Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system

In this paper, the time-optimal feedrate planning problem under confined feedrate, axis velocity, axis acceleration, axis jerk, and axis tracking error for a high-order CNC servo system is studied. The problem is useful in that the full ability of the CNC machine is used to enhance the machining productivity while keeping the machining precision under a given level. However, the problem is computationally challenging. The main contribution of this paper is to approximate the problem nicely by a finite-state convex optimization problem which can be solved efficiently. The method consists of two key ingredients. First, a relationship between the tracking error and the input signal in a high-order CNC servo system is established. As a consequence, the tracking error constraint is reduced to a constraint on the kinematic quantities. Second, a novel method is introduced to relax the nonlinear constraints on kinematic quantities to linear ones. Experimental results are used to validate the proposed method.     

输入受限下自主水下航行器路径跟踪的级联控制

针对自主水下航行器的路径跟踪控制问题,首先,将基于路径坐标系和虚拟向导概念建立的跟踪误差方程转换成一种新的级联系统表示形式,该级联系统由一个位置误差名义系统和与之级联的速度和航向误差子系统组成,与常规控制器求解相比,解耦了位置误差与速度和航向误差子系统;其次,利用滤波反步法对速度和航向子系统进行求解,避免了反步法对虚拟控制量解析求导引起的“计算膨胀”的不足,并通过构造辅助系统对滤波误差和输入受限下的控制量残差进行补偿,基于李雅普诺夫稳定性理论保证了速度和航向子系统的有界收敛;再次,通过级联系统理论证明闭环跟踪误差系统所有信号的一致最终有界;最后,通过仿真实验验证所提级联控制的有效性.     

A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length

There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profile with desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processes which make generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ahead trajectory generation method which determines the deceleration stage according to the fast estimated arc length and the reverse interpolation of each curve at every sampling time. This results in a feedrate trajectory generation with jerk-limited acceleration profiles for the NURBS curves. The feedrate profile is adjusted dynamically according to the geometrical path constraint determined by chord error for the curved path. A NURBS curve by two different kinematics conditions was used as a means to test the feasibility of the developed interpolation scheme and command generator.     

ANALYSIS AND DESIGN OF FEEDBACK CONTROL SYSTEMS WITH TRACKING ERRORS SQUARE

In this study, a command tracking error square control scheme is first proposed for analysis and design of feedback control systems. One of the tracking errors is low‐pass filtered and used in the feedback loop for gain adaptation; the other is used in the forward loop for command tracking control. The overall systems are nonlinear feedback systems, and can be reconfigured to an automatic gain control (AGC) loop with command tracking error input. The stability and robustness of the controlled systems are verified by time response, frequency response, and large parameter variation testing with a simple illustrating example and are finally applied to a complicated electro‐hydraulic velocity servo system with large load disturbance.     

Robust tracking in nonlinear systems

A nonlinear feedback multivariable controller is used to implement multivariable tracking in a nonlinear system. The tracking error is measured by a general function of system state and the input command. The controller is robust in the sense that the tracking error is ultimately bounded in the presence of modeling errors. Free parameters, which affect the form of the controller, allow flexibility in determining such factors as: the size of the ultimate bound, the rate of error decay, excursion of the control, conditions on the class of modeling errors, and the level of system gain. Restrictive assumptions on the structure of the model and the modeling errors are required but they are treated in a transformation framework which allows the generalization of similar conditions which appear in the prior literature. These assumptions hold for robotic manipulators. This application is investigated at some length and it appears that the resulting control scheme may have advantages over others which have been proposed in the robotics literature.     

Feedback control of tri-layer polymer actuators to improve their positioning ability and speed of response

Improving positioning ability of electroactive polymer actuators typified by polypyrrole (PPy) through feedback control of their position has been considered. The actuators operate in air, as opposed to their predecessors. One of the problems associated with the actuators is the forward relaxation/creep or drift, which occurs after the full reduction and oxidation processes are completed. A high-resolution laser displacement sensor was used to detect the position of the cantilever-type polymer actuators and the classical, yet effective, Proportional, Integral and Derivative (PID) control method has been employed to generate the appropriate control input in order to make sure that no drift occurs in the user-specified position of the actuators. A set of experimental results with and without feedbacking the position data are presented to demonstrate the efficacy of the control method for improving the positioning ability and the speed of response. The rise time is reduced by more than 500 times and the position tracking error is less than 10% for a time-varying user-specified position command.     

Iterative learning control and repetitive control for engineering practice

This paper discusses linear iterative learning and repetitive control, presenting general purpose control laws with only a few parameters to tune. The method of tuning them is straightforward, making tuning easy for the practicing control engineer. The approach can then serve the same function for learning/repetitive control, as PID controllers do in classical control. Anytime one has a controller that is to perform the same tacking command repeatedly, one simply uses such a law to adjust the command given to an existing feedback controller and achieves a substantial decrease in tracking error. Experiments with the method show that decreases by a factor between 100 and 1000 in the RMS tracking error on a commercial robot, performing a high speed trajectory can easily be obtained in 8 to 12 trials for learning. It is shown that in engineering practice, the same design criteria apply to learning control as apply to repetitive control. Although the conditions for stability are very different for the two problems, one must impose a good transient condition, and once such a condition is formulated, it is likely to be the same for both learning and repetitive control.     

Command shaping control for micro-milling operations

Micro milling requires both high speed and high accuracy in order to economically produce parts with features on the scale of 1 μm. Micro mills are smaller and more flexible than traditional large-scale machines. Therefore, vibration of the machine structure is a significant problem. Given that micro milling requires high positioning precision, even small vibrations in the controller dynamics are problematic. The small-scale operation has considerably lower tool/workpiece interaction forces than traditional-scale milling. These low cutting forces have minimal effect on the machine structural response. Therefore, the dominant dynamic factor in exciting vibration can be the machine tool motion, rather than the workpiece/tool interaction. Given this realization, properly shaping the motions of the micro mill is a promising approach to reduce vibration. This paper presents a nonlinear command-shaping technique to reduce the vibrations of a micro mill that can be implemented with a standard CNC controller. The robustness of this technique to modeling errors and disturbances is investigated. Theoretical proofs and experimental demonstrations of the command-shaping technique are presented. The improved performance from the command shaping enables higher throughput and improved accuracy of the micro mill.     

Experimental evaluation of dialogue types for data entry

An experiment evaluating four basic types of data entry dialogue with regard to speed showed a clear interaction between type of dialogue and type of data. A form-based dialogue was fastest for many ordered data, while a command dialogue was faster for unordered data. There was no significant difference between the number of errors at each dialogue type. The lowest performance times across data types were reached with an extended command dialogue with a built-in facility for command-less, ordered input. This dialogue type gave low performance times for all data types. A study of the subjects' preference regarding interaction mode in the command dialogues showed that most subjects preferred an interaction mode which optimized speed at the cost of less feedback and less opportunity for error control. This can be expressed in terms of dialogue gears: a majority of the subjects chose a high gear of interaction. This did not, however, result in a higher error rate for those subjects.     

Experimental study of contouring accuracy for CNC machines executing curved paths with constant and curvature-dependent feedrates

Experiments to measure and improve the contouring accuracy of CNC machines executing curved paths with strong curvature and variations of curvature at high feedrates are reported, using P and PI controllers with a wide range of gains. The experiments are based on test curves exhibiting (a) a steady increase of curvature; (b) a periodic curvature variation between fixed minima and maxima; and (c) a sudden “spike” in the curvature profile. For the P controller, the curvature-dependent feedrate yields a diminution of the contour error by up to an order of magnitude, compared to constant feedrate. The curvature-dependent feedrate appears to be most advantageous in situations exemplified by case (c), since it affords a dramatic suppression of local contour error with a modest increase in traversal time. Moreover, the improvement in contour accuracy is relatively insensitive to the P gain. The results are less predictable when the curvature-dependent feedrate is used in conjunction with PI control, because of its more “active” response to the excitation arising from the varying path geometry and feedrate.     

基于参考输入优化的变速风电机组最大化风能捕获方法

变速风电机组在额定风速以下应用最大功率点跟踪实现最大化风能捕获. 然而, 大惯量风电机组在面对快 速波动的湍流风速时, 因转速调节慢而难以保持运行于最大功率点. 本文研究进一步发现, 平均转速跟踪误差与整 体的风能捕获效率并非单调关系, 这使得当前以减小转速跟踪误差为目标的控制器设计难以有效提升风电机组的 发电效率. 为此, 本文以提升风能捕获效率(而非减小转速跟踪误差)为目标, 提出一种基于参考输入优化的风电机 组最大化风能捕获方法. 考虑到参考转速对风能捕获效率的复杂影响难以准确建模, 本文借助深度确定性策略梯度 (DDPG)强化学习算法实现参考输入优化. 仿真结果表明该方法能够有效提升湍流风下变速风电机组的风能捕获效 率.     

Iterative learning control for integrated system of robot and machine tool

This study is concerned with the integrated system of a robot and a machine tool. The major task of robot is loading the workpiece to the machine tool for contour cutting. An iterative learning control (ILC) algorithm is proposed to improve the accuracy of the finished product. The proposed ILC is to modify the input command of the next machining cycle for both robot and machine tool to iteratively enhance the output accuracy of the robot and machine tool. The modified command is computed based on the current tracking/contour error. For the ILC of the robot, tracking error is considered as the control objective to reduce the tracking error of motion path, in particular, the error at the endpoint. Meanwhile, for the ILC of the machine tool, contour error is considered as the control objective to improve the contouring accuracy, which determines the quality of machining. In view of the complicated contour error model, the equivalent contour error instead of the actual contour error is taken as the control objective in this study. One challenge for the integrated system is that there exists an initial state error for the machine tool dynamics, violating the basic assumption of ILC. It will be shown in this study that the effects of initial state error can be significantly reduced by the ILC of the robot. The proposed ILC algorithm is verified experimentally on an integrated system of commercial robot and machine tool. The experimental results show that the proposed ILC can achieve more than 90% of reduction on both the RMS tracking error of the robot and the RMS contour error of the machine tool within six learning iterations. The results clearly validate the effectiveness of the proposed ILC for the integrated system.     

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and the predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and the predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.      

Adaptive-feedrate interpolation for parametric curves with a confined chord error

Recently, modern manufacturing systems have been designed which can machine arbitrary parametric curves while greatly reducing data communication between CAD/CAM and CNC systems. However, a constant feedrate and chord accuracy between two interpolated points along parametric curves are generally difficult to achieve due to the non-uniform map between curves and parameters. A speed-controlled interpolation algorithm with an adaptive feedrate is proposed in this paper. Since the chord error in interpolation depends on the curve speed and the radius of curvature, the feedrate in the proposed algorithm is automatically adjusted so that a specified limit on the chord error is met. Both simulation and experimental results for non-uniform rational B-spline (NURBS) examples are provided to verify the feasibility and precision of the proposed interpolation algorithm.     

The feedrate scheduling of NURBS interpolator for CNC machine tools

This paper proposes an off-line feedrate scheduling method of CNC machines constrained by chord tolerance, acceleration and jerk limitations. The off-line process for curve scanning and feedrate scheduling is realized as a pre-processor, which releases the computational burden in real-time task. The proposed method first scans a non-uniform rational B-spline (NURBS) curve and finds out the crucial points with large curvature (named as critical point) or G⁰ continuity (named as breakpoint). Then, the NURBS curve is divided into several NURBS sub-curves using curve splitting method which guarantees the convergence of predictor–corrector interpolation (PCI) algorithm. The suitable feedrate at critical point is adjusted according to the limits of chord error, centripetal acceleration and jerk, and at breakpoint is adjusted based on the formulation of velocity variation. The feedrate profile corresponding to each NURBS block is constructed according to the block length and the given limits of acceleration and jerk. In addition, feedrate compensation method for short NURBS blocks is performed to make the jerk-limited feedrate profile more continuous and precise. Because the feedrate profile is established in off-line, the calculation of NURBS interpolation is extremely efficient for CNC high-speed machining. Finally, simulations and experiments with two free-form NURBS curves are conducted to verify the feasibility and applicability of the proposed method.     

受限指令预设性能自适应反演控制器设计

针对一类含参数不确定性的输入和状态受限的非线性系统,提出一种受限指令预设性能自适应反演控制器设计方法.采用自适应反演方法,同时考虑输入和状态受限构建受限指令滤波器,以解决“计算膨胀”的问题;引入伪控制减缓方法对误差进行补偿;最后考虑了补偿跟踪误差的瞬态性能.通过Lyapunov理论对所设计的控制器进行稳定性分析,并通过仿真实例验证了所提出方法的正确性和有效性.     

Finite-time command filter-based adaptive tracking control for nonstrict feedback nonlinear systems with full-state restrictions and unmodeled dynamics

The finite-time command filter tracking control for a class of nonstrictly feedback nonlinear systems with unmodeled dynamics and full-state constraints is investigated in this paper. The hyperbolic tangent function is used as a nonlinear mapping technique to solve the obstacle of the full-state constraints. A new adaptive finite time control method is proposed through command filtering reverse engineering, and the shortcomings of the dynamic surface control (DSC) method are overcome by the error compensation mechanism. Dynamic signal is designed to handle dynamical uncertain terms. Normalization signal is designed to handle input unmodeled dynamics. Unknown nonlinear functions are approximated by radial basis function neural networks. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop system are semi-globally consistent and finally bounded and the output tracking error converges in finite time. Two numerical examples are utilized to verify the effectiveness of the proposed control approach.     

Command-induced vibration analysis using input shaping principles

Input shaping is a well-established technique used for reducing the vibratory response of dynamic systems. Analytical tools are available for systems utilizing input shaping. These tools aid in performance analysis by providing intuitive and computationally simple methods for determining key system attributes, such as the residual vibration in response to a command. This paper describes methods whereby arbitrary reference commands may be interpreted as input-shaped commands. This capability allows input shaping analysis tools to be used on systems without input shapers. Experimental results obtained from an industrial 10-ton bridge crane validate the theoretical developments.     

An output-based adaptive iterative learning controller for high relative degree uncertain linear systems

In this paper, we derive an output tracking error model based on signals filtered from plant input and output, and then present a new output-based adaptive iterative learning controller for repeatable linear systems with unknown parameters, high relative degree, initial resetting error, input disturbance and output noise. The proposed controller solves the important robustness issues without assuming the bounds of uncertainties to be sufficiently small and can be applied to high relative degree plants without using output differentiation. Control parameters are updated between successive iterations so as to compensate for unknown system parameters and uncertainties. It is shown that the internal signals inside closed-loop learning system remain bounded and the output tracking error will asymptotically converge to a profile tunable by some design parameters. Furthermore, the learning speed is easily improved if the learning gain is increased.     

支持向量机和AdaBoost目标跟踪新方法

在目标跟踪领域,目标检测对跟踪的效果起决定性作用,提出一种用支持向量机进行目标跟踪的方法。采用AdaBoost算法选择最具有代表性的Harr特征,将选择出来的特征作为支持向量机训练器的输入数据来训练目标检测分类器。为了加速检测速度,使用了层叠加速检测算法。实验结果表明,该算法不但提高了识别的正确率,而且大大提高了检测速度。