Abstract
A constant matrix, bi constant vector fields, are used to approximate nonlinear systems in neighborhoods of equilibrium points. The original nonlinear model is takeQ into account when a precise control is required and non-linearities significantly affect the desired dynamic behaviour. This is the case for instance in the design of autopilots for highperformance aircrafts ([30], [31]), in space-craft attitude control [14], in the feedback control of high-speed, high-precision robot arms [7], in the stabilization of electric power systems and in the regulation of electric machines [23]. To this purpose adaptive control schemes and more recently geometric nonlinear control techniques have been proposed.
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References
Anderson, P. M., Fouad, A. A., ‘Power system control and stability,’ Iowa State University Press, Ames, 1977.
Balestrino A., De Maria G., Zinober A.S.I., ‘Nonlinear adaptive model following control,’ Automatica, vol. 20, 5, 559–568, 1984.
Balestrino G., De Maria G., Sciavicco L., ‘Hyperstable adaptive model following control of nonlinear plants,’ System and Control Letters, vol. 1, 232–236, 1982.
Balestrino G., De Maria G., Sciavicco L., ‘An adaptive model following control for robotic manipulators,’ Trans, ASME J. Dyn. Syst. Meas. Control, vol. 105, 1983.
Boothby W.M., ‘Some comments on global linearization of nonlinear systems,’ System of Control Letters, vol. 4, 143–147, 1984.
Boothby, W. M. ‘Global feedback linearizability of locally linearizable systems,’ this volume.
Brady M., Hollerbach J., Johnson T., Lozano-Perez T., Mason M. eds., Robot Motion, Planning and Control. MIT Press, 1982.
Brockett, R.W., ‘Feedback invariants for nonlinear systems,’ IFAC Congress, Helsinki, 1115–1120, 1978.
Cesareo G., Marino R., ‘Nonlinear control theory and symbolic algebraic manipulation,’ MTNS ’83, Beer Sheva, Israel; Lecture Notes in Control and Inf. Sci., no, 58, 725–740, Springer Verlag, 1984.
Cesareo G., Marino R., ‘On the application of computer algebra to nonlinear control theory,’ EUROSAM Conf. Cambridge U.K.: Lecture Notes in Comp. Sci., no. 174, 35–46, Springer Verlag, 1984.
Cesareo G., Marino R., ‘The use of symbolic computation for power system stabilization: an example of computer-aided design,’ INRIA Conf, Nice ’84; Lecture Notes in Control and Inf. Sci., vol. 63, 598–611, Springer Verlag, 1984.
Cheng, D., Tarn T.J., Isidori A., ‘Global feedback linearization of nonlinear systems,’ 23rd CDD Conference, Las Vegas, 74–83, 1984.
Dayawansa, W., Boothby, W. M., Elliott, D. L., ‘Global state and feedback equivalence of nonlinear systems,’ System and Control Letters, vol. 6, 229–234, 1985.
Dwyer, T. A. W., ‘Exact nonlinear control of large angle rotational maneuvers,’ IEEE Trans. Autom. Control. Vol. 29, 9, 769–774, 1984.
Hunt L.R., Su R., Meyer G., ‘Design for multi-input nonlinear systems,’ Diff, Geo, Control Theory, Brockett R., Millmann R., Sussmann H. Eds., 268–298, Birkhäuser, 1983,
Hunt L.R., Su R., Meyer G., ‘Global transformations of nonlinear systems,’ IEEE Trans. Autom. Control, vol. AC-27, 1982.
Krener, A. J., ‘On the equivalence of control systems and linearization of nonlinear systems,’ SIAM J. Control and Opt., vol. 11, 670–676, 1973.
Krener A.J., Isidori A., Respondek W., ‘Partial and robot linearization by feedback,’ Proc. 22nd IEEE Conf. on Decision and Control, 126–130, 1983.
Krener, A. J., ‘Approximate linearization by state feedback and coordinate change,’ System and Control Letters, vol. 5, 181–185, 1984.
Jakubczyk B., Respondek W., ‘On linearization of control systems,’ Bull. Acad. Pol. Sci., Ser. Sci. Math., vol. 28, 517–522, 1980.
Irving, E., Barrett, J. P., Charcossey, C., Monville, J., ‘Improving power network stability and unit stress with adaptive generator control,’ Automatica, vol. 15, 31–46, 1979.
Isidori, A., Krener, A. J., Monaco, S., Gori-Giorgi, C., ‘Nonlinear decoupling via feedback: a differential geometric approach,’ IEEE Trans, Autom. Control, vol. 26, 331–345, 1981.
Marino R., ‘Feedback equivalence of nonlinear systems with applications to power system equations,’ Doctoral Dissertation, Washington University, St. Louis, MO, 1982.
Marino R., Nicosia S., ‘Linear model following control and feedback equivalence to linear controllable systems,’ Int. J. of Control, vol. 39, 3, 473–485, 1984.
Marino R., ‘On the stabilization of power systems with a reduced number of controls,’ INRIA Conf. Nice ’84; Lecture Notes in Control and Inf. Sci., vol. 62, 259–274, Springer Verlag, 1984.
Marino, R., “On the largest feedback linearizable subsystem,” to appear in System and Control Letters.
Marino, R., ‘An example of nonlinear regulator,’ IEEE Trans. Autom. Control, vol. 29, 3, 276–279, 1984.
Marino, R., Boothby, W. M., Elliott, D. L., ‘Geometric properties of linearizable control systems,’ Mathematical Systems Theory, vol. 18, 97–123, 1985.
Marino, R., Ilic-Spong, M., ‘Stabilization and voltage regulation of electric power systems with (P,Q) load buses preserved,’ Proc. Conference on Decision and Control, Fort Lauderdale, Florida, 1985.
Meyer G., Cicolani L., ‘Applications of nonlinear system inverses to automatic flight control design-system concepts and flight evaluations,’ Agardograph 251 on Theory and Applications of Opt. Control Aero. Systems, P. Kant ed., 1980.
Meyer, G., Su, R., Hunt, L. R., “Application of nonlinear transformations to automatic flight control,” Automatica, vol. 20, 1, 103–107, 1984.
Nicosia S., Tomei P., ‘Model reference adaptive control algorithms for industrial robots,’ Automatica, 20, 5, 635–644, 1984.
Respondek, W., ‘Global aspects of linearization equivalence to polynomial forms and decomposition of nonlinear control systems,’ this volume.
Respondek W., to appear in Proc. MTNS ’85 Conference, Stockholm, June 85, C. Byrnes and A. Lindquist eds., Elsevier, Amsterdam.
Su, R., ‘On the linear equivalence of nonlinear systems,’ System and Control Letters, vol. 2, 48–52, 1982.
Su, R., Meyer, G., Hunt, L. R., ‘Robustness in nonlinear control,’ Differential Geometric Control Theory Conference, Birkhäuser, Boston, R. W. Brockett, R. S. Milemann, H. J. Sussmann, Eds., vol. 27, 316–337, 1983.
Utkin U.I., Sliding Modes and their Applications in Variable Structure Systems. MIR Moscow (English translation), 1978.
Van der Schaft, A. J., ‘Linearization and input-output decoupling for general nonlinear systems,’ System & Control Letters, vol. 5, 27–33, 1984.
Young K.K.D., ‘Design of variable structure model following control systems,’ IEEE Trans. Autom. Control, vol. AC-23, 1079–1085, 1978.
Zaborszky, J., Whang, K. W., Prasad, K. V., Katz, I. N., ‘Local feedback stabilization of large interconnected power systems in emergencies,’ Automatica, no. 17, vol. 5, 673–686, 1981.
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© 1986 D. Reidel Publishing Company
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Marino, R. (1986). Feedback Linearization Techniques in Robotics and Power Systems. In: Fliess, M., Hazewinkel, M. (eds) Algebraic and Geometric Methods in Nonlinear Control Theory. Mathematics and Its Applications, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4706-1_27
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DOI: https://doi.org/10.1007/978-94-009-4706-1_27
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