In this paper, a new systematic controller synthesis methodology for use with highly nonlinear multivariable and nonautonomous systems with application to a class of multivariable nonlinear aerospace systems is presented. The procedure is applied to a typical liquid propellant engine, and the performance of the resulting new control system is presented. In this research, the nonlinear dynamic model of the engine, which includes both soft and hard nonlinearities, is developed. The systematic controller design procedure is based on describing function models of the engine coupled with a new multivariable exact model matching procedure.

1.
Nassirharand
,
A.
, and
Karimi
,
H.
,
2002
, “
Input/Output Characterization of Highly Nonlinear Multivariable Systems
,”
Adv. Eng. Software
,
33
, pp.
825
830
.
2.
Santana, A., Jr., Barbosa, F. I., and Niwa, M., 2000, “Modeling and Robust Analysis of a Liquid Rocket Engine,” 36th AIAA Joint Propulsion Conference and Exhibit, Huntsville, Alabama, 8 pages.
3.
Schinstock
,
D. E.
,
Scott
,
D. A.
, and
Haskew
,
Tim A.
,
1988
, “
Modeling and Estimation for Electromechanical Thrust Vector Control of Rocket Engines
,”
AIAA J.
,
14
, pp.
440
446
.
4.
Lorenzo
,
C. F.
,
Ray
,
A.
, and
Holmes
,
M. S.
,
2001
, “
Nonlinear Control of a Reusable Rocket Engine for Life Extension
,”
AIAA J.
,
17
, pp.
998
1004
.
5.
Nassirharand, A., and Taylor, J. H., 1990, “Synthesis of Linear PID Controllers for Nonlinear Multivariable Systems,” in Proceedings of American Control Conference, San Diego, CA, pp. 2223–2228.
6.
Katebi
,
S. D.
, and
Katebi
,
M. R.
,
1987
, “
Combined Frequency and Time Domain Technique for the Design of Compensators for Nonlinear Feedback Control Systems
,”
Int. J. Syst. Sci.
,
18
, pp.
2001
2017
.
7.
Slotine, J. J., and Li, W., 1991, Applied Nonlinear Control, Prentice–Hall.
8.
Hunt
,
L. R.
,
Su
,
R.
, and
Meyer
,
G.
,
1987
, “
Global Transformation of Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
28
, pp.
24
30
.
9.
Slotine
,
J. J.
, and
Sastry
,
S. S.
,
1983
, “
Tracking Control of Nonlinear Systems Using Sliding Surfaces With Application to Robot Manipulation
,”
Int. J. Control
,
38
, pp.
465
492
.
10.
Utkin
,
V.
,
1983
, “
Variable Structure Systems With Sliding Modes
,”
IEEE Trans. Autom. Control
,
22
, pp.
212
222
.
11.
Itkis, U., 1976, Control Systems of Variable Structures, John Wiley, Inc.
12.
Horowitz
,
I. M.
,
1976
, “
Synthesis of Feedback Systems With Nonlinear Time-Varying Uncertain Plant to Satisfy Quantitative Performance Specifications
,”
Proc. IEEE
,
64
, pp.
123
130
.
13.
Taylor
,
D. G.
et al.
,
1989
, “
Adaptive Regulation of Nonlinear Systems With Unmodeled Dynamics
,”
IEEE Trans. Autom. Control
,
34
, pp.
405
412
.
14.
Nagurka
,
M. L.
, and
Yen
,
V.
,
1990
, “
Fourier-Based Optimal Control of Nonlinear Dynamic Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
112
, pp.
17
26
.
15.
Suzuki, A., and Hedrick, J. Karl, 1985, “Nonlinear Controller Design by an Inverse Random-Input Describing Function Methods,” in Proceedings of the American Control Conference, Boston, MA, pp. 1236–1241.
16.
Taylor, J. H., 1983, “A Systematic Nonlinear Controller Design Approach Based on Quasilinear Models,” in Proceedings of the American Control Conference, San Francisco, CA, pp. 141–145.
17.
Taylor, J. H., and Strobel, K. L., 1985, “Nonlinear Control System Design Based on Quasilinear System Models,” in Proceedings of the American Control Conference, Boston, MA, pp. 1242–1247.
18.
Nassirharand
,
A.
,
1991
, “
Design of Dual-Range Linear Controllers for Nonlinear Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
113
, pp.
590
596
.
19.
Nassirharand
,
A.
,
Taylor
,
J. H.
, and
Reid
,
K. N.
,
1988
, “
Controller Design for Nonlinear Systems Based on Simultaneous Stabilization Theory and Describing Function Models
,”
ASME J. Dyn. Syst., Meas., Control
,
110
, pp.
134
143
.
20.
Nassirharand
,
A.
, and
Taylor
,
J. H.
,
1991
, “
Frequency-Domain Modeling of Nonlinear Multivariable Systems
,”
Control Theory Adv. Technol.
,
7
, pp.
201
214
.
21.
Nassirharand
,
A.
,
1988
, “
Identification of Frequency Domain Models for Nonlinear Systems
,”
Adv. Eng. Software
,
10
, pp.
195
201
.
22.
Reklaitis, G. V., Ravindran, A., and Ragsdell, K. M., 1983, Engineering Optimization, John Wiley, Inc.
23.
Beliayev, E. N., Chevanov, V. K., and Chervakov, V. V., 1999, Mathematical Modeling of Working Process in Liquid Propellant Rocket Engines, MAI Publications, Moscow (in Russian).
You do not currently have access to this content.