A method is presented that can often reduce the number of scheduling parameters for gain-scheduled controller implementation by transformation of the system representation using parameter-dependent dimensional transformations. In some cases, the reduction in parameter dependence is so significant that a linear parameter-varying system can be transformed to an equivalent linear time invariant (LTI) system, and a simple example of this is given. A general analysis of the parameter-dependent dimensional transformation using a matrix-based approach is then presented. It is shown that, while some transformations simplify gain scheduling, others may increase the number of scheduling parameters. This work explores the mathematical conditions causing an increase or decrease in varying parameters resulting from a given transformation, thereby allowing one to seek transformations that most reduce the number of gain-scheduled parameters in the controller synthesis step.

1.
Shimomura
,
T.
, 2003, “
Hybrid Control of Gain-Scheduling and Switching: A Design Example of Aircraft Control
,”
Proceedings of the American Control Conference
,
Denver, CO
, Jun. 4–6, pp.
4639
4644
.
2.
Rugh
,
W. J.
, 1991, “
Analytical Framework for Gain Scheduling
,”
IEEE Control Syst. Mag.
0272-1708,
11
, pp.
79
84
.
3.
Bruzelius
,
F.
, 2002, “
LPV-Based Gain Scheduling, An H-Infinity-LMI Aproach
,”
Signals and Systems
,
Chalmers University of Technology
,
Goteborg
, pp.
112
.
4.
Choi
,
D. J.
, and
Park
,
P. G.
, 2001, “
Guaranteed Cost LPV Output-Feedback Controller Design for Nonlinear Systems
,”
Proceedings of the 2001 IEEE International Symposium on Industrial Electronics
,
Pusan, Korea
, Jun. 12–16, pp.
1198
1203
.
5.
Lee
,
C. H.
, and
Chung
,
M. J.
, 2001, “
Gain-Scheduled State Feedback Control Design Technique for Flight Vehicles
,”
IEEE Trans. Aerosp. Electron. Syst.
0018-9251,
37
(
1
), pp.
173
182
.
6.
Leith
,
D. J.
, and
Leithead
,
W. E.
, 2000, “
On Formulating Nonlinear Dynamics in LPV Form
,”
Proceedings of the 39th IEEE Conference on Decision and Control
,
Sydney, Australia
, Dec., pp.
3526
3527
.
7.
Fedigan
,
S. J.
,
Knospe
,
C. R.
, and
Williams
,
R. D.
, 1998, “
Gain-Scheduled Control for Substructure Properties
,”
Proceedings of the 1998 American Control Conference
, Jun. 24–26, pp.
1205
1209
.
8.
Wang
,
F.
, and
Balakrishnan
,
V.
, 2002, “
Improved Stability Analysis and Gain-Scheduled Controller Synthesis for Parameter-Dependent Systems
,”
IEEE Trans. Autom. Control
0018-9286,
47
, pp.
720
734
.
9.
Corriga
,
G.
,
Guia
,
A.
, and
Usai
,
G.
, 1998, “
An Implicit Gain-Scheduling Controller for Cranes
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
6
(
1
), pp.
15
20
.
10.
Tavakoli
,
S.
, and
Tavakoli
,
M.
, 2003, “
Optimal Tuning of PID Controllers for First Order Plus Time Delay Models Using Dimensional Analysis
,”
The Fourth IEEE International Conference on Control and Automation
,
Canada
, pp.
942
946
.
11.
Astrom
,
K. J.
,
Hang
,
C. C.
,
Persson
,
P.
, and
Ho
,
W. K.
, 1992, “
Toward Intelligent PID Control
,”
Automatica
0005-1098,
28
, pp.
1
9
.
12.
Brennan
,
S.
, and
Alleyne
,
A.
, 2001, “
Robust Scalable Vehicle Control via Non-Dimensional Vehicle Dynamics
,”
Veh. Syst. Dyn.
0042-3114,
36
(
4–5
), pp.
255
278
.
13.
Brennan
,
S.
, and
Alleyne
,
A.
, 2001, “
Using a Scale Testbed: Controller Design and Evaluation
,”
IEEE Control Syst. Mag.
0272-1708,
21
(
3
), pp.
15
26
.
14.
Brennan
,
S.
, and
Alleyne
,
A.
, 2005, “
Dimensionless Robust Control With Application to Vehicles
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
13
(
4
), pp.
624
630
.
15.
Ghanekar
,
M.
,
Wang
,
D. W. L.
, and
Heppler
,
G. R.
, 1997, “
Scaling Laws for Linear Controllers of Flexible Link Manipulators Characterized by Nondimensional Groups
,”
IEEE Trans. Rob. Autom.
1042-296X,
13
(
1
), pp.
117
127
.
16.
Fox
,
R. W.
, and
McDonald
,
A. T.
, 1992,
Introduction to Fluid Mechanics
,
4th ed.
,
Wiley
,
New York
.
17.
Bridgman
,
P. W.
, 1943,
Dimensional Analysis
, 3rd printing, revised ed.,
Yale University Press
,
New Haven
.
18.
Szirtes
,
T.
, 1998,
Applied Dimensional Analysis and Modeling
,
McGraw-Hill
,
New York
.
19.
Buckingham
,
E.
, 1914, “
On Physically Similar Systems Illustrations of the Use of Dimensional Equations
,”
Phys. Rev.
0031-899X,
4
(
4
), pp.
345
376
.
20.
Hailu
,
H.
, and
Brennan
,
S.
, 2005, “
Use of Dimensional Analysis to Reduce the Parametric Space for Gain-Scheduling
,”
Proceedings of the 2005 American Control Conference
,
Portland, OR
, Jun. 8–10.
21.
Franklin
,
G. F.
,
Powell
,
J. D.
, and
Emami-Naeini
,
A.
, 1994,
Feedback Control of Dynamic Systems
,
3rd ed.
,
Addison-Wesley
,
Reading, MA
.
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