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Scheduled controllers for linear systems with bounded actuators. (English) Zbl 1038.93032

State and output feedback controllers are designed for disturbance attentuation in linear systems with bounded actuators. The controller is scheduled according to the proximity to the origin of the state of the plant in the state-feedback case and the compensator state in the case of output feedback. This procedure yields a linear parameter-varying structure for the controller that allows for higher-gain and hence higher-performance controllers as the states move closer to the origin. The main results give sufficient conditions for the satisfaction of a parameter-dependent performance measure without violating the saturation bounds. Linear splines are used to obtain solutions that can be obtained by standard LMI software. Examples – including an open-loop unstable system – highlight the application of the results.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
93C73 Perturbations in control/observation systems
65D07 Numerical computation using splines
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[1] Abedor, J.; Nagpal, K.; Poolla, K., A linear matrix inequality approach to peak-to-peak gain minimization, International Journal of Robust and Nonlinear Control, 6, 899-927 (1996) · Zbl 0862.93028
[2] Antsaklis, P.; Michel, A. N., Linear systems (1997), McGraw-Hill: McGraw-Hill New York
[3] Boyd, S.; Balakrishnan, V., Linear matrix inequalities in system and control theory, SIAM Studies in Applied Mathematics, 15, 77-90 (1994)
[4] Campo, P. J.; Morari, M., Robust control of processes subject to saturation nonlinearities, Computers in Chemical Engineering, 14, 4/5, 343-358 (1990)
[5] Feron, E.; Apkarian, P.; Gahinet, P., Analysis and synthesis of robust control control systems via parameter-dependent Lyapunov functions, IEEE Transactions on Automatic Control, 41, 7, 1041-1046 (1996) · Zbl 0857.93088
[6] Garcia, G.; Tarbouriech, S., Stabilization with eigenvalue placement of a norm-bounded uncertain system by bounded inputs, International Journal of Robust and Nonlinear Control, 9, 10, 599-616 (1999) · Zbl 0959.93022
[7] Garcia, G.; Tarbouriech, S.; Suarez, R.; Alvarez-Ramirez, J., Nonlinear bounded control for norm-bounded uncertain systems, IEEE Transactions on Automatic Control, 44, 6, 1254-1258 (1999) · Zbl 1136.93335
[8] Gutman, P.; Hagander, P., A new design of constrained controllers for linear systems, IEEE Transactions on Automatic Control, 30, 1, 22-33 (1985) · Zbl 0553.93052
[9] Henrion, D.; Garcia, G.; Tarbouriech, S., Piecewise linear robust control of systems with input constraints, European Journal of Control, 15, 157-166 (1999) · Zbl 0955.93039
[10] Kapila, V., & Grigoroadis, K. (Eds.) (2002). Actuator saturation control, control engineering series; Kapila, V., & Grigoroadis, K. (Eds.) (2002). Actuator saturation control, control engineering series
[11] Kappor, N.; Teel, A. R.; Daoutidis, P., An anti-windup design for linear systems with input saturation, Automatica, 34, 5, 559-574 (1998) · Zbl 1040.93513
[12] Kothare, M.; Campo, P. J.; Morari, M.; Nett, C. N., A unified framework for the study of anti-windup designs, Automatica, 30, 12, 1869-1883 (1994) · Zbl 0825.93312
[13] Lee, H. L., & Spillman, M. (1997). A parameter-dependent performance criteria for linear parameter-varying systems. In Proceedings of CDC; Lee, H. L., & Spillman, M. (1997). A parameter-dependent performance criteria for linear parameter-varying systems. In Proceedings of CDC
[14] Lin, Z., Global control of linear systems with saturating actuators, Automatica, 34, 7, 897-905 (1998) · Zbl 0934.93059
[15] Lin, Z.; Saberi, A., A semi-global low-and-high gain design technique for linear systems with input saturation—stabilization and disturbance rejection, International Journal of Robust and Nonlinear Control, 5, 381-398 (1995) · Zbl 0833.93046
[16] Lin, Z.; Saberi, A.; Teel, A. R., Simultaneous \(L_p\)-stabilization and internal stabilization of linear systems subject to input saturation-state feedback case, Systems and Control Letters, 25, 219-226 (1995) · Zbl 0877.93101
[17] Masubuchi, I., Kume, A., & Shimemura, E. (1998). Spline-type solution to parameter-dependent LMIs. In Proceedings of CDC; Masubuchi, I., Kume, A., & Shimemura, E. (1998). Spline-type solution to parameter-dependent LMIs. In Proceedings of CDC
[18] Megretski, A. (1996). \(L_2\)Proceedings of 13th IFAC world congressVol. D; Megretski, A. (1996). \(L_2\)Proceedings of 13th IFAC world congressVol. D
[19] Nguyen, T.; Jabbari, F., Output feedback controller for disturbance attenuation with actuator amplitude and rate saturation, Automatica, 36, 9, 1339-1346 (2000) · Zbl 0959.93505
[20] Rotea, A. R., The generalized \(h_2\) control problem, Automatica, 29, 2, 373-385 (1993) · Zbl 0772.93027
[21] Scorletti, G.; Folcher, J. P.; El Ghaoui, L., Output feedback control with input saturationLMI design approaches, European Journal of Control, 7, 6, 567-579 (2001) · Zbl 1293.93639
[22] Srivastava, S., & Jabbari, F. (2000). Scheduled controllers for disturbance attenuation of systems with bounded inputs. In Proceedings of ACC; Srivastava, S., & Jabbari, F. (2000). Scheduled controllers for disturbance attenuation of systems with bounded inputs. In Proceedings of ACC
[23] Stoorvogel, A. A., & Saberi, A. (Eds.) (1999). Special Issue on control problems with constraint, International Journal of Robust and Nonlinear Control\(9\); Stoorvogel, A. A., & Saberi, A. (Eds.) (1999). Special Issue on control problems with constraint, International Journal of Robust and Nonlinear Control\(9\)
[24] Teel, A. R., Linear systems with input nonlinearitiesGlobal stabilization by scheduling a family of \(H_∞\)-type controllers, International Journal of Robust and Nonlinear Control, 5, 399-411 (1995) · Zbl 0834.93040
[25] Wredenhagen, G. F.; Belanger, P. R., Piecewise linear LQ control for systems with input constraints, IEEE Transactions on Automatic Control, 30, 3, 403-416 (1994) · Zbl 0800.93519
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