The performance of proposed Acc/Dec processor was tested and confirmed in a retrofitted milling machine. The experiments were conducted under the same motion conditions as those in the simulation study so that the results obtained by both ways can be compared.
7.1. System configuration
Figure 14 presents the schematic diagram of the test apparatus and Fig. 15 shows the block diagram of the AC servo drive including a current-loop IP controller and transmission system for
Fig. 14. Schematic diagram of experiment.
single axis. The continuous-time transfer function from the current command i* to the motor angular velocity w is of relative order three.
w(s)
i*(s) = kiikt
LJs3+ (RJ + LB + kip·J)s2+ (RB + kike + kii·J + kii·B)s + kii·B (31)
Fig. 15. Block diagram of the AC servo driver system and transmission system.
in which kt is the motor torque constant and ke is the motor back e.m.f. constant; L and R are the inductance and the resistance of the motor stator, respectively; J is the equivalent load inertia (which is a synthetic value of the motor rotor inertia, the pulley inertia and the equivalent table inertia) and B is the equivalent viscous damping (which is a synthetic value of the motor rotor viscous damping, the pulley viscous damping, the belt viscous damping and the equivalent table viscous damping); kip and kii are the proportional gain and the integral gain corresponding to the IP current-loop controller.
Although the above transfer function can be derived analytically, the values of the parameters in Eq. (31) are not readily available. Specifically, the equivalent load inertia and the equivalent viscous damping are so complicated that they are hardly evaluated. For ease of controller design, the high gain of current-loop control is always used in practice; consequently, the transfer function can be simplified as a first-order model of
Gp(s)= b
s + a (32)
where a= B/J and b = Kt/J [9]
The frequency response of the above transfer function from the current command (i.e., torque command) input to the angular velocity output was obtained by HP3562 control system analyzer.
In the underlying system, the torque command 10 volt corresponds to the motor rated torque 4.802 N-m and the angular velocity feedback from encoder is converted into voltage by ONO SOKKI FV-900 F/V converter for further analysis. The estimated models for the x and y axes, respectively, are given as follows
Gpx(s)= 33.518
s + 14.45 (33a)
Gpy(s)= 32.07
s + 13.823 (33b)
Since the x axis is mounted on the y axis, the pole of the transfer function for the x axis is farther away from the origin than that for the y axis.
The semi-closed loop, i.e., feedback signal from the encoder of servo motor, is employed in
our servo control system. Figure 16 shows the block diagram of the semi-closed loop servo control system, in which the digital velocity and position controllers are implemented. Here we use the PI velocity controller to handle the velocity loop control. The parameters of the velocity controller, proportional gain Kp and integral gain Ki, are set based on the design specifications that the rise time of velocity response is 33 msec and without overshoot, according to the typical CNC specifications. Specifically, Kp = 0.0422, Ki = 0.0094 for the x axis and Kp = 0.0442, Ki = 0.0098 for the y axis. The position loop controllers for the x axis and y axis are only pure gain equaling to 30 sec⫺1
7.2. Discussions
In the feed drive dynamic system, the decrease of circle radius may come from two origins, i.e., the Acc/Dec after interpolation and servo delay. Thus, the total decreased radius is the sum-mation of above two effects, or,
⌬Rtotal= ⌬Rservo+⌬RAcc/Dec (34)
When the position loop gains in the x axis and y axis are the same, the decreased radius yielded by servo delay can be approximated as [10]
⌬Rservo⬵ V2tan
2·R·PG2 (35)
And the term, ⌬RAcc/Dec, is described previously in Section 3.
The experimental results of circular motion with tangent velocity 15000 BLU/sec, radius of motion 4000 BLU/sec and sampling time T=0.004 sec are shown in Fig. 17, where the protrusion error is due to lost motion, occurring from the transmission system including pulley, timing belt and ball screw, and friction between mechanical contact surfaces. The decreased radius from the servo delay, according to Eq. (35), is 31 BLU. If this value is subtracted from the experimental results for each Acc/Dec profile, we will obtain quite similar profiles as those in the simulation study in Fig. 13. It is apparent that our design scheme is superior to the others since it has the smallest radius error.
Fig. 16. Semi-closed loop servo control scheme.
Fig. 17. Experimental results of circular motion with tangent velocity 15000 BLU/sec and radius of motion 4000 BLU.
8. Conclusion
This study has presented a relatively simple but novel strategy for the Acc/Dec design, which can be applied to all kinds of motion control applications, e.g., CNC machine tools, and robotic manipulators. A systematic procedure is developed on the basis of the discrete time FIR filter design technique with three necessary conditions, together with the analysis of the contouring error caused by the Acc/Dec scheme. The proposed Acc/Dec algorithm is very flexible in that it creates space for users to use more sophisticated profiles to closely match the system limitations for high performance motion control.
Acknowledgement
The authors would like to thank the National Science Council of the Republic of China for financial support of this manuscript under Contract No. NSC85-2612-E-009-035
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