Tracking Control of Automatic Pipe Cutting Robot with Magnetic Binder

Transcription

1 Materials Science Forum Vols (2006) pp online at (2006) Trans Tech Publications, Switzerlan Tracking Control of Automatic Pipe Cutting Robot with Magnetic Biner Sungsoo Rhim 1, a an Soon-Geul Lee 2, b 1, 2 Department of Mechanical Engineering, Kyung Hee University, Republic of Korea a ssrhim@khu.ac.kr, b sglee@khu.ac.kr Keywors: automatic pipe cutting, wheele robot, learning control, magnetic biner Abstract. An automatic pipe cutting/weling robot with a magnetic biner, which is name APCROM, is evelope an its tracking control is stuie in this paper. Using magnetic force the four-wheele mobile robot bins itself to the pipe an executes automatic pipe cutting/weling process. As APCROM rotates aroun the cylinrical pipe lai in the gravitational fiel, the gravity effect on the movement of the robot varies. The varying gravitational effect eteriorates the tracking performance of the robot an egraes the quality of the pipe cutting/weling process. To maintain a constant velocity an consistent cutting/weling performance, the authors aopt a repetitive learning controller, which learns through practice the require effort to cancel the tracking errors. Analysis results an experimental results verify the effectiveness of the propose control scheme. Introuction Not only to replace human labor that becomes harer to fin but also to improve the quality of the processes the automation of pipe cutting an weling has been initiate an many automate machines have been evelope [1]. Pipe cutting (an/or weling) machines for circular pipes, unlike the planar plates, nee to move aroun the circumference of the cylinrical pipes an they must hol themselves onto the pipe against the gravity. Many types of bining systems for pipe cutting machines have been evise but most of them use supplementary attachment such as chains or rails to bin cutting machines on the pipe [2]. Not only cumbersome but quite restrictive is to use those extra jigs for the engagement of the machines onto (from) the pipe. A four-wheele automatic pipe cutting robot with a magnetic biner, calle APCROM, which has been evelope at Kyung Hee University [3], bins itself to the surface of the pipe using a magnet installe at the bottom of the robot an executes unmanne cutting tasks. Compare to the supplementary-jig approach the magnetic biner significantly shortens the time require for the engagement an the isengagement of the machine. Moreover it oes not require ifferent jigs for ifferent shapes or sizes of pipes. During the cutting process APCROM rotates aroun the pipe lai in the gravitational fiel an the gravity effect on the movement of APCROM varies as it rotates. The cutting quality is eteriorate with irregularity in cutting spee cause by the varying gravity effect. In aition to the varying gravity effect there are other types of nonlinear isturbances that woul eteriorate the performance of APCROM. The backlash in the riving system an the slip between the wheels of APCROM an the pipe result in jerking motion an egrae the cutting process. Consiering the repetitive characteristic of the pipe cutting task, the authors introuce a repetitive learning controller to maintain a constant velocity an consistent cutting performance of the process. The learning controller estimates, through practice, the control input require to achieve the perfect tracking of a perioic esire trajectory. Unlike a typical aaptive control scheme, which often assumes a specific moel of the plant an then seeks to estimate unknown parameters within that moel, learning controllers require very little a priori knowlege of the plant to be controlle [4,5]. For the compensation of the tracking error of APCROM moving aroun the cylinrical pipe, it is essential to estimate the accurate angular position of APCROM at a given time. However, it is not trivial task to measure the accurate absolute angular position of APCROM in the presence of the significant slip at the wheel an the backlash in the riving train. In the paper two control schemes All rights reserve. No part of contents of this paper may be reprouce or transmitte in any form or by any means without the written permission of the publisher: Trans Tech Publications Lt, Switzerlan, (ID: /04/07,17:47:34)

2 1202 Progress on Avance Manufacture for Micro/Nano Technology 2005 Reuction Gear DC Motor Ajusting Hanle Magnet Chamber 170 mm Wheel 220 mm (a) Fig. 1. Picture an schematic iagram of APCROM. (b) are implemente; a) a conventional PD controller with the encoer-base position estimation, an b) a PD controller combine with a multirate repetitive learning controller (MRLC) using the encoer-base position estimation. Analysis results an experimental results valiate the effectiveness of MRLC in enhancing the tracking performance of APCROM. System configuration A picture an a schematic iagram of APCROM are shown in Fig. 1. APCROM has been esigne in a way to minimize the weight an to set up the smallest with an height. APCROM has a magnet chamber at the bottom, where a permanent magnet is containe. Using the ajusting hanle at the top of the robot, an operator can move the magnet chamber up an own an ajust the gap between the magnet an the pipe. The normal magnetic force varies along with the istance between the magnet an the pipe surface. APCROM uses a DC motor an a worm reuction gear train to rive wheels. The well-aligne four ientical wheels are riven by chain mechanism that transmits torque from the reuction gear train. The motor is perfectly seale, so it fits well into the inustrial application where the operating conition is quite hostile. An encoer is irectly attache at the motor to obtain the real-time relative position of APCROM on the pipe. Figure 2 shows a free-boy iagram of APCROM moving along the surface of a pipe, where R is the raius of the pipe, m is the mass of APCROM, r is the raius of the wheel, τ is the torque exerte on the wheel by the riving system, F mag is the magnetic bining force, F u is the friction force an represents the angular position of APCROM on the pipe. From Fig. 2 we can obtain an equation of motion as Eq. 1, where the position-epenent nonlinear effect of the gravity is apparent. ( Fmag mg sin ) mg cos m( R h) µ θ θ = && θ. (1) Control system Consiering the perioic nature of the operating conitions for the pipe cutting process, the authors introuce a repetitive learning controller in the iscrete-time omain for the task of accurate positioning of APCROM. A repetitive learning controller exploits the cyclic nature of a system by using the error signal from previous perios to correct an refine the current feeforwar plant input. This proceure can be shown to rive the tracking error to zero for a stable plant in the absence of transients an noise [6,7]. For its straightforwar implementation an relatively small computational

3 Materials Science Forum Vols Fig. 2. Free-boy iagram of APCROM on pipe. requirements, the bypass repetitive learning controller among many types of learning controllers is consiere in this paper. The orer of a iscrete-time repetitive learning controller is irectly proportional to its sample rate an to the perio of the esire trajectory to be tracke. A iscrete repetitive learning controller which has too high a sample rate may exhibit unesirable high frequency characteristics, be unstable, an incur excessively large learning cycle length which results in excessive memory storage costs. To avoi such potential problems in pipe cutting process where the typical cycle time is more than a few minutes, a multirate repetitive learning controller (MRLC) evelope in [6] is implemente in the iscrete-time omain for the task of accurately positioning APCROM. Figure 3 (a) shows the block iagram representing the general form of the bypass type MRLC, where T is the plant sample perio an k is an integer greater than 1. By sampling at a relatively slower rate, a MRLC seeks to avoi potential problems of high sampling repetitive learning controllers, without the nee to have the plant's sample rate slowe own. Down-sampling is implemente using a linear weighte average an up-sampling using linear interpolation. In the figure, K L > 0 is the learning gain, Q(z) is a lea compensator, an R(z)=1/(z N -1), which is a NkT time-elay positive feeback loop, where NkT is the perio of the esire trajectory to be tracke. We require that K L an Q(z) be chosen such that the stability criterion in [6,7] is satisfie. R(z) may be expresse as the sum of N first-orer transfer functions as shown in Eq. 2: N ai R( z) = (2) z z i= 1 i where a i is the ith unetermine coefficient an z i =exp(j2πi/n) are the pole locations. The frequency of z 1, which is 2 π / N, is calle the funamental frequency an the N -1 integer multiples of the funamental frequency are calle the harmonic frequencies. The funamental frequency is selecte to be the largest frequency whose harmonics contain all of the task an isturbance frequencies. In this way the MRLC puts marginally stable poles at the same frequencies as the task an isturbance frequencies. This creates an infinite loop gain at these frequencies an thus, rives the error signal theoretically to zero. A(z) is a linear weighte averaging filter, I(z) is the linear interpolation (up-sampling) filter, * enotes own-sampling, D(z) is a conventional PD controller an G(z) represents the transfer function of APCROM. Then, the feeback controller output v is calculate as Eq. 3. { 1 C } L C V z = A z D z G z D z Θ z K A z D z G z I z R z V z (3)

4 1204 Progress on Avance Manufacture for Micro/Nano Technology 2005 x _ e Down-sample T T KLQ( z) R( z) Up-sample kt T MRLC H( z) x θ u fb _ e A( z) D( z) v v u fb MRLC K R ( z) L u learn I( z) G( z) θ ulearn (a) (b) Fig. 3. Block-iagram of multirate repetitive learning controller: (a) by-pass type multirate learning controller (b) multirate learning controller implemente. where V(z), Θ( z) an ( z) Θ represent the iscrete signal v, θ, an θ shown in Fig.3 (b), respectively. G ( z ) is the close-loop transfer function of the feeback system an calculate as c c /( 1 ) G z = G z G z D z. Down-sampling both sies of (3) yiels the own-sample version of the feeback control output which is represente in (4) an (5) V z = H z Θ z K Q z R z H z V z, (4) L N ( z 1) H ( z) V z = Θ N z z 1 K Q z R z H z L where H ( z) = A( z) D( z) I( z) /( 1 G( z) D( z) ), H( z) A( z) D( z) G z I( z) = C. H(z) represents the asymptotically stabilize plant. By assuming that Θ (z) is the output of an up-sampler, that Θ z = I ( z) Θ z, the close-loop transfer function becomes is, MRLC (5) Θ z K LQ z R z H z = Gc( z) D( z) Θ z 1 K LQ z R z H z At the funamental frequency an at the harmonic frequencies, we fin that. (6) ( V ( z) ) A( z) D( z) E( z) Equation 7 shows that MRLC can reuce the tracking error own to zero at the funamental frequency an at the harmonic frequencies. If the funamental frequency of the learning controller is selecte to be the largest frequency whose harmonics contain all of the task an isturbance frequencies, MRLC can reuce the tracking error of the plant successfully. Experiments ( ) 0 = =. (7) z= ai z= a i For experiments a real-time iscrete control system has been implemente using MATLAB Simulink xpc Target. The encoer connecte to the riving motor sens its information to the control loop structure on the target PC. The resultant encoer resolution for APCROM angular isplacement is

5 Materials Science Forum Vols Fig. 4. Perioic reference trajectory: esire angular position (left) an esire angular velocity (right). Fig. 5. Measure responses of APCROM with a conventional PD controller: (a) measure angular position, (b) angular position tracking error, an (c) calculate feeback control effort. Fig. 6. Measure response of APCROM with a PD controller an a MRLC using encoer estimation: (a) measure tracking error, (b) learne MRLC effort, an (c) feeback control effort. 7.42x10-5 ra/pulse. The motor amplifier has /-5volt input range. The raius of the steel pipe is 170mm. We have experimentally implemente the following two controllers. 1) a PD feeback controller using the encoer-base position estimation 2) a PD controller with a MRLC using the encoer-base position estimation, The sampling rate of the control system is set to 200 Hz an the own-sampling ratio for the multirate controller is set to 5. Figure 4 shows the perioic esire trajectory we have use in experiments. It is a trapezoial velocity profile with relatively long uration of constant velocity movement. The amplitue of isplacement is π ra an the perio is 130 sec. With this commaning input, APCROM shoul move half a roun ownwar along the pipe an then half a roun upwar aroun the pipe in 130 sec. Figure 5 shows APCROM responses for the first control scheme where only a conventional PD controller is implemente using the encoer-base angular position estimation alone. Plot (a) shows the angular position measure by the encoer, plot (b) shows the tracking error an plot (c) shows the calculate feeback effort. It is observe that the tracking error an the control effort have a very strong perioic characteristic. Figure 6 shows APCROM responses for the secon control scheme where a MRLC is implemente in conjunction with a PD controller using the encoer-base position estimation. Plot (a) shows the angular position tracking error, plot (b) shows the fee-forwar effort learne by the

6 1206 Progress on Avance Manufacture for Micro/Nano Technology 2005 MRLC, an plot (c) shows the feeback effort. During the first cycle the feeback controller solely manages the control process an the learning controller learns the require fee-forwar effort from the observe tracking error. As soon as the secon cycle begins the learning controller applies the learne effort from the first cycle an the tracking error ecreases rastically almost own to the noise level. The repetitive error is cancelle by the MRLC effort an the feeback controller responses only to the non-repetitive isturbances. Conclusions The tracking control of an automatic pipe cutting robot with a magnetic biner calle APCROM is stuie. Consiering the perioic nature of the pipe cutting process an the relatively long cycle time, a multi-rate repetitive learning controller (MRLC) is implemente to learn an compensate the significant time-varying gravitational isturbances. Two control schemes using a conventional PD controller, a MRLC, an the angular position estimations base on the encoer are experimentally implemente on a real-time control system. The analysis an experimental results verifies the effectiveness of the MRLC. References [1] S. J. Na: J. of Korean Weling Society Vol. 9 (1991), p. 1. [2] S. Y. Chang an S. J. Lee: J. of Korean Weling Society Vol. 14, (1996), p. 7. [3] M.-C. Lee an S.-G. Lee: Proc of Int Conf on Contrl, Auto, an Sys, Seoul, Korea, Vol. 1, (2001), p [4] S. Arimoto, K.S. Narenra, E.: Aaptive an Learning Systems (Plenum Press, New York 1982), p [5] K. L. Moore: Iterative Learning Control for Deterministic Systems (Lonon, Springer-Verlag, 1993). [6] N. Saegh, A.-P. Hu, an C. James: ASME J. of Dyn Sys, Meas, an Contrl, Vol. 124, (2002), p [7] S. Rhim, A.-P. Hu, N. Saegh, an W. J. Book: ASME J. of Dyn Sys, Meas, an Contrl, Vol. 123, (2001), p. 385.