Applications of integrated motion controllers for precise CNC machines

The error resources of precise motion control systems are basically categorized into linear and nonlinear effects. To realize the precise motion of industrial computer numerical control (CNC) machines, this paper presents an integrated motion control structure with modular algorithms, including both the linear control and the nonlinear compensation. In the linear control design, this study applies three algorithms: (1) feedforward control to address the tracking errors, (2) cross-coupled control to reduce the contouring errors, and (3) digital disturbance observer to lessen the effects of modeling errors and disturbances in real applications. The results indicate that the linear motion controller achieves greatly improved accuracy in both tracking and contouring by reducing the servo lags and mismatched dynamics of the different axes. However, the adverse effect due to friction still exists and cannot be eliminated by applying the linear motion controller only. This study further integrates the nonlinear compensator and develops friction estimation and compensation rules for CNC machines. The digital signal processors are suitable to implement all the developed linear and nonlinear algorithms, and the present controllers have been successfully applied to industrial CNC machines. Experimental results on a vertical machining center indicate that, under different feed rates, the CNC machine with the integrated motion controller significantly reduces the maximum contouring error by 135% on average.     

基于DSP的机械臂约束预测控制系统设计

针对机械臂的实时控制问题,基于约束预测控制,提出了一种机械臂实时运动控制方法。介绍了机械臂动力学模型并进行了线性化处理,以降低算法复杂度、保证实时性。设计了轨迹跟踪控制器和约束预测控制器,其中轨迹跟踪控制器采用最优反馈控制律,可确保机械臂按参考轨迹运动;而约束预测控制器则在考虑机械臂物理约束的情况下,为跟踪控制器提供最优参考轨迹。以DSP作为核心控制器,搭建了机械臂控制系统,同时给出了硬件和软件设计方法。以梯形和三次多项式轨迹为例,进行了系统功能测试,测试结果表明了所述控制系统的可行性和有效性。     

一种双轴直驱平台新型同步渐近跟踪控制设计

针对双轴直驱平台伺服系统中存在同步进给的问题,提出一种交叉耦合迭代学习控制器与自适应加加速度控制器相结合的新型同步控制方法。首先,构建同步误差,利用交叉耦合控制器解决双轴的耦合问题;设计自适应PD型学习律减小同步误差,实现双轴协调同步。采用模型前馈控制补偿系统的参数不确定性,提高系统的响应速度。自适应加加速度控制器抑制系统中外部扰动、摩擦力等不确定性因素,实现系统的渐近跟踪控制。加加速度积分后形成反馈控制律,保证了控制信号的稳定性和连续性。设计自适应更新律,使鲁棒增益实现指数收敛并削弱测量噪声对系统的影响,增强系统的鲁棒性。系统实验结果表明,该方法能够明显地提高系统的同步性能,改善双轴直驱平台伺服系统的控制精度。     

Experimental implementation of Taylor series expansion error compensation on a bi-axial CNC machine

In this paper, a new model-based Taylor series expansion error compensation (TSEEC) strategy is proposed to improve the contouring accuracy for computer numerically controlled (CNC) machines. In TSEEC, the contour error compensation problem is formulated as a Taylor series expansion problem, in which the value of the contour error is expanded around the reference points and the compensation components are calculated as the deviations from the reference points. Simulations show that, with perfect knowledge of the axial dynamics, zero contour errors can be achieved with TSEEC for both linear and circular contours. Due to modeling errors, external disturbances, and measurement noise, some modifications and experimentation need to be made to determine suitable parameters for implementation of the TSEEC scheme on a real machine. These measurements include a low-pass filter, a choice of a compensation target, and a compensation gain. Experimental results show the effectiveness of TSEEC in reducing contour errors and demonstrate the superiority of TSEEC over inverse feedforward compensation and cross-coupled control in improving the contouring accuracy.     

Adaptive backstepping-based tracking control design for nonlinear active suspension system with parameter uncertainties and safety constraints

This paper proposes a novel constraint adaptive backstepping based tracking controller for nonlinear active suspension system with parameter uncertainties and safety constraints. By introducing the virtual control input and reference trajectories, the adaptive control law is developed to stabilize both of the vertical and pitch motions of vehicle body using backstepping technique and Lyapunov stability theory, and further to track the predefined reference trajectories within a finite time, which not only ensure the safety performance requirements, but also achieve improvements in riding comfort and handling stability of vehicle active suspension system. Next, the stability analysis on zero dynamics error system is conducted to ensure that all the safety performance indicators are all bounded and the corresponding upper bounds are estimable. Finally, a numerical simulation is provided to verify the effectiveness of the proposed controller and to address the comparability between the classical Barrier–Lyapunov Function based adaptive tracking controller and the proposed controller.     

高质量加工中四次多项式速度规划算法研究

通过分析数控机床加工时常用的速度规划算法,针对加工过程中由于加速/减速时速度不平滑、加速度及加加速度突变导致数控机床振动的问题,提出一种四次多项式加减速控制方法,并给出了四次速度方程的详细推导步骤,然后介绍了基于四次多项速度规划的参数曲线插补方法。该方法能保证数控机床在高速加工过程中的速度、加速度及加加速度实现连续变化,缓解高速加工产生的过冲。仿真实验表明,四次多项式速度规划算法能够使机床实现柔性加减速控制,从而满足高质量加工的要求。     

基于可变预测时域及速度的车辆路径跟踪控制

非线性模型预测控制(NMPC)在车辆路径跟踪控制中的应用日益广泛,但目前的研究成果中尚未深入考虑预测时域和速度对车辆路径跟踪控制性能的影响。为此,分析了预测时域、速度与车辆路径跟踪控制性能之间的关系;采用三次多项式拟合获得了能够保证车辆路径跟踪横向误差小于0.1 m的最佳预测时域和参考速度的控制律;改进了用于车辆路径跟踪控制的NMPC控制器,且改进后的NMPC控制器的性能通过仿真进行了验证。仿真结果表明:改进后的NMPC控制器的横向误差在0.092 8 m以内,航向误差在0.072 4 rad以内。相比传统NMPC控制器,改进后的NMPC控制器将最大横向误差减小了4.267 1 m以上,将最大航向误差减小了0.392 7 rad以上,路径跟踪控制性能得到了较大幅度的提高。     

Electronic cam motion generation with special reference to constrained velocity, acceleration, and jerk

Electronic cam motion involves velocity tracking control of the master motor and trajectory generation of the slave motor. Special concerns such as the limits of the velocity, acceleration, and jerk are beyond the considerations in the conventional electronic cam motion control. This study proposes the curve-fitting of a Lagrange polynomial to the cam profile, based on trajectory optimization by cubic B-spline interpolation. The proposed algorithms may yield a higher tracking precision than the conventional master-slaves control method does, providing an optimization problem is concerned. The optimization problem contains three dynamic constraints including velocity, acceleration, and jerk of the motor system.     

Sensorless jerk monitoring using an adaptive antisymmetric high-order FIR filter

In the computerized numerical controllers (CNC) machine-tool processes many finishing and wear problems are related to jerk (derivative of acceleration). Since jerk sensors are expensive and scarce, a sensorless approach is presented as novelty. By taking the incoming signal from a digital incremental encoder included in the standard servo-loop of a CNC machine, the jerk is calculated with a new digital signal processing technique. The contribution of this work focuses on a simple high-order FIR filter with an adaptive algorithm that makes it possible to extract the jerk from the digital position measurement in a sensorless fashion. The algorithm reaches a good approximation to the expected jerk shape by overcoming the intrinsic quantization noise in the digital measurement and the changing dynamical conditions of a real machining process. The algorithm is tested on simulations and over one real CNC machine achieving great similarity between analytical and monitored jerk. It preserves most of the important jerk characteristics like peaks and coarse shape, getting a maximum of 2% of average jerk error on simulations, and 5% of average jerk error on real experiments. This computational efficient algorithm reaches a processing rate up to 760,000 samples per second in an FPGA implementation, which makes it suitable for high speed applications.     

Cascade control of superheated steam temperature with neuro-PID controller

In this paper, an improved cascade control methodology for superheated processes is developed, in which the primary PID controller is implemented by neural networks trained by minimizing error entropy criterion. The entropy of the tracking error can be estimated recursively by utilizing receding horizon window technique. The measurable disturbances in superheated processes are input to the neuro-PID controller besides the sequences of tracking error in outer loop control system, hence, feedback control is combined with feedforward control in the proposed neuro-PID controller. The convergent condition of the neural networks is analyzed. The implementation procedures of the proposed cascade control approach are summarized. Compared with the neuro-PID controller using minimizing squared error criterion, the proposed neuro-PID controller using minimizing error entropy criterion may decrease fluctuations of the superheated steam temperature. A simulation example shows the advantages of the proposed method.     

Data-driven model reference control of MIMO vertical tank systems with model-free VRFT and Q-Learning

This paper proposes a combined Virtual Reference Feedback Tuning–Q-learning model-free control approach, which tunes nonlinear static state feedback controllers to achieve output model reference tracking in an optimal control framework. The novel iterative Batch Fitted Q-learning strategy uses two neural networks to represent the value function (critic) and the controller (actor), and it is referred to as a mixed Virtual Reference Feedback Tuning–Batch Fitted Q-learning approach. Learning convergence of the Q-learning schemes generally depends, among other settings, on the efficient exploration of the state-action space. Handcrafting test signals for efficient exploration is difficult even for input-output stable unknown processes. Virtual Reference Feedback Tuning can ensure an initial stabilizing controller to be learned from few input-output data and it can be next used to collect substantially more input-state data in a controlled mode, in a constrained environment, by compensating the process dynamics. This data is used to learn significantly superior nonlinear state feedback neural networks controllers for model reference tracking, using the proposed Batch Fitted Q-learning iterative tuning strategy, motivating the original combination of the two techniques. The mixed Virtual Reference Feedback Tuning–Batch Fitted Q-learning approach is experimentally validated for water level control of a multi input-multi output nonlinear constrained coupled two-tank system. Discussions on the observed control behavior are offered.     

运动控制中点到点控制曲线的性能研究

计算了点到点运动控制中能量最优的速度轮廓——抛物线速度轮廓。分析了常用的梯形速度曲线和S型速度曲线。以S型速度曲线为参照对象，分析了三角函数型速度曲线和高阶多项式插值曲线的加速度以及加加速度的特性。     

Precision tracking control of a horizontal arm coordinate measuring machine in the presence of dynamic flexibilities

One of the major sources that affect measurement accuracy and limit the use of high motion speeds in coordinate measuring machines (CMM) is the position error. In fact, static and dynamic probe errors are more direct factors in measuring machine accuracy, but are not the subject of this research. However the accuracy of acquisition of component position errors using a CMM in motion is also of importance, hence the dynamics of a CMM need to be considered. Therefore, this research aims to model the dynamics of a horizontal arm CMM by considering drive flexibility at joints and evaluates the characteristics of the system for fine motion control purposes. Design of a precision tracking controller (PTC) to perform superior tracking for enhancing the measurement accuracy and the probing speed in providing less inspection time at high motion speeds is carried out. A dynamic model for the CMM is developed including drive flexibilities represented with lumped springs at the joints. Due to the non-collocated nature of the control scheme in the flexible CMM dynamics, a non-minimum phase system is observed in the proposed CMM model. Using the derived CMM model with joint flexibilities, tracking motion control simulations are conducted at different probing speeds for the cases where a PI controller and a feedback PTC are employed. A comparison of the PI controller with the feedback PTC is also performed. Results demonstrate that the effects of joint flexibilities on the contour error and probing speeds are significant and the PI controller is not capable of providing good accuracy during challenging tasks such as corner tracking. However, the simulation results indicated that by using the proposed feedback precision tracking controller, contour errors in corner tracking that are caused by joint flexibilities can be reduced effectively .     

Robust integral of neural network and precision motion control of electrical–optical gyro-stabilized platform with unknown input dead-zones

Parametric uncertainty associated with unmodeled disturbance always exist in physical electrical–optical gyro-stabilized platform systems, and poses great challenges to the controller design. Moreover, the existence of actuator deadzone nonlinearity makes the situation more complicated. By constructing a smooth dead-zone inverse, the control law consisting of the robust integral of a neural network (NN) output plus sign of the tracking error feedback is proposed, in which adaptive law is synthesized to handle parametric uncertainty and RISE robust term to attenuate unmodeled disturbance. In order to reduce the measure noise, a desired compensation method is utilized in controller design, in which the model compensation term depends on the reference signal only. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded (GUUB) tracking stability of servo systems recently. An asymptotic tracking performance in the presence of unknown dead-zone, parametric uncertainties and various disturbances, which is vital for high accuracy tracking, is achieved by the proposed robust adaptive backstepping controller. Extensively comparative experimental results are obtained to verify the effectiveness of the proposed control strategy.     

Experimental performance analysis of an inverse dynamics CNC compensation scheme for high-speed execution of curved toolpaths

Experimental results from the implementation of an inverse dynamics compensation scheme on a three-axis CNC mill with an open-architecture software controller are presented. The scheme amounts to imposing a continuously variable displacement on the commanded toolpath, which compensates for the physical limitations (inertia and damping) of each machine axis, producing accurate execution of the prescribed toolpath. Numerical values for the dimensionless parameters that characterize the second-order inverse dynamics model are determined by feeding input and output data from machine runs into a system identification software tool. For a basic P-type controller, exact a priori solutions for the modified path geometry are possible, allowing implementation by simple alterations to the real-time interpolator. The experimental results based on a P-type controller indicate that the inverse dynamics scheme is highly effective in suppressing both feed (lag/lead) error and contour error (deviation from the desired path), even at high feedrates along strongly curved toolpaths. The scheme thus provides a practical means of achieving smooth and accurate execution of free-form paths, without appealing to more complicated “active” control strategies.     

Analysis and experiments of iterative learning-control system with uncertain dynamics

An iterative error compensation approach is proposed in this article to improve the accuracies of high speed, computer-controlled machining processes. It is well known that the high-speed computer-numerically-controlled (CNC) machines are extremely useful in terms of manufacturing mass-produced parts. The proposed method uses an iterative learning technique that adopts the servo commands and cutting error experienced in previous maneuvers as references to current compensative actions. Moreover, non-repetitive disturbances and nonlinear dynamics of the cutting processes, and servo systems of the CNC machine that greatly affect the convergence of the learning-control systems were also studied in this research. State feedback and output feedback techniques were adopted in the proposed controller design. In addition to the stability analysis, a 1 degree-of-freedom servo positioning system is constructed to evaluate the performance of our proposed learning control approach. Both the simulation and experimental results verify the effectiveness of our approach.     

数控运动中加加速度连续的加减速方法

为保证机床运动的平滑性,减少数控机床冲击与振动的影响,研究了数控机床动力学数学模型,从理论上分析造成机床冲击与振动的根源;提出一种加加速度连续的加减速方法,推导了运动轮廓不同阶段的运动表达式;对该加减速算法进行了合理简化,以满足数控系统实时性要求;利用搭建的数控试验台对S曲线加减速方法和本文所研究加减速方法作进行了对比。结果表明,所研究方法可使轮廓运动更加平滑,更具柔性,但运行时间略长。     

Design and accuracy analysis of a metamorphic CNC flame cutting machine for ship manufacturing

The current research of processing large size fabrication holes on complex spatial curved surface mainly focuses on the CNC flame cutting machines design for ship hull of ship manufacturing. However, the existing machines cannot meet the continuous cutting requirements with variable pass conditions through their fixed configuration, and cannot realize high-precision processing as the accuracy theory is not studied adequately. This paper deals with structure design and accuracy prediction technology of novel machine tools for solving the problem of continuous and high-precision cutting. The needed variable trajectory and variable pose kinematic characteristics of non-contact cutting tool are figured out and a metamorphic CNC flame cutting machine designed through metamorphic principle is presented. To analyze kinematic accuracy of the machine, models of joint clearances, manufacturing tolerances and errors in the input variables and error models considering the combined effects are derived based on screw theory after establishing ideal kinematic models. Numerical simulations, processing experiment and trajectory tracking experiment are conducted relative to an eccentric hole with bevels on cylindrical surface respectively. The results of cutting pass contour and kinematic error interval which the position error is from –0.975 mm to +0.628 mm and orientation error is from –0.01 rad to +0.01 rad indicate that the developed machine can complete cutting process continuously and effectively, and the established kinematic error models are effective although the interval is within a ‘large' range. It also shows the matching property between metamorphic principle and variable working tasks, and the mapping correlation between original designing parameters and kinematic errors of machines. This research develops a metamorphic CNC flame cutting machine and establishes kinematic error models for accuracy analysis of machine tools.     

重复学习控制及其在机械工程中的应用

介绍重复学习控制的基本原理，简要回顾近年来重复学习控制的研究发展状况，从连续和离散系统两方面给出了系统稳定性、静态跟踪特性等方面的结论；列举其在机器人、机床、磁盘驱动器、轧钢机等方面的应用；最后给出其在直线伺服单元中的应用实例。     

RTDS implementation of an improved sliding mode based inverter controller for PV system

This paper proposes a novel approach for testing dynamics and control aspects of a large scale photovoltaic (PV) system in real time along with resolving design hindrances of controller parameters using Real Time Digital Simulator (RTDS). In general, the harmonic profile of a fast controller has wide distribution due to the large bandwidth of the controller. The major contribution of this paper is that the proposed control strategy gives an improved voltage harmonic profile and distribute it more around the switching frequency along with fast transient response; filter design, thus, becomes easier. The implementation of a control strategy with high bandwidth in small time steps of Real Time Digital Simulator (RTDS) is not straight forward. This paper shows a good methodology for the practitioners to implement such control scheme in RTDS. As a part of the industrial process, the controller parameters are optimized using particle swarm optimization (PSO) technique to improve the low voltage ride through (LVRT) performance under network disturbance. The response surface methodology (RSM) is well adapted to build analytical models for recovery time (R_t), maximum percentage overshoot (MPOS), settling time (T_s), and steady state error (E_ss) of the voltage profile immediate after inverter under disturbance. A systematic approach of controller parameter optimization is detailed. The transient performance of the PSO based optimization method applied to the proposed sliding mode controlled PV inverter is compared with the results from genetic algorithm (GA) based optimization technique. The reported real time implementation challenges and controller optimization procedure are applicable to other control applications in the field of renewable and distributed generation systems.