This paper investigates the use of optimal l1 and H model reference optimal feedforward control to enhance the tracking performance of a linear motor drive. Experimental work is presented which studies the effects of signal preview, tracking constraint, and reference model choice on tracking performance. Suboptimal l1 control where the closed-loop system has a zero on the unit circle due to integral action in the feedback controller is given special attention, and is seen to give near optimal performance for the system under study here. For the specific trajectory employed here, the best performing feedforward controllers were experimentally seen to reduce by more than half the maximum and rms tracking errors of the H optimal feedback closed-loop systems.

1.
Alter, D. M., and Tsao, T-C, 1995, “Control of Linear Motors for Machine Tool Feed Drives: Hx Optimal Feedback for Dynamic Stiffness,” to appear ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL.
2.
Alter, D. M., 1994, Control of Linear Motors for Machine Tool Feed Drives, Ph.D. Dissertation, Univ. of Illinois at Urbana-Champaign.
3.
Alter
D. M.
, and
Tsao
T.-C.
,
1994
, “
2-D Exact Model Matching with Application to Repetitive Control
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
116
, pp.
2
9
.
4.
Dahleh
M. A.
, and
Pearson
J. B.
,
1987
, “
l1-Optimal Feedback Controllers for MIMO Discrete-Time Systems
,”
IEEE Transactions on Automatic Control
, Vol.
32
, No.
14
, pp.
314
322
.
5.
Franklin, G. F., and Powell, J. D., 1981, Digital Control of Dynamic Systems, Addison-Wesley, Reading, MA, pp. 190–195.
6.
Tomizuka
M.
,
1987
, “
Zero-Phase Error Tracking Controller for Digital Control
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
109
, pp.
65
68
.
7.
Tsao
T-C.
,
1994
, “
Optimal Feedforward Digital Tracking Controller Design
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
116
, pp.
583
592
.
8.
Vidyasagar
M.
,
1991
, “
Further Results on the Optimal Rejection of Persistent Bounded Disturbances
,”
IEEE Transactions on Automatic Control
, Vol.
36
, pp.
642
652
.
9.
Vidyasagar, M., 1985, Control System Synthesis: A Factorization Approach, The MIT Press, Cambridge, MA, pp. 174–178.
10.
Zames
G.
, and
Francis
B. A.
,
1983
, “
Minimax Sensitivity, and Optimal Robustness
,”
IEEE Transactions on Automatic Control
, Vol.
28
, pp.
585
601
.
11.
Ziemer, R. E., Tranter, W. H., and Fannin, D. R., 1983, Signals and Systems: Continuous and Discrete, Macmillan, New York, pp. 388–419.
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