this problem and has a significant effect on reducing the robot’s tracking error.By taking Delta robot as an example,a method for parameter tuning of the fixed gain motion controller is presented.Having identifying the parameters of the servo system in the frequency domain by the sinusoidal excitation,the PD+feedforward control strategy is proposed to adapt to the varying inertia loads,allowing the controller parameters to be tuned by minimizing the mean square tracking error along a typical trajectory.A set of optimum parameters is obtained through computer simulations and the effectiveness of the proposed approach is validated by experiments on a real prototype machine.Let the traveling plate undergoes a specific trajectory and the results show that the tracking error can be reduced by at least 50%in comparison with the conventional auto-tuning and Z-N methods.The proposed approach is a whole workspace optimization and can be applied to the parameter tuning of fixed gain motion controllers.     

An accurate system for onsite calibration of electronic transformers with digital output

Calibration systems with digital output are used to replace conventional calibration systems because of principle diversity and characteristics of digital output of electronic transformers. But precision and unpredictable stability limit their onsite application even development. So fully considering the factors influencing accuracy of calibration system and employing simple but reliable structure, an all-digital calibration system with digital output is proposed in this paper. In complicated calibration environments, precision and dynamic range are guaranteed by A/D converter with 24-bit resolution, synchronization error limit is nanosecond by using the novelty synchronization method. In addition, an error correction algorithm based on the differential method by using two-order Hanning convolution window has good inhibition of frequency fluctuation and inter-harmonics interference. To verify the effectiveness, error calibration was carried out in the State Grid Electric Power Research Institute of China and results show that the proposed system can reach the precision class up to 0.05. Actual onsite calibration shows that the system has high accuracy, and is easy to operate with satisfactory stability.     

Extension of IMC tuning correlations for non-self regulating (integrating) processes

The filter term of a PID with Filter controller reduces the impact of measurement noise on the derivative action of the controller. This impact is quantified by the controller output travel defined as the total movement of the controller output per unit time. Decreasing controller output travel is important to reduce wear in the final control element. Internal Model Control (IMC) tuning correlations are widely published for PI, PID, and PID with Filter controllers for self regulating processes. For non-self regulating (or integrating) processes, IMC tuning correlations are published for PI and PID controllers but not for PID with Filter controllers. The important contribution of this work is that it completes the set of IMC tuning correlations with an extension to the PID with Filter controller for non-self regulating processes. Other published correlations (not based upon the IMC framework) for PID with Filter controllers fix the filter time constant at one-tenth the derivative time regardless of the model of the process. In contrast, the novel IMC correlations presented in this paper calculate a filter time constant based upon the model of the process and the user's choice for the closed-loop time constant. The set point tracking and disturbance rejection performance of the proposed IMC tunings is demonstrated using simulation studies and a bench-scale experimental system. The proposed IMC tunings are shown to perform as well as various PID correlations (with and without a filter term) while requiring considerably less controller action.     

Ultra-precise tracking control of piezoelectric actuators via a fuzzy hysteresis model

In this paper, a novel Takagi-Sugeno (T-S) fuzzy system based model is proposed for hysteresis in piezoelectric actuators. The antecedent and consequent structures of the fuzzy hysteresis model (FHM) can be, respectively, identified on-line through uniform partition approach and recursive least squares (RLS) algorithm. With respect to controller design, the inverse of FHM is used to develop a feedforward controller to cancel out the hysteresis effect. Then a hybrid controller is designed for high-performance tracking. It combines the feedforward controller with a proportional integral differential (PID) controller favourable for stabilization and disturbance compensation. To achieve nanometer-scale tracking precision, the enhanced adaptive hybrid controller is further developed. It uses real-time input and output data to update FHM, thus changing the feedforward controller to suit the on-site hysteresis character of the piezoelectric actuator. Finally, as to 3 cases of 50 Hz sinusoidal, multiple frequency sinusoidal and 50 Hz triangular trajectories tracking, experimental results demonstrate the efficiency of the proposed controllers. Especially, being only 0.35% of the maximum desired displacement, the maximum error of 50 Hz sinusoidal tracking is greatly reduced to 5.8 nm, which clearly shows the ultra-precise nanometer-scale tracking performance of the developed adaptive hybrid controller.