Most engineered systems designed under heavy external constraints share similar dynamics. Using a dimensionless model as system representation, a dimensionless robust controller can be designed and implemented for a class of dynamically similar systems that are different in size. Dimensionless transformations of time scale, inputs and outputs determine a nominal plant model and plant-to-plant uncertainties in a dimensionless form. Using parameter-dependent normalization, a normalized dimensionless model can be derived that has low level of plant-to-plant uncertainties. The benefit of this dimensional analysis is demonstrated by the analysis of a passenger vehicle model for yaw rate control with a database consisting of 36 sets of vehicle data.

1.
Brennan, S., and Alleyne, A., 2003. “Generalized h-infinity vehicle control utilizing dimensional analysis.” American Control Conference, 2003. Proceedings of the 2003, 5, June, pp. 3774–3780.
2.
Brennan, S., Alleyne, A., and DePoorter, M., 1998. “The illinois roadway simulator-a hardware-in-the-loop testbed for vehicle dynamics and control.” American Control Conference, 998. Proceedings of the 1998, 1, June, pp. 24–26.
3.
Brennan, S., and Alleyne, A., 2002. “H-infinity vehicle control using non-dimensional perturbation measures.” American Control Conference, 2002. Proceedings of the 2002, 3, May, pp. 2534–2539.
4.
Szirtes, T., 1998. Applied dimensional analysis and modeling. New York: McGraw Hill.
5.
Buckingham
E.
,
1914
. “
On physical systems: Illustration of the use of dimensional equations
.”
Physical Review
,
4
, pp.
345
379
.
6.
Brennan
S.
, and
Alleyne
A.
,
2005
. “
Dimensionless robust control with application to vehicles
.”
IEEE Transactions on Control Systems Technology
,
13
(
4
), July, pp.
624
630
.
7.
Freudenberg, K., 1990. “Scaling down the plant condition number scales up the size of uncertainty.” Decision and Control, 1990., Proceedings of the 29th IEEE Conference on, 3, Dec, pp. 1195–1196.
8.
Brennan, S., 2002. “On size and control: The use of dimensional analysis in control design.” PhD thesis, University of Illinois at Urbana-Champaign.
9.
Wong, J. Y., 2001. Theory of Ground Vehicles, 3rd ed. John Wiley & Sons.
10.
Hosaka, M., and Murakami, T., 2004. “Yaw rate control of electric vehicle using steer-by-wire system.” Advanced Motion Control, 2004. AMC ’04. The 8th IEEE International Workshop on, March, pp. 31–34.
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