Robust contouring control for biaxial feed drive systems

Contouring control is an effective method of providing precision machine tool control, and various such methods have been proposed to date. However, most existing methods require prior exact knowledge of feed drive dynamics. This paper presents a robust contouring control system design that takes into account dynamics modelling errors and disturbances such as friction. We first present a controller design for biaxial feed drive systems that enables assignment of controller gains, for reducing the error component orthogonal to the desired contour curve, independent of the tangential error component. Although this design provides better control performance with small control input variance, an inherent contour error exists because of the difficulty in calculating the exact contour error for any contour curve in real time. To address this problem, a reference adjustment method is used to estimate the actual contour error. A robust contouring controller is proposed based on the variable structure control. The effectiveness of the robust controller is demonstrated by experimental results using circular and non-circular contour curves.     

Performance robustness and stiffness analysis on a machine tool servo design

The machine tool servo design is very different from the traditional high performance servo systems. Traditional servo design depends heavily on a precise system model so that frequency domain or time domain compensation techniques can be applied, and many synthesis tools such as LQG, H_∞, or LMI, … are available based on this concept. While these synthesis tools are becoming very useful in many situations, they are not used in the machine tool servo design. Most high performance machine tool systems still rely on the more primitive PID or PDF controllers in conjunction with complicated friction and temperature compensation algorithms. This paper investigates the different approaches based on a house-designed servo control board. With the ability to change the servo control algorithms on a test machine tool, the performance robustness and servo stiffness were tested both numerically and experimentally. The numerical tests conducted with PID, PDF, and LQG controllers showed that the PID controller is the easiest to achieve good performance, but the PDF controller contains the best performance robust margin. Experimental results also indicated that the PDF controller exhibits far superior robustness properties over the other two controllers.     

多轴CNC机床耦合轮廓误差补偿方法

介绍了CNC机床耦合轮廓误差补偿方法的原理及设计方法。首先分析了非耦合的轮廓控制系统,给出了轮廓误差的定义及算法,引入了耦合轮廓控制的概念。以两轴CNC机床为例,介绍了耦合轮廓控制系统的结构及设计方法。最后讨论了耦合轮廓控制的效果及需要进一步研究的问题。     

A decoupled path-following control algorithm based upon the decomposed trajectory error

This paper proposes a new path-following control algorithm for the machine tool servo systems. The control system first decomposes the contouring error into the normal tracking error and the advancing tangential error. A dynamic decoupling procedure is then applied to the system dynamics. Finally, a dynamic decoupled controller is proposed to compensate the decomposed tangential and the normal tracking errors. The normal control minimizes the perpendicular tracking error while the tangential control maintains a desired feed rate. The proposed method is applied to the control of an experimental x–y table. Experimental results show that the proposed control can achieve good tracking and trajectory following characteristics. The new algorithm also enables the design of a non-overshooting controller along the path. This will result in a no-overcutting process for the machine tool operation.     

A two-layered cross coupling control scheme for a three-dimensional motion control system

A two-layered modeling and compensation scheme is proposed to reduce the contouring error of a three-dimensional motion control system. In the proposed scheme, the contouring error model of the three-dimensional motion control system is divided into two layers: the top layer and the bottom layer. The proposed multi-layered structure of the contouring error model presents more flexibility in the control system design because the cross coupling controllers in different layers can be designed separately. In this paper, a nonlinear PI controller and a position error compensator are designed in the bottom layer in order to achieve high contouring accuracy in the XY plane, while a unilateral compensator is designed in the top layer to further reduce contouring error in the three dimensional space. Finally, experiments are performed to verify the performance of the proposed two-layered modeling and compensation scheme. Experiment results show that the designed two-layered cross coupling controller can obtain higher contouring accuracy than traditional cross coupling controller both in the XY plane and in the XYZ space.     

Experimental investigation on high-performance coordinated motion control of high-speed biaxial systems for contouring tasks

The recently developed global task coordinate frame (TCF) is utilized to synthesize a high-performance contouring controller with cogging force compensation for a linear-motor-driven biaxial gantry to test the practically achievable high-speed/high-accuracy contouring performance. Specifically, the approach employs the global task coordinate formulation to meet the stringent control performance requirements for high-speed and large-curvature coordinated contouring tasks. Moreover, the approach explicitly takes into account the specific characteristics of cogging forces existed in linear motors for the controller design as model compensation to further improve practical contouring performance. Physically intuitive discontinuous projection modifications are used to ensure all the on-line estimates within their known bounds. Robust control terms are also constructed to effectively attenuate the effect of model compensation errors due to various uncertainties for a theoretically guaranteed transient performance and steady-state tracking accuracy in general. Comparative experiments are carried out on an industrial linear-motor-driven biaxial gantry and the results verify the effectiveness of the proposed cogging force compensations - a contouring tracking accuracy improvement of 30% is achieved. Experimental results also validate the rather excellent contouring performance of the proposed controller for high-speed/high-accuracy contouring tasks in actual implementation in spite of various parametric uncertainties and uncertain disturbances.     

Position command shaping control in a retrofitted milling machine

A position command shaping controller, hybrid structure of feedforward controller and cross-coupling controller, for accurate contouring in motion control is proposed in this paper. The feedforward controller can improve tracking performance of single axis and the cross-coupling controller guarantees the reduction in contour error for multi-axis motion. When compared with the conventional motion system, this new structure has the advantage that the compensators have a simpler design process than conventional ones and so does its stability analysis. The proposed compensators (or controllers) are evaluated and compared experimentally with a traditional controller on a microcomputer controlled dual-axis positioning system. The experimental results show that the new hybrid structure reduces remarkably the tracking error and contour error. In addition, this new controller can be implemented easily on a majority of motion systems in use today via reprogramming the reference position command subroutine.     

Adaptive two-degree-of-freedom control of feed drive systems

Feed drive systems are widely used in industrial applications, and many efforts for improving their precision control have been made thus far. One of the basic approaches for improving the control accuracy of feed drive systems is to design a controller based on the internal model principle, which states that for a control system to track a reference signal without a steady state error, it needs to include a generator of the reference signal. Feed-forward controllers, such as the zero phase error tracking controller (ZPETC) proposed by Tomizuka, are also employed for improving control performance. However, prior knowledge of plant dynamics and/or reference signal properties is required for both the internal model principle and the feed-forward controller based designs. For precision control, plant dynamics should be identified in real time because feed drive dynamics are affected by varying conditions, such as frictional and thermal effects. This paper presents a new type of adaptive control for arbitrary reference tracking, which requires neither plant dynamics nor reference signal properties for controller design. This type of controller can also reduce the effect of unknown disturbances. The control system is designed using a discrete-time plant model and consists of adaptive feed-forward and feedback controllers. This design is then applied to a feed drive system with a ball screw drive. The effectiveness of the proposed design is demonstrated by simulation and experimental results, which was obtained by applying the proposed control system to an unknown reference signal whose property is varied during control.     

A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools

Nonlinear and configuration-dependent five-axis kinematics make contouring errors difficult to estimate and control in real time. This paper proposes a generalized method for the on-line estimation and control of five-axis contouring errors. First, a generalized Jacobian function is derived based on screw theory in order to synchronize the motions of linear and rotary drives. The contouring error components contributed by all active drives are estimated through interpolated position commands and the generalized Jacobian function. The estimated axis components of contouring errors are fed back to the position commands of each closed loop servo drive with a proportional gain. The proposed contouring error estimation and control methods are general, and applicable to arbitrary five-axis tool paths and any kinematically admissible five-axis machine tools. The proposed algorithms are verified experimentally on a five-axis machine controlled by a modular research CNC system built in-house. The contouring errors are shown to be reduced by half with the proposed method, which is simple to implement in existing CNC systems.     

Intelligent cross-coupled fuzzy feedrate controller design for CNC machine tools based on genetic algorithms

In this paper, an intelligent contour control strategy has been investigated to improve the contour error of CNC machine tools. An uncoupled contour control system is first analyzed and then a cross-coupled controller is added in the control loop to form a cross-coupled contour control system. An algorithm for an on-line estimation of the contour error in arbitrary curved contouring is also proposed. To further reduce the contour error, a cross-coupled fuzzy feedrate control scheme is presented. The controller parameters are all optimized by a genetic based learning algorithm. Experimental results show that the proposed control scheme is effective to improve the contouring accuracy of CNC machine tools.     

数控机床动态轨迹误差仿真与优化研究

在介绍数控机床加工轨迹运动控制原理的基础上,对数控机床动态轨迹误差进行了仿真研究,得出数控机床动态轨迹误差与拟加工曲线的曲率和机床进给速度相关的结论。在待加工的工件几何曲线曲率已定情况下,提出了变进给速度的数控机床动态轨迹误差优化策略,仿真结果表明:该控制策略能够有效地减少机床动态轨迹误差量,提高相关轨迹曲线的加工精度。     

Multibody dynamic modeling of five-axis machine tool vibrations and controller

A computationally efficient, reduced-order multibody dynamic model of a five-axis machine tool is presented. The machine tool is modeled by substructures assembled via flexible springs and damping elements at interfaces which affect the machining performance. NC tool path commands are processed by the linear acceleration-based motion trajectory filters and fed to the axis servo controllers through an inverse kinematic model of the machine. The computed motor torque commands are applied to the structural dynamic model of the machine at the motor connections. The experimentally validated model predicts the performance of the five-axis CNC machine's controller along the tool path.     

Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics

Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. By synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool–workpiece interface for error compensation.     

Accuracy enhancement of five-axis machine tool based on differential motion matrix: Geometric error modeling,identification and compensation

This paper presents the precision enhancement of five-axis machine tools according to differential motion matrix, including geometric error modeling, identification and compensation. Differential motion matrix describes the relationship between transforming differential changes of coordinate frames. Firstly, differential motion matrix of each axis relative to tool is established based on homogenous transformation matrix of tool relative to each axis. Secondly, the influences of errors of each axis on accuracy of tool are calculated with error vector of each axis. The sum of these influences is integration of error components of machine tool in coordinate system of tool. It endows the error modeling clear physical meaning. Moreover, integrated error components are transformed to coordinate frame of working table for integrated error transformation matrix of machine tools. Thirdly, constructed Jacobian is established using differential motion matrix of each axis without extra calculation to compensate the integrated error components of tool. It makes compensation easy and convenient with reuse of intermediate. Fourthly, six-circle method of ballbar is developed based on differential motion matrix to identify all ten error components of each rotary axis. Finally, the experiments are carried out on SmartCNC500 five-axis machine tool to testify the effectiveness of proposed accuracy enhancement with differential motion matrix.     

Tool path generation and error control method for multi-axis NC machining of spatial cam

In this paper, based on the homogeneous coordinate transformation and conjugate surface theory, a tool path generation method is developed for generating spatial cam in order to establish the interface between the design and manufacture of this class of product. The mathematical error (chordal deviation) between the design and manufacture surface has been analysed and used as a basis for selecting the tool path control point. Moreover, the developed tool path generation method is verified through a cutting simulation software with solid model. It is also verified through the trial cut with model materials on a five-axis numerical controlled machine. The results show that the mathematical error of the cam surface can be controlled within given tolerance by the proposed method.     

A grey prediction fuzzy controller for constant cutting force in turning

Constant force control is gradually becoming an important technique in the modern manufacturing process. Especially, constant cutting force control is a useful approach in increasing the metal removal rate and the tool life for turning systems. However, turning systems generally have non-linear with uncertainty dynamic characteristics. Designing a model-based controller for constant cutting force control is difficult because an accurate mathematical model in the turning system is hard to establish. Hence, this study employed a model-free fuzzy controller to control the turning system in order to achieve constant cutting force control. Nevertheless, the design of the traditional fuzzy controller (TFC) presents difficulties in finding control rules and selecting an appropriate membership function. To solve this problem, a grey-theory algorithm was introduced into the TFC to predict the next output error of the system and the error change, rather than the current output error of the system and the current error change, as input variables of the TFC. This design of the grey prediction fuzzy controller (GPFC) cannot only simplify the TFC design, but also achieves the desired result in TFC implementation. To confirm the applicability of the proposed intelligent controllers, this work retrofitted an old lathe for a turning system to evaluate the feasibility of constant cutting force control. The GPFC has better control performance in constant cutting force control than does the TFC, as verified in experimental results.     

Discrete-time robust adaptive multi-axis control for feed drive systems

This paper presents a robust adaptive controller design for multi-axis feed drives systems. The proposed method is designed to compensate for the coupling effects among multiple axes that are neglected in most feed drive controllers. Because inertial force from one axial motion affects the contact force between mechanical parts in other axes, the magnitude of friction at the contact surface varies. Considering this coupling effect in controller designs can improve control performance. Because the coupling effect cannot be known in advance, and it varies with respect to environmental conditions such as temperature, this paper first presents an adaptive controller design. Next, the design is extended to have robust stability for unanticipated plant modelling errors disturbances, because the robustness of adaptive controllers is known to be low due to the complex mechanism of controllers and estimators of plant model parameters. The design problem of the robust controller is formulated as a minimization problem under the linear matrix inequality constraints. The effectiveness of the adaptive multi-axis controller is demonstrated by comparative experiments with an adaptive controller that neglects the coupling effect. In addition, the robust adaptive controller is confirmed to be effective by comparison with a non-robust adaptive controller.     

Tracking control and active disturbance rejection with application to noncircular machining

Control systems are usually required to track reference signals while operating under the influence of disturbances. A fast tool servo system for noncircular machining application works under such conditions, resulting in large control efforts. This paper presents a linear active disturbance rejection controller design for a voice coil motor-driven fast tool servo system for noncircular machining application. The controller is designed through an extended state observer to estimate and compensate the variant dynamics of the system, nonlinearly variable cutting load, and other uncertainties. Then, a simple proportional derivative controller produces the control law. To improve the tracking performance of the fast tool servo, the tracking error from the trial-cutting workpiece is added to the reference input and used as feed-forward error compensation. In such a combined control arrangement, the active disturbance rejection controller provides active disturbance rejection ability for the controller, and the feed-forward error compensation controller improves the tracking precision. Both the tracking control and disturbance rejection performances are thus enhanced. In real-time control and implementation, the effects of finite word length, position feedback resolution, and short sampling period are analyzed and addressed. Machining experiments are conducted, and the results illustrate the control system synthesis procedures and a substantial improvement over the tracking error generated by the linear active disturbance rejection controller alone.     

Modeling and improvement of dynamic contour errors for five-axis machine tools under synchronous measuring paths

In this paper, a contour error model of the tool center point (TCP) for a five-axis machine tool is proposed to estimate dynamic contour errors on three types of measuring paths. A servo tuning approach to achieve five-axis dynamic matching is utilized to improve contouring performance of the cutting trajectory. The TCP control function is developed to generate measuring trajectories where five axes are controlled simultaneously to keep the TCP at a fixed point. The interpolation method of the rotary axes with S-shape acceleration/deceleration (ACC/DEC) is applied to plan smooth five-axis velocity profiles. The contour error model for five axes is derived by substituting five-axis motion commands into servo dynamics models. The steady state contour error (SSCE) model is demonstrated to illustrate three particular dynamic behaviors: the single-circle with amplitude modulation, double-circle effect and offset behavior. Furthermore, the model is also utilized to investigate the behaviors of dynamic contour errors change in 3D space. The factors that affect dynamic contour errors, including the initial setup position, feedrate and five-axis servo gains, are analyzed. With the developed servo tuning process under the measuring paths (CK1, CK2 and CK4), the contour errors caused by servo mismatch are reduced remarkably. Finally, experiments are conducted on a desktop five-axis engraving machine to verify the proposed methodology can improve dynamic contouring accuracy of the TCP significantly.     

Bézier polygons for the linearization of dual NURBS curve in five-axis sculptured surface machining

Motivated by the excellent performance of three-axis NURBS interpolation, this paper presents a numerically efficient and accuracy controllable five-axis sculptured surface machining method with dual NURBS curve. Unlike the traditional three-axis NURBS interpolation, a dual NURBS format of the five-axis toolpath is developed to accurately and smoothly describe the tool movement in the part coordinate system. Different from the subdivision methods using the Taylor series expansion or inverse function, a piece-wise Bézier curve method is implemented to fast subdivide the NURBS curve within the user-defined tolerance. A generic rotation tool center point management module is also designed to realize the coordinate transformation and adaptive nonlinear error control for major five-axis machine tools. The overall effectiveness of the proposed five-axis NURBS machining scheme is demonstrated by the five-axis machining of an impeller’s flow channel.