• Journal of the Korean Society for Precision Engineering
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• v.22 no.12 s.177
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• pp.51-60
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• 2005

This paper describes a robust control scheme for high-speed and long stroke scanning motion of high precision linear motor system consisting of linear motor, air bearing guide and position measurement system using heterodyne interferometer. Nowadays, semiconductor process and inspection of wafer or LCD need high speed and long travel length for their high throughput and extremely small velocity fluctuations or tracking errors. In order to satisfy these conditions, linear motor system are widely used because they have large thrust force and do not need motion conversion mechanisms such as ball screw, rack & pinion or capstan with which the system are burdened. However linear motors have a problem called force ripple. Force ripple deteriorates the tracking performances and makes periodic position errors. So, force ripple must be compensated. To maximize the tracking performance of linear motor system, we propose the control scheme which is composed of a robust control method, Time Delay Controller (TDC) and a feedforward control method, Zero Phase Error Tracking Control (ZPETC) for accurate tracking a given trajectory and an adaptive force ripple compensation (AFC) algorithm fur estimating and compensating force ripple. The adaptive ripple compensation is continuously refined on the basis of tracking error. Computer simulation results based on modeled parameters verify the effectiveness of the proposed control scheme for high-speed, long stroke and high precision scanning motion and show that the proposed control scheme can achieve a sup error tracking performance in comparison to conventional TDC control.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.197-208
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• 2005

We consider the problem for approximate solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter $H\;\in$ (0,1/2). The error of the approximate solution for the explicit Euler scheme is investigated.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.129-130
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• 2011

• Transactions of the Korean Society of Machine Tool Engineers
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• v.17 no.5
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• pp.44-51
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• 2008

In this paper, the optimal tuning of a cross-coupled controller linked with the feedforward controller is studied to reduce contouring and tracking errors of a bi-axial servomechanisms by using the previously developed integrated tuning method. The CCC system for an arbitrary curve, which is combined with the feedforward controller, is formulated by a state-space based on a series of linear motion trajectories. An optimal tuning problem is formulated as a nonlinear constrained optimization problem including relevant controller parameters of the servo. To verify the effectiveness of the proposed optimal tuning procedure, linear and circular motion experiments are performed on the xy-table. Experimental results confirm that both tracking and contouring errors are significantly reduced by applying the proposed control and tuning system.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.6
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• pp.62-69
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• 2002

For improving the motion accuracy of hydrostatic table, corrective machining algorithm is proposed in this paper. The algorithm consists of three main processes. reverse analysis is performed firstly to estimate rail profile from measured linear and angular motion error, in the algorithm. For the next step, corrective machining information is decided as referring to the estimating rail profile. Finally, motion errors on correctively machined rail are analized by using motion error analysis method proposed in the previous paper. These processes can be iterated until the analized motion errors are satisfied with target accuracy. In order to verify the validity of the algorithm theoretically, motion errors by the estimated rail, after corrective machining, are compared with motion errors by true rail assumed as the measured value. Estimated motion errors show good agreement with assumed values, and it is confirmed that the algorithm is effective to acquire the corrective machining information to improve the accuracy of hydrostatic table.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.2
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• pp.60-67
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• 2004

For improving the motion accuracy of hydrostatic tables, a corrective machining algorithm is proposed in this paper. The algorithm consists of three main processes. The reverse analysis is performed firstly to estimate the rail profile from the measured linear and angular motion error, in the algorithm. For the next step, the corrective machining information is obtained based upon the estimated rail pronto. Finally, the motion errors on the correctively machined rail are analyzed by using the motion error analysis method. These processes are iterated until the analyzed motion errors are satisfactory within the target accuracy. In order to verify the validity of the algorithm theoretically, the motion errors calculated by the estimated rail after the corrective machining process, are compared with those by the true rail which is previously assumed as the initially measured value. The motion errors calculated using the estimated rail show good agreement with the assumed values, and it is shown that the algorithm is effective in acquiring the corrective machining information to improve the accuracy of hydrostatic tables.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.692-695
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• 2000

This paper is concerned with Accuracy Design of LM Guide System in Machine Tools. Elastic deformation of bearing is calculated by Hertz contact theory and motion error of LM block is analyzed. A new algorithm using block stiffness is proposed fur the analysis of motion accuracy of the table. The best advantage of this algorithm is fast analysis speed because it isn't necessary iteration processes for satisfying equilibrium equation of the table. Motion errors of the table analyzed under artificial form error of rail theoretically and experimentally. Only one of two rails is bent by putting a thickness gauge into horizontal direction. This form error of rail is measured by gap sensor against the other rail. Then, motion errors of the table are predicted by proposed new algorithm theoretically and measured by laser interferometer. Measurements are carried out by changing the preload and thickness. The results show that the table motion errors are reduced from 1/2 to 1/60 times than form error of rail according to its height and width. And the effect of preloading is almost negligible.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.8
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• pp.906-912
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• 2012

This paper presents the new method for a six-degree-of-freedom (DOF) motion measurement and those dynamic characterizations in an ultraprecision linear stage using angle sensor-implemented grating interferometry. It consists of a diffractive optical element, a corner cube, four separate two-dimensional position sensitive detectors, four photodiodes and auxiliary optics components. From the previous study, it was confirmed that the proposed optical system could measure a six-DOF motion error in a linear stage. In this article, six-DOF motion dynamic characteristics of the stage were investigated through the step response and with respect to the conditions with a different speed of a slide table. As a result, the natural frequency and damping ratio according to a six-DOF direction was obtained. Also, it was seen that the speed of slide table had an significant effect on a six-DOF displacement motion, especially, X, which was considered as the effect of friction mechanism and local elastic mechanical deformation in a slide guide.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.479-484
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• 1996

This paper describes a method of measuring tilt motion. This method measures the tilt motion of drilling machines using a laser interferometer, a simple sliding linear bearing, measurement of the probe and the LSC(least square center) method. The next order of business is discussing the procedure of measurement. First, The measured position is considered to be the point of contact between the drill shank and the probe. The revolution of the drill axis delivers the point of contact to the probe. Second, because the laser interferometer is attached on the sliding linear bearing, any movement of probe influences laser reflector. Thus, the laser program displays the moving factor of laser reflector. Namely, this is tilt factor. Third. the points of measurement are a full circle which has 8 points (each are 45$^{\circ}$), After it is finished measuring the 8 points, let the spindle of the drilling machine move down about 5 cm. Repeating this procedure three times, we can get tilt motion's values which are calculated by LSC method. Many error factors affect the accurate measurement of tilt motion. However in this paper we ignore some error factors because they are less significant than tilt motion.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.466-469
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• 1995

This paper presents a design and performance of the 6 D.O.F linear motion table with a magnetic bearing suspension. The linear positioning of the table with a 150mm stroke is driven by a brushless DC Linear motor and the other attitudes of the stage are controlled by the analog PD controller with magnetic bearing actuators. Each magnetic bearing unit which consists of 3 electromagnets, 3 capacitance probes and 3 backup bearings affords controlled forces by detecting the air gap between the probes and guideways. An integral type capacitance probe amplifier is equipped on the upper plate of the table so that the probe line to the probe amplifier can be shorter therefore the problems due to the stray capacitance and noise can be reduced. Form the pitch-yaw errormeasured by the autocollimator, the vertical and horizont straightness errors of the table are derived that they are maintained below 1.mu. m over 100mm stroke. The positioning accuracy of the linear motion is maintained below 2 .mu. m and the repeatability error is below 1 .mu. m