Acceleration-bounded control for discrete time linear systems
System, Structure and Control, Volume # 3 | Part# 1
Authors
Bender, Fernando Augusto; da Silva, Joao Manoel Gomes
Digital Object Identifier (DOI)
10.3182/20071017-3-BR-2923.00082
Page Numbers:
512-517
Index Terms
anti-windup,saturation,L2 performance,discrete time,LMI
Abstract
A method for synthesizing dynamic output feedback controllers for discrete time systems presenting actuators constrained in amplitude, rate and acceleration is proposed. The considered controller structure, composed by two saturating integrator blocks and a linear compensator, allows to deliver to the actuator input a signal inside all its bounds. Anti-windup loops in the controller are simultaneously designed and add degrees of freedom to the synthesis process, besides improving performance. Sufficient LMI conditions for such stabilizing controller existence are derived and exemplified. Optimization problems for maximizing disturbance tolerance and rejection are considered.
References
[1] A. Bateman and Z. Lin. An analysis and design
method for linear system under nested saturation.
Syst. and Cont. Letters, 48:41-52, Jan.
2002.
[2] J. M. Gomes da Silva Jr. and S. Tarbouriech.
Anti-windup design with guaranted regions of
stability: an lmi-based approach. IEEE Trans.
on Aut. Cont., 50:106-111, 2005.
[3] J. M. Gomes da Silva Jr., D. Limon, and
T. Alamo. Dynamic output feedback for
discrete-time systems under amplitude and rate
actuator constraints. In Proc. of 44th IEEE
Conference on Decision and Control, Sevilla,
2005.
[4] J. M. Gomes da Silva Jr., F. Lescher, and D. Eckhard.
Design of time-varying controllers for
discrete-time linear systems with input saturation.
IET Proc. on Control Theory and Applications
, (1):155-162, Jan. 2007.
[5] Tingshu Hu and Zongli Lin. Control Systems
with Actuator Saturation: Analysis and Design.
Birkhäuser, Boston, 2001.
[6] V. Kapila and K. Grigoriadis. Actuator Saturation
Control. Marcel Dekker, Inc., New York, Feb.
2002.
[7] V. Kapila and W. M. Haddad. Fixed-structure
controller design for systems with actuator amplitude
and rate nonlinearities. Int. J. of Cont.,
73:520-530, Jun. 2000.
[8] V. Kapila, H. Pan, and M. S de Queiroz. Lmi-based
control of linear systems with actuator
amplitude and rate nonlinearities. In Proc.
of the 38th IEEE Conference on Decision and
Control, pages 1413-1418, Phoeniz, AZ, 1999.
[9] T. Kiyama and T. Iwasaki. On the use of multiloop
circle criterion for saturating control synthesis.
Syst. and Cont. Letters, 41:105-114,
2000.
[10] Z. Lin. Semi-global stabilization of linear systems
with position and rate-limited actuators. Systems
and Control Letters, 30:1-11, 1997.
[11] T. Nguyen and F. Jabbari. Output feedback controllers
for disturbance attenuation with actuator
amplitude and rate saturation. Automatica,
36:1339-1346, 2000.
[12] H. Pan and V. Kapila. LMI-based control of
discrete-time systems with actuator amplitude
and rate nonlinearities, volume Actuator Saturation
Control, chapter 6, pages 135-159. Marcel
Dekker Inc., New York, 2002.
[13] C. Scherer, P. Gahinet, and M. Chilali. Multiobjective
output feedback control via lmi optimization.
IEEE Trans. on Aut. Cont., 42:896-
911, July 1997.
[14] G. Shi, A. Saberi, and A. A. Stoorvogel. On
Lp performance with global internal stability
for linear systems with actuators subject to
amplitude and rate saturations. In Proceedings
of the 19th American Control Conference, pages
730-734, Chicago, IL, Jun. 2000.
[15] A. A. Stoorvogel and A. Saberi. Output regulation
for linear systems to amplitude plus rate saturating
actuators. Int. J. of Rob. and Nonlinear
Cont., 9:631-657, Oct. 1999.
[16] S. Tarbouriech and G. Garcia. Control of uncertain
systems with bounded inputs, page 186.
Springer Verlag., Berlin, 1997.
[17] S. Tarbouriech, C. Prieur, and J. M. Gomes da
Silva Jr. Stability analysis and stabilization of
systems presenting nested saturations. IEEE
Trans. on Aut. Cont., 51:1364-1371, 2006.
[18] F. Tyan and D. S. Bernstein. Dynamic output
feedback compensation for linear systems with
independent amplitude and rate saturation. Int.
J. of Cont., 67:89-116, Jan. 1997.
