Kaan Erkorkmaz

High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation

Reference trajectory generation plays a key role in the computer control of machine tools. Generated trajectories must not only describe the desired tool path accurately, but must also have smooth kinematic profiles in order to maintain high tracking accuracy, and avoid exciting the natural modes of the mechanical structure or servo control system. Spline trajectory generation techniques have become widely adopted in machining aerospace parts, dies, and molds for this reason; they provide a more continuous feed motion compared to multiple linear or circular segments and result in shorter machining time, as well as better surface geometry. This paper presents a quintic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration profiles. The spline interpolation is realized with a novel approach that eliminates feedrate fluctuations due to parametrization errors. Smooth accelerations and decelerations are obtained by imposing limits on the first and second time derivatives of feedrate, resulting in trapezoidal acceleration profiles along the toolpath. Finally, the reference trajectory generated with varying interpolation period is re-sampled at the servo loop closure period using fifth order polynomials, which enable the original kinematic profiles to be preserved. The proposed trajectory generation algorithm has been tested in machining a wing surface on a three axis milling machine, controlled with an in house developed open architecture CNC.

Sliding Mode Controller Design for High Speed Feed Drives

Abstract An adaptive sliding mode control technique is presented for the control of high speed feed drives. The proposed control system is robust against uncertainties in the drives parameters, maximizes the bandwidth within physical limitations, and compensates for external disturbances such as friction and cutting force. The algorithm is briefly presented, followed by machining tests conducted with contour milling of circles and diamond trajectories. The contour errors are compared against those of a pole placement controller with feedforward friction and servo dynamics compensation. It is shown that the sliding mode controller has practical advantages in rapid tuning and implementation, but requires smooth reference trajectory generation.

High speed CNC system design. Part III : high speed tracking and contouring control of feed drives

A servo control system capable of delivering rapid and accurate feed motion is a necessity for high speed machine tools. The control law must be designed to provide a high tracking bandwidth as well as adequate disturbance rejection and parameter variation robustness, in order minimize the following errors in each axis. This also contributes to the minimization of the contour errors in the machined part. This paper provides a systematic approach for designing such a control law. Position, velocity, and disturbance estimates are obtained using a Kalman filter. The feedback loop is closed using a pole placement controller with disturbance cancellation, in order to counteract the detrimental effects of friction, cutting forces, and drive parameter variations. The overall tracking bandwidth is widened by compensating for the closed loop dynamics in a feedforward manner. Also, the tracking errors due to friction transients at the corners and arc quadrants are reduced by precompensating for the expected friction forces. The contribution of each component in the control scheme to the contouring accuracy has been experimentally verified, and the overall contouring performance has been demonstrated in high speed machining tests. The experimental results were obtained using the smooth trajectory generation algorithm and identified axis and friction models which have been presented in Parts I and II respectively, of this paper.

Feedrate Optimization for Spline Interpolation In High Speed Machine Tools

Abstract A feedrate optimization technique has been developed for minimizing the cycle time in machining spline toolpaths. Axis velocity, torque and jerk limits are considered throughout the motion in order to ensure smooth and linear operation of the servo drives with minimal tracking error. Feed modulation is achieved by manipulating segment durations which define the overall minimum jerk feed profile. Long toolpaths are handled by applying a windowing technique. The optimized feed profile allows nonzero acceleration and jerk values at segment connections, resulting in continuous and smooth motion within the velocity, torque, and jerk limits of the drives. The cycle time reduction obtained with the proposed technique is demonstrated in high speed contouring experiments.

High bandwidth control of ball screw drives

This paper presents a tracking control strategy for high speed ball screw drives. Rigid body motion is controlled using adaptive sliding mode control. Torsional vibrations are modeled, experimentally identified, and compensated in the control law using notch filtering and active cancellation techniques. Attenuation of torsional resonances improves the stability margins and enables high positioning bandwidth to be achieved. The axis friction is experimentally identified and cancelled out in feedforward, in order to improve the positioning accuracy at motion reversals. The developed control law is verified experimentally on a high speed ball screw drive, where a tracking accuracy of 1.6 um is maintained while traversing the axis at 1000 mm/sec feed and 1 g acceleration.

Virtual Computer Numerical Control System

This paper presents a comprehensive virtual simulation model for CNC systems. The Virtual CNC (VCNC) has a modular architecture, allowing a real CNC to be prototyped quickly from standard library functions for feed drive models, feedback devices, axis control laws, and trajectory interpolation. Additional CNC modules can easily be prototyped and integrated to the VCNC by the user. Various application examples are presented which include the prediction of contour errors, auto-tuning of feed drive controllers, toolpath and feed modification for improved cornering, and rapid identification of closed loop drive dynamics. Detailed experimental verification is presented for each algorithm.

A Control Systems Concept Inventory Test Design and Assessment

Any meaningful initiative to improve the teaching and learning in introductory control systems courses needs a clear test of student conceptual understanding to determine the effectiveness of proposed methods and activities. The authors propose a control systems concept inventory. Development of the inventory was collaborative and iterative. The diagnostic test was administered to students before (pre) and after (post) student learning activities. Test responses were analyzed to provide instructors with feedback on their teaching. Using classical test theory and item response theory, aggregated results were analyzed to assess internal consistency and measurement error, respectively. Students demonstrated an improvement from pre- to post-test scores, showing gains of 23%-34% in understanding of new concepts learned. The internal consistency of the test has ranged from 0.61 to 0.68. It can be shown that the precision of the test is highest in the score range of 33%-66%, which is where most post-test scores occurred.

Precision Tracking Controller Design for High Speed Feed Drives

This paper investigates the effectiveness of adaptive sliding mode control (SMC) for precision tracking in high speed machine tool drives. Dynamics of the feed drive, comprising of rigid body motion, guideway friction and ball screw vibrations, are identified. Two strategies are developed. The first one considers rigid body dynamics in the plant and compensates for the resonance with a notch filter. The second controller considers the first torsional mode as part of the plant and actively suppresses its vibrations. The two controllers are evaluated in frequency domain analyses and simulations. The results indicate that the notch filter based design is easier to implement and possesses comparable tracking, disturbance rejection, and robustness to the mode-compensating SMC. The simulation results are verified in tracking tests where 1.5 [um] of accuracy is achieved at a feed speed of 250 [mm/sec].Copyright

Design and Optimization of a Voice Coil Actuator for Precision Motion Applications

There has been increasing attention to the use of voice coil actuators (VCAs) for precision motion applications. In this paper, a detailed design of a cylindrical VCA is presented. Different options for the overall configuration are evaluated according to various criteria and design variables are defined for the chosen configuration. After that, optimization parameters are derived to maximize the performance in a precision motion application by maximizing the acceleration and minimizing the heat dissipation. Design parameters are optimized using finite element analysis to evaluate the magnetic properties. Optimization is carried out using the bulk volume of coil, which allowed electrical properties to be later characterized via the selection of wire gauge. Calculations for evaluating resistance, inductance, current drain, and voltage supply requirements for dc and dynamic cases are presented. Magnetic field predictions and formulations used in force calculations are verified in experiments.

High speed contouring control for machine tool drives

High speed machining technology has been rapidly adopted in aerospace, die and mold manufacturing industry for its high productivity. High speed machine tools require a rigid structure, thermally and dynamically stable spindles with high power, and fast feed drives which are able to track complex tool paths accurately at feed speeds up to 40 [m/min] with high accelerations over 1 [g]. The design of trajectory generation and control algorithms play a crucial role in realizing the accuracy requirement for high speed feed motion. This thesis presents a systematic approach to designing a smooth trajectory generation algorithm and a high performance control system for machine tool feed drives. A jerk limited trajectory generation algorithm employing trapezoidal acceleration profiles is developed to minimize discontinuity and harmonics in actuation force. The original position commands with varying interpolation period are re-sampled at control loop frequency via fifth order polynomials. The generated smooth trajectory commands for individual axes are delivered to a control system designed for accurate tracking and disturbance robustness. Axis dynamics are first stabilized via pole-placement control. Overall bandwidth is increased with a zero phase error tracking controller to minimize tracking errors. Disturbance rejection and parameter variation robustness is achieved using a Kalman filter based disturbance observer. Friction forces are compensated for in feedforward to improve the tracking accuracy at sharp corners and circular quadrants. On top of these, the contour error is also estimated in real-time and used in cross-coupling control via PID controllers, to achieve additional contouring accuracy in the presence of cutting forces. The effectiveness of the proposed trajectory generation and control scheme is verified both in simulations and in experiments, where a high speed x-y table driven by linear motors is used.