×

Research on gain scheduling. (English) Zbl 0976.93002

The paper surveys the current status of research and some future possibilities, by including classical approaches to gain scheduling, as well as recent trends, without focusing on particular engineering areas. The text is structured in seven sections as follows: (1) Introduction; (2) Gain scheduling – provides a general presentation and comments advantages/disadvantages; (3) Linear parameter-varying (LPV) plant descriptions – reviews two ways in which such models can arise; (4) Linearization gain scheduling – discusses recently developed analytical aspects; (5) LPV design methods – emphasizes connections to linear matrix-inequality-based constructions of \(H_\infty\) optimal control; (6) Stability and performance; (7) Current directions. Several examples are considered and revisited in different sections.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B51 Design techniques (robust design, computer-aided design, etc.)
93C10 Nonlinear systems in control theory
93B18 Linearizations
15A39 Linear inequalities of matrices
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Apkarian, P., On the discretization of LMI-synthesized linear parameter-varying controllers, Automatica, 33, 4, 655-661 (1997) · Zbl 0879.93016
[2] Apkarian, P.; Adams, R., Advanced gain-scheduling techniques for uncertain systems, IEEE Transactions on Control Systems Technology, 6, 1, 21-32 (1998)
[3] Apkarian, P.; Gahinet, P., A convex characterization of gain-scheduled \(H∞\) controllers, IEEE Transactions on Automatic Control, AC-40, 5, 853-864 (1995) · Zbl 0826.93028
[4] Apkarian, P.; Gahinet, P.; Becker, G., Self-scheduled H-infinity control of linear parameter-varying systems: A design example, Automatica, 31, 9, 1251-1261 (1995) · Zbl 0825.93169
[5] Åström, K. J.; Wittenmark, B., Adaptive control (1995), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0217.57903
[6] Bailey, R. L., Cederquist, A. L., Florek, J. J., Hart, D. L., & Meitzler, A. H. (1978). An IIEC-2 low-emission concept car. SAE Paper No. 780206, Society of Automotive Engineers.; Bailey, R. L., Cederquist, A. L., Florek, J. J., Hart, D. L., & Meitzler, A. H. (1978). An IIEC-2 low-emission concept car. SAE Paper No. 780206, Society of Automotive Engineers.
[7] Balas, G., Fialho, I., Lee, L., Nalbantoglu, V., Packard, A., Tan, W., Wemhoff, E., Wolodkin, G., & Wu, F. (1997). Theory and application of linear parameter varying control techniques. Workshop notes: American Control Conference, June.; Balas, G., Fialho, I., Lee, L., Nalbantoglu, V., Packard, A., Tan, W., Wemhoff, E., Wolodkin, G., & Wu, F. (1997). Theory and application of linear parameter varying control techniques. Workshop notes: American Control Conference, June.
[8] Bamieh, B., & Giarré, L. (1999). Identification of linear parameter varying models. Proceedings of the 38th IEEE conference on decision and control, Phoenix, AZ, December.; Bamieh, B., & Giarré, L. (1999). Identification of linear parameter varying models. Proceedings of the 38th IEEE conference on decision and control, Phoenix, AZ, December.
[9] Becker, G.; Packard, A., Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback, Systems & Control Letters, 23, 205-215 (1994) · Zbl 0815.93034
[10] Bequette, W., & Doyle, F. J. (2000). A review of gain scheduled control in chemical process systems, submitted for publication.; Bequette, W., & Doyle, F. J. (2000). A review of gain scheduled control in chemical process systems, submitted for publication.
[11] Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia, PA: SIAM.; Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia, PA: SIAM. · Zbl 0816.93004
[12] Buschek, H. (1997). Robust autopilot design for future missile systems. Proceedings of the AIAA guidance, navigation, and control conference, New Orleans, LA. AIAA Paper No. A97-37172.; Buschek, H. (1997). Robust autopilot design for future missile systems. Proceedings of the AIAA guidance, navigation, and control conference, New Orleans, LA. AIAA Paper No. A97-37172.
[13] Canale, R. P., Winegarden, S. R., Carlson, C. R., & Miles, D. L. (1978). General motors phase II catalyst system. SAE Paper No. 780205, Society of Automotive Engineers.; Canale, R. P., Winegarden, S. R., Carlson, C. R., & Miles, D. L. (1978). General motors phase II catalyst system. SAE Paper No. 780205, Society of Automotive Engineers.
[14] Cloutier, J. R., D’Souza, C. N., & Mracek, C. P. (1996a). Nonlinear regulation and nonlinear H-infinity control via the state-dependent Riccati equation technique, Part 1, theory. Proceedings of the first international conference on nonlinear problems in aviation and aerospace. Daytona Beach, FL (pp. 117-130).; Cloutier, J. R., D’Souza, C. N., & Mracek, C. P. (1996a). Nonlinear regulation and nonlinear H-infinity control via the state-dependent Riccati equation technique, Part 1, theory. Proceedings of the first international conference on nonlinear problems in aviation and aerospace. Daytona Beach, FL (pp. 117-130).
[15] Cloutier, J. R., D’Souza, C. N., & Mracek, C. P. (1996b). Nonlinear regulation and nonlinear H-infinity control via the state-dependent riccati equation technique, Part 2, examples. Proceedings of the first international conference on nonlinear problems in aviation and aerospace, Daytona Beach, FL (pp. 130-147).; Cloutier, J. R., D’Souza, C. N., & Mracek, C. P. (1996b). Nonlinear regulation and nonlinear H-infinity control via the state-dependent riccati equation technique, Part 2, examples. Proceedings of the first international conference on nonlinear problems in aviation and aerospace, Daytona Beach, FL (pp. 130-147).
[16] Cook, J. A., Grizzle, J. W., & Sun, J. (1996). Engine control. In W.S. Levine, The control handbook (pp. 1261-1274) New York: IEEE Press (Chapter 74.1).; Cook, J. A., Grizzle, J. W., & Sun, J. (1996). Engine control. In W.S. Levine, The control handbook (pp. 1261-1274) New York: IEEE Press (Chapter 74.1).
[17] Desoer, C. A., Slowly varying system \(ẋ= A(t) x\), IEEE Transactions on Automatic Control, AC-14, 6, 780-781 (1969)
[18] Doyle, J. C., Wall, J. E., & Stein, G. (1982). Performance and robustness analysis for structured uncertainty. Proceedings of the 21st IEEE conference on decision and control, December (pp. 629-636).; Doyle, J. C., Wall, J. E., & Stein, G. (1982). Performance and robustness analysis for structured uncertainty. Proceedings of the 21st IEEE conference on decision and control, December (pp. 629-636).
[19] Draper, C. S., Flight control, Journal of the Royal Aeronautical Society, 59, 451-477 (1955)
[20] Gregory, P. C. (Ed.) (1959). Proceedings of the self adaptive flight control systems symposium, Wright-Patterson AFB. OH. WADC Technical Report 59-49.; Gregory, P. C. (Ed.) (1959). Proceedings of the self adaptive flight control systems symposium, Wright-Patterson AFB. OH. WADC Technical Report 59-49.
[21] Gumbleton, J. J., & Bowler, L. L. (1982). General motors computer command control system development. SAE Paper No. 82091, Society of Automotive Engineers.; Gumbleton, J. J., & Bowler, L. L. (1982). General motors computer command control system development. SAE Paper No. 82091, Society of Automotive Engineers.
[22] Howard, R. W., Automatic flight controls in fixed wing aircraft: The first 100 years, Aeronautical Journal, 77, 533-562 (1973)
[23] Huang, Y., & Lu, W.-M. (1996). Nonlinear optimal control: Alternatives to Hamilton-Jacobi equation. Proceedings of the 35th Conference on Decision and Control, Kobe, Japan (pp. 3942-3947).; Huang, Y., & Lu, W.-M. (1996). Nonlinear optimal control: Alternatives to Hamilton-Jacobi equation. Proceedings of the 35th Conference on Decision and Control, Kobe, Japan (pp. 3942-3947).
[24] Hyde, R. A.; Glover, K., The application of scheduled H-infinity controllers to a vstol aircraft, IEEE Transactions on Automatic Control, 38, 7, 1021-1039 (1993)
[25] Källström, C. G.; Åström, K. J.; Thorell, N. E.; Eriksson, J.; Sten, L., Adaptive autopilots for tankers, Automatica, 15, 241-254 (1979)
[26] Kamen, E. W.; Khargonekar, P. P., On the control of linear systems whose coefficients are functions of parameters, IEEE Transactions on Automatic Control, AC-29, 1, 25-33 (1984) · Zbl 0593.93042
[27] Kaminer, I.; Pascoal, A.; Hallberg, E.; Silvestre, C., Trajectory tracking for autonomous vehicles: An integrated approach to guidance and control, Journal of Guidance, Control, and Dynamics, 21, 1, 29-38 (1998) · Zbl 0908.93048
[28] Kaminer, I.; Pascoal, A. M.; Khargonekar, P. P.; Coleman, E., A velocity algorithm for the implementation of gain-scheduled controllers, Automatica, 31, 8, 1185-1191 (1995) · Zbl 0839.93037
[29] Kelemen, M., A stability property, IEEE Transactions on Automatic Control, 31, 8, 766-768 (1986) · Zbl 0607.34047
[30] Kellett, M. G. (1991). Continuous scheduling of H-infinity controllers for a ms760 paris aircraft. In P.H. Hammond, Robust control system design using H-infinity and related methods (pp. 197-223). London, England: Institute of Measurement and Control.; Kellett, M. G. (1991). Continuous scheduling of H-infinity controllers for a ms760 paris aircraft. In P.H. Hammond, Robust control system design using H-infinity and related methods (pp. 197-223). London, England: Institute of Measurement and Control.
[31] Kelly, J. H., & Evers, J. H. (1997). An interpolation strategy for scheduling dynamic compensators. Proceedings of the AIAA guidance, navigation, and control conference, New Orleans, LA. AIAA Paper No. A97-37173.; Kelly, J. H., & Evers, J. H. (1997). An interpolation strategy for scheduling dynamic compensators. Proceedings of the AIAA guidance, navigation, and control conference, New Orleans, LA. AIAA Paper No. A97-37173.
[32] Khalil, H. K., Nonlinear systems (1996), Prentice-Hall: Prentice-Hall Upper Saddle River, NJ · Zbl 0626.34052
[33] Khalil, H. K.; Kokotovic, P. V., On stability properties of nonlinear systems with slowly varying inputs, IEEE Transactions on Automatic Control, 36, 2, 229 (1991) · Zbl 0766.93068
[34] Lawrence, D. A.; Rugh, W. J., On a stability theorem for nonlinear systems with slowly varying inputs, IEEE Transactions on Automatic Control, 35, 7, 860-864 (1990) · Zbl 0715.93054
[35] Lawrence, D. A.; Rugh, W. J., Gain scheduling dynamic linear controllers for a nonlinear plant, Automatica, 31, 3, 381-390 (1995) · Zbl 0825.93192
[36] Leith, D. J.; Leithead, W. E., Appropriate realization of gain-scheduled controllers with application to wind turbine regulation, International of Control, 65, 2, 223-248 (1996) · Zbl 0875.93348
[37] Leith, D. J.; Leithead, W. E.; Lawrence, D. A.; Rugh, W. J., Comments on Gain scheduling dynamic linear controllers for a nonlinear plant, Automatica, 34, 8, 1041-1043 (1998) · Zbl 0962.93055
[38] Leonessa, A., Haddad, W. M., & Chellaboina, V. (1988). Nonlinear system stabilization via stability-based switching. Proceedings of the 37th IEEE conference on decision and control, Tampa, FL (pp. 2983-2996).; Leonessa, A., Haddad, W. M., & Chellaboina, V. (1988). Nonlinear system stabilization via stability-based switching. Proceedings of the 37th IEEE conference on decision and control, Tampa, FL (pp. 2983-2996).
[39] Masaki, K., Aono, S., Akaeda, M., & Minami, H. (1978). Development of the Nissan electronically controlled carburetor system. SAE Paper No. 780204, Society of Automotive Engineers.; Masaki, K., Aono, S., Akaeda, M., & Minami, H. (1978). Development of the Nissan electronically controlled carburetor system. SAE Paper No. 780204, Society of Automotive Engineers.
[40] McConley, M. W., Appleby, B. D., Dahleh, M. A., & Feron, E. (1997). Control Lyapunov function approach to robust stabilization of nonlinear systems. Proceedings of the American control conference, Albuquerque, NM, June (pp. 416-419).; McConley, M. W., Appleby, B. D., Dahleh, M. A., & Feron, E. (1997). Control Lyapunov function approach to robust stabilization of nonlinear systems. Proceedings of the American control conference, Albuquerque, NM, June (pp. 416-419).
[41] McRuer, D.; Graham, D., Eighty years of flight control: triumphs and pitfalls of the systems approach, Journal of Guidance and Control, 4, 4, 353-362 (1981)
[42] Nichols, R. A.; Reichert, R. T.; Rugh, W. J., Gain scheduling for H-infinity controllers: A flight control example, IEEE Transactions on Control Systems Technology, 1, 2, 69-79 (1993)
[43] Niemann, H., & Stoustrup, J. (1999). An architecture for implementation of multivariable controllers. Proceedings of the American control conference, San Diego, CA, June (pp. 4029-4032).; Niemann, H., & Stoustrup, J. (1999). An architecture for implementation of multivariable controllers. Proceedings of the American control conference, San Diego, CA, June (pp. 4029-4032).
[44] Osder, S. S. (1996). Evolution of automatic flight controls. Material from a short course at Honeywell Air Transport Division.; Osder, S. S. (1996). Evolution of automatic flight controls. Material from a short course at Honeywell Air Transport Division.
[45] Packard, A., Gain-scheduling via linear fractional transformations, Systems and Control Letters, 22, 79-92 (1994) · Zbl 0792.93043
[46] Packard, A.; Zhou, K.; Pandey, P.; Leonhardson, J.; Balas, G., Optimal, constant I/O similarity scaling for full-information and state-feedback control problems, Systems & Control Letters, 19, 217-280 (1992) · Zbl 0772.49021
[47] Paddison, F. C., The Talos control system, Johns Hopkins APL Technical Digest, 3, 2, 154-156 (1982)
[48] Reichert, R., Dynamic scheduling of modern-robust-control autopilot designs for missiles, IEEE Control Systems Magazine, 12, 5, 35-42 (1992)
[49] Rivard, J. G. (1973). Closed-loop electronic fuel injection control for the internal combustion engine. SAE Paper No. 73005, Society of Automotive Engineers.; Rivard, J. G. (1973). Closed-loop electronic fuel injection control for the internal combustion engine. SAE Paper No. 73005, Society of Automotive Engineers.
[50] Rugh, W. J. (1983). Linearization about constant operating points: An input-output viewpoint. Proceedings of the IEEE conference on decision and control, San Antonio, TX (pp. 1165-1169).; Rugh, W. J. (1983). Linearization about constant operating points: An input-output viewpoint. Proceedings of the IEEE conference on decision and control, San Antonio, TX (pp. 1165-1169).
[51] Rugh, W. J., Analytical framework for gain-scheduling, IEEE Control Systems Magazine, 11, 1, 79-84 (1991)
[52] Scherer, C.; Gahinet, P.; Chilali, M., Multiobjective output-feedback control via LMI optimization, IEEE Transactions on Automatic Control, AC-42, 7, 896-911 (1997) · Zbl 0883.93024
[53] Seiter, R. E., & Clark, R. J. (1978). Ford three-way catalyst and feedback fuel control system. SAE Paper No. 780203, Society of Automotive Engineers.; Seiter, R. E., & Clark, R. J. (1978). Ford three-way catalyst and feedback fuel control system. SAE Paper No. 780203, Society of Automotive Engineers.
[54] Shahruz, S. M.; Behtash, S., Design of controllers for linear parameter-varying systems by the gain scheduling technique, Journal of Mathematical Analysis and Applications, 168, 1, 195-217 (1992) · Zbl 0778.93027
[55] Shamma, J. S.; Athans, M., Analysis of nonlinear gain scheduled control systems, IEEE Transactions on Automatic Control, AC-35, 8, 898-907 (1990) · Zbl 0723.93022
[56] Shamma, J. S.; Athans, M., Guaranteed properties of gain scheduled control of linear parameter-varying plants, Automatica, 27, 3, 898-907 (1991) · Zbl 0723.93022
[57] Shamma, J. S., & Cloutier, J. R. (1992). Trajectory scheduled missile autopilot design. Proceedings of the first IEEE conference on control applications, Dayton, OH, September.; Shamma, J. S., & Cloutier, J. R. (1992). Trajectory scheduled missile autopilot design. Proceedings of the first IEEE conference on control applications, Dayton, OH, September.
[58] Shamma, J. S.; Xiong, D., Set-valued methods for linear parameter varying systems, Automatica, 35, 6, 1081-1089 (1999) · Zbl 0940.93044
[59] Stein, G.; Hartmann, G. L.; Hendrick, R. C., Adaptive control laws for F-8 flight test, IEEE Transactions on Automatic Control, 22, 5, 758-767 (1977)
[60] Stilwell, D. J.; Rugh, W. J., Interpolation of observer state feedback controllers for gain scheduling, IEEE Transactions on Automatic Control, 44, 6, 1225-1229 (1999) · Zbl 0955.93043
[61] Stilwell, D. J.; Rugh, W. J., Stability preserving interpolation methods for the synthesis of gain scheduled controllers, Automatica, 36, 5, 665-671 (2000) · Zbl 0988.93032
[62] Sureshbabu, N.; Rugh, W. J., Output regulation with derivative information, IEEE Transactions on Automatic Control, 40, 10, 1755-1766 (1995) · Zbl 0843.93028
[63] Tan, H.; Rugh, W. J., Nonlinear overtaking optimal control: Sufficiency, stability, and approximation, IEEE Transactions on Automatic Control, 43, 12, 1703-1718 (1998) · Zbl 0954.49019
[64] Tu, K.-H., & Shamma, J. S. (1998). Nonlinear gain-scheduled control design using set-valued methods. Proceedings of the American control conference, Philadelphia, PA.; Tu, K.-H., & Shamma, J. S. (1998). Nonlinear gain-scheduled control design using set-valued methods. Proceedings of the American control conference, Philadelphia, PA.
[65] Waymeyer, W. K. (1997). History information on gain scheduling. Personal communication.; Waymeyer, W. K. (1997). History information on gain scheduling. Personal communication.
[66] Wu, F., & Grigoriadis, K. M. (1999). LPV-based control of systems with amplitude and rate actuator saturation constraints. Proceedings of the American control conference, San Diego, CA, June (pp. 3191-3195).; Wu, F., & Grigoriadis, K. M. (1999). LPV-based control of systems with amplitude and rate actuator saturation constraints. Proceedings of the American control conference, San Diego, CA, June (pp. 3191-3195).
[67] Wu, F.; Yang, X. H.; Packard, A.; Becker, G., Induced \(L2\)-norm control for LPV systems with bounded parameter variation rates, International Journal of Control, 6, 9/10, 983-998 (1996) · Zbl 0863.93074
[68] Yu, J.; Sideris, A., \(H∞\) control with parametric Lyapunov functions, Systems & Control Letters, 30, 57-69 (1997) · Zbl 0901.93019
[69] Zhou, K.; Doyle, J. C.; Glover, K., Robust and optimal control (1996), Prentice-Hall: Prentice-Hall Upper Saddle River, NJ · Zbl 0999.49500
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.