Controller strategy for a 6 DOF piezoelectric translation stage

Transcription

1 UCR-ROC-93 Controller strateg for a 6 DOF pieoelectric translation stage E.. Buice, H. ang,. T. mith, R. J. Hocken, D.. Trumper, D. Otten, R. M. eugling March 4, 6 EUEN 6th International Conference Baden, ustria Ma 8, 6 through June, 6

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3 Controller strateg for a 6 DOF pieoelectric translation stage Eric. Buice, *, Hua ang, tuart T. mith, Robert J. Hocken, David. Trumper, David Otten, and Richard M. eugling 3 Center for recision Metrolog, UNC Charlotte, NC 83, U. Massachusetts Institute of Technolog, Cambridge, M 39, U. 3 awrence ivermore National aborator, ivermore, C 9455, U *Corresponding author: esbuice@uncc.edu (E.. Buice) bstract controller for the third generation, 6 degree-of-freedom (DOF) pieoelectric translation stage shown in Figure is presented. This was tested b monitoring all si coordinate motions using an orthogonal arra of si, high-resolution capacitance gages. The full 6 DOF matri transformations and controller block diagrams for this sstem have been measured and the sstem operated under closed loop control. Results of earl eperiments to determine the open loop response functions as well as preliminar results showing the closed loop response for the 3 linear translations are presented in this abstract. The ultimate goal of this project is to incorporate this 6 DOF stage within a long range - scanning sstem for nanometer pick-and-place capabilit over an area of 5 5 mm. The control strateg and earl results from this sstem will be presented. Introduction This document discusses a 6 ais controller for a fine motion stage translator comprising a moving platform that is connected to a base via 6 pieoelectric actuators. The ultimate goal of this project is to incorporate this 6 DOF stage within a long range - scanning sstem for nanometer pick-and-place capabilit over an area of 5 5 mm. The control strateg and earl results from this sstem will be presented. Eperimental arrangement During these initial tests, motion of the moving platform of the stage was monitored b a nest of si capacitance gages that monitored displacements against a cube mounted on top of the platform. It is noted that this cube added a further 36 gm to the moving stage at an offset of 75 mm from the center of the stage thereb altering its dnamic characteristics in terms of both damping and pole position, see results.

4 mathematical model indicating ke geometric parameters of the eperimental set-up is shown in Fig.. In this figure, the moving platform is represented b the lower, larger, rectangular block. The three actuator pairs in coordinates, and are identified b their orientation with the first subscript indicating that it is an actuator and the second subscripts and B identifing each actuator of the pair. s shown the latter subscript is chosen so that a counterclockwise rotation would correspond to an etension of actuator and a contraction of actuator B. imilar notation is used for the capacitance gages with the eception that the first subscript is a to identif the parameter as representing a probe. The parameter represents the separation between probe and actuator pairs with the subscripts discriminating between them. To determine poles and eros B in the function of the frequenc response matri, initial dnamic tests,b using a dnamic signal analer B were performed under open-loop control. These tests also indicate the cross coupling between coordinates. B 6 DOF controller has been,b developed and further tests were performed under closed-loop control. B stem model and control Figure : Model of the fine motion platform and capacitance-based position sensors For the purpose of control, it is necessar to transform from the motion in the aes of the moving platform to an actuator drive demand as well as a transformation between the probe signals and the motion of the upper block. Based on the model of figure, the latter transformation to derive the motion of the center of the upper measurement block q (it is the control of this column matri that is the goal of the control sstem) from the probe measurements is given b

5 {} [ ]{ } B q = = or B B B () The transformation between the actuator displacements and an estimate of the motion of the upper blockq is given b { } [ ]{} q or = + = B B B () With the eception of one coupling term in and, the orthogonalit of the actuator pairs enables these transformations to be separated into three compact sets of transformations that are treated as nearl independent control loops for econom of computation. The function of all components ecept for the plant are carried out b the computer and dce sstem. Matri computation and controller design is carried out in Mathworks Matlab while the resultant algorithms are processed in real time using dce D3 controller hardware. t this present time, a simple integral controller is emploed. The control error is computed as the difference between the measured displacements computed from the transformation of equation (). The controller output is then transferred to the actuators after the transformation given b equation ().

6 Results For brevit, the results shown are restricted to those of linear translation onl. more complete discussion will be presented at the conference. Figure shows the open loop frequenc response of the platform in the three linear aes. Coordinate Gravest ole height The gravest mode frequencies mode (H) 8 3 (db) 6 indicated b the poles in figure was lowest in the & directions, see adjacent table. This was mainl due to the large offset between mass centroid 54 6 of the capacitance electrode target 8 3 block to the ais of the corresponding actuator pair while the ais drive was coincident. Figure 3 shows the closed loop response to a force in with the Gain (db) Frequenc (H) Figure : Open loop frequenc responses of the three linear aes Gain (db) Frequenc (H) Figure 3: Closed loop response to demand in ais with measured coupling in & simultaneousl measured responses in the other two aes. mplitude of ecitation in was nm so that -3 db corresponds to an rms amplitude of 3 nm which is approaching the measurement resolution in these eperiments. References [] This work was performed under the auspices of the U.. Department of Energ b Universit of California, awrence ivermore National aborator under contract No. W- 745-Eng-48. [] eugling R.M., ebrun T, mith.t., Howard..,, si degree-of-freedom precision motion stage, Rev. ci. Instrum., 73(6), [3] ang H., eugling R.M., Jain., Fagan T., mith.t., Hocken R.J., David Otten and David. Trumper, 4, coarsefine motion control stage; preliminar studies, roc. E., 34,