Mechatronic design, actuator optimization, and control of a long stroke linear nano-positioner

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.precisioneng.2018.01.007 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, mechatronic design, actuator optimization and controls of a long-stroke (20 mm) linear nano-positioner are presented. The mechatronic design is described in terms of the stage's most prominent features regarding mechanical design, assembly, actuator configuration, and power supply. A novel air-bearing/bushing arrangement has been used in which the commonly employed double shaft arrangement is replaced with a single shaft supported by an air bearing from the bottom to constrain the roll motion. The assembly is greatly simplified by exploiting the self-aligning property of the air-bushings which are held in the housings by O-rings. Also, the footprint of the stage is reduced. Voice coil actuators (VCA) in moving magnet mode have been used in complementary double configuration for uniformity of force response. The performance objectives of previously optimized VCA's as standalone actuators are re-evaluated in this configuration. It is observed that while the performance objectives decrease a bit, the desirability of the design point is still retained. Controller design has been made for the current control and position control loops. Heydemann's method for the compensation of encoder quadrature detection errors is implemented. The positioning resolution of the stage as measured from the sensor output is experimentally determined to be +/-5 nm. Dynamic Error Budgeting (DEB) method has been used to analyze the contributing factors to the positioning error, and sensor broadband noise is determined to be the major contributor. The actual positioning accuracy of the stage is estimated by DEB to be 0.682 nm root-mean-square (RMS). The trajectory following accuracy is determined to be +/-15 nm. It is expected that trajectory following accuracy can substantially improve if more advanced compensation methods for encoder quadrature errors are implemented.Natural Sciences and Engineering Research Council of Canada [RGPIN-03879]Engage grant EGP [436910-12

Optimal trajectory generation and precision tracking control for multi-axis machines

This thesis presents experimentally verified smooth trajectory generation, feedrate optimization, and high performance control algorithms developed for multi-axis Cartesian machine tools. New spline parameterization and interpolation schemes are introduced that yield smooth contouring motion with minimal feedrate fluctuation along arbitrarily shaped toolpaths. The first approach is based on optimizing the toolpath geometry to yield minimal discrepancy between the spline parameter and arc length increments, resulting in an Optimally Arc Length Parameterized (OAP) quintic spline. This spline exhibits minimal feedrate fluctuation when interpolated at constant parameter increments. The second approach is based on scheduling the spline parameter to yield the desired arc displacement, hence the desired feedrate profile accurately, without having to re-parameterize the spline toolpath. The feedrate correction polynomial and iterative interpolation techniques developed for this purpose are shown to improve the feedrate consistency with reliable convergence properties, at small computational cost, making these methods viable for real-time implementation in the CNC executive. A jerk continuous feedrate optimization technique is introduced for minimizing the cycle time, while preserving the motion smoothness and tracking accuracy for traveling along spline toolpaths. Feedrate modulation is achieved by varying the travel duration of each segment and fitting the resulting C3 continuous minimum jerk displacement profile. This results in continuous velocity, acceleration, and jerk transitions spanning the entire motion along the toolpath, allowing smoother feed motion with shorter cycle time compared to piecewise constant feedrate modulation method used in current CNC systems. The feed drive dynamics of a three axis machining center are identified in detail in order to develop a controller with high tracking accuracy and bandwidth. The linear rigid body dynamic comprising of inertia and viscous friction are determined using a modified least squares scheme, which considers the existence of Coulomb friction in the parameter estimation process. The nonlinear friction model is refined by jogging the axes back and forth at various speeds, and observing the equivalent friction torque through a Kalman filter. The structural dynamics of the ball screw mechanism are identified by conducting frequency response tests, while the axis is already in motion, in order to decouple the interfering effect of stick-slip friction. The torsional vibrations of the lead screw, as well as translational vibrations of the table resulting from the torsional and axial vibrations of the lead screw, are experimentally identified. The modal characteristics of the ball screw are combined with the rigid body dynamics and guideway friction, resulting in a detailed drive model which is used for motion control law design. Two robust, adaptive sliding mode controllers have been designed, one which considers only the rigid body motion, and the second which also considers the torsional vibrations of the ball screw. Notch filtering of the first resonant mode is also investigated as a practical alternative to active vibration control, yielding successful experimental results when used in conjunction with the rigid body based sliding mode controller. Feedforward friction compensation has been added, to improve the contouring performance at circular arc quadrants and sharp corners, where the friction disturbance undergoes a discontinuous change due to axis velocity reversal. The proposed control techniques have been validated in simulations and high speed tracking and contouring experiments. The methods developed in this thesis have been evaluated on a three axis machining center, and are directly applicable to other Cartesian configured multi-axis systems, such as electronic component assembly or photolithography machines. Their extension to non-Cartesian axis configurations would require the kinematic chain and dynamic model of the machine to be considered in the control law design and trajectory generation algorithms.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat

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.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat

Modal Analysis, Metrology, and Error Budgeting of a Precision Motion Stage

In this study, a precision motion stage, whose design utilizes a single shaft supported from the bottom by an air bearing and voice coil actuators in complementary double configuration, is evaluated for its dynamic properties, motion accuracy, and potential machining force response, through modal testing, laser interferometric metrology, and spectral analysis, respectively. Modal testing is carried out using two independent methods, which are both based on impact hammer testing. Results are compared with each other and with the predicted natural frequencies based on design calculations. Laser interferometry has been used with varying optics to measure the geometric errors of motion. Laser interferometry results are merged with measured servo errors, estimated thermal errors, and the predicted dynamic response to machining forces, to compile the error budget. Overall accuracy of the stage is calculated as peak-to-valley 5.7 μm with a 2.3 μm non-repeatable part. The accuracy measured is in line with design calculations which incorporated the accuracy grade of the encoder scale and the dimensional tolerances of structural components. The source of the non-repeatable errors remains mostly equivocal, as they fall in the range of random errors of measurement in laser interferometry like alterations of the laser wavelength due to air turbulence

Linear Time-Invariant Model Identification Algorithm for Mechatronic Systems Based on MIMO Frequency Response Data

This article describes a new frequency- domain multi-input multioutput linear time-invariant (LTI) system identification algorithm for accurate model construction suitable for motion control systems. The proposed method can capture the effects of time-delay, lightly damped poles (structural resonances), as well as highly damped complex or real poles, and direct or derivative-like terms. The effectiveness of the algorithm has been validated using experimental frequency response measurements obtained from different types of motion control mechanisms. The proposed algorithm has also been compared with “ tfest ” and “ modalfit ” functions in MATLAB. Over these methods, nearly two orders of magnitude improvement is observed in the closeness of the model prediction, in terms of root mean square of the frequencywise modeling error