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Output feedback stabilization of linear systems with unknown additive output sinusoidal disturbances. (English) Zbl 1360.93559
Summary: The output feedback exponential stabilization problem is addressed for known linear stabilizable and detectable systems when the measured output is affected by sinusoidal disturbances generated by an unknown exosystem and only an upper bound on the exosystem order is supposed to be known. Necessary and sufficient conditions are given: in particular a solution to the problem exists if and only if the set of exosystem eigenvalues is disjoint from the set of system eigenvalues. Two adaptively stabilizing control algorithms are proposed: the first one drives the state of the given system exponentially to zero when the actual disturbances are exactly modeled by the exosystem. When the exosystem overmodels the actual disturbances, an online detector of the number of excited frequencies is included in the second more complex algorithm: the exponentially converging estimates of the system state variables are then used to drive the state of the given system exponentially to zero. An illustrative example with a disturbance containing a variable number of frequencies is worked out in details and simulated.

93D15 Stabilization of systems by feedback
93C73 Perturbations in control/observation systems
93B35 Sensitivity (robustness)
Full Text: DOI
[1] Ariyur, K.B.; Krstic, M., Feedback attenuation and adaptive cancellation of blade vortex interaction on a helicopter blade element, IEEE trans control syst technol, 7, 5, 596-605, (1999)
[2] Blasko, V.A., A novel method for selective harmonic elimination in power electronic equipment, IEEE trans power electron, 22, 1, 223-228, (2007)
[3] Bittanti, S.; Moiraghi, L., Active control of vibrations in helicopters via pole assignment techniques, IEEE trans control syst technol, 2, 4, 343-350, (1994)
[4] Bastin, G.; Gevers, M., Stable adaptive observers for nonlinear time varying systems, IEEE trans autom control, 33, 7, 650-658, (1988) · Zbl 0676.93037
[5] Bodson, M., Rejection of periodic disturbances of unknown and time-varying frequency, Int J adapt control signal process, 19, 2-3, 67-88, (2005) · Zbl 1076.93517
[6] Bodson, M.; Douglas, S.C., Adaptive algorithms for the rejection of periodic disturbances with unknown frequency, Automatica, 33, 12, 2213-2221, (1997) · Zbl 0900.93146
[7] De Wit, C.C.; Praly, L., Adaptive eccentricity compensation, IEEE trans control syst technol, 8, 5, 757-766, (2000)
[8] Chen, D.; Paden, B., Adaptive linearization of hybrid step motors: stability analysis, IEEE trans autom control, 38, 6, 874-887, (1993) · Zbl 0800.93657
[9] Francis, B.; Wonham, W., The internal model principle of control theory, Automatica, 12, 5, 457-465, (1976) · Zbl 0344.93028
[10] Francis, B., The linear multivariable regulator problem, SIAM J control optim, 15, 3, 486-505, (1977) · Zbl 0382.93025
[11] Kandil, T.H.; Khalil, H.K.; Vincent, J.; Grimm, T.L.; Hartung, W.; Popielarski, J.; York, R.C.; Seshagiri, S., Adaptive feed forward cancellation of sinusoidal disturbances in superconducting RF cavities, Nucl instrum methods phys res A, 550A, 514-520, (2005)
[12] Kuo, S.; Morgan, D., Active noise control systems: algorithms and DSP implementations, (1996), Wiley New York, NY
[13] Marino, R.; Tomei, P., Global adaptive observers for nonlinear systems via filtered transformations, IEEE trans autom control, 37, 8, 1239-1245, (1992) · Zbl 0764.93047
[14] Marino, R.; Santosuosso, G.; Tomei, P., Robust adaptive observers for nonlinear systems with bounded disturbances, IEEE trans autom control, 46, 6, 967-972, (2001) · Zbl 1059.93501
[15] Marino, R.; Tomei, P., Output regulation for linear systems via adaptive internal model, IEEE trans autom control, 48, 12, 2199-2202, (2003) · Zbl 1364.93714
[16] Marino, R.; Santosuosso, G.L.; Tomei, P., Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency, Automatica, 39, 10, 1755-1761, (2003) · Zbl 1054.93031
[17] Marino, R.; Santosuosso, G.L., Regulation of linear systems with unknown exosystems of uncertain order, IEEE trans autom control, 52, 2, 352-359, (2007) · Zbl 1366.93297
[18] Marino, R.; Tomei, P., Nonlinear control design-geometric, adaptive and robust, (1995), Prentice Hall London · Zbl 0833.93003
[19] Nikiforov, V.O., Adaptive nonlinear tracking with complete compensation of unknown disturbances, Eur J control, 4, 1, 132-139, (1998) · Zbl 1047.93550
[20] Landau, I.D.; Constantinescu, A.; Rey, D., Adaptive narrow band disturbance rejection applied to an active suspension- an internal model principle approach, Automatica, 41, 4, 563-574, (2005) · Zbl 1061.93526
[21] Liu, J.; Yang, Y., Stability of the frequency adaptive control technique and its application to compact disk drives, Control eng pract, 13, 5, 629-639, (2005)
[22] Sastry, S.S.; Bodson, M., Adaptive control: stability, convergence, and robustness, (1989), Prentice Hall · Zbl 0721.93046
[23] Saks, A.; Bodson, M.; Khosla, P., Experimental results of adaptive periodic disturbance cancellation in a high performance magnetic disk drive, ASME J dyn syst meas control, 118, 3, 416-424, (1996) · Zbl 0858.93052
[24] Serrani, A.; Isidori, A.; Marconi, L., Semiglobal nonlinear output regulation with adaptive internal model, IEEE trans autom control, 46, 8, 1178-1194, (2001) · Zbl 1057.93053
[25] Serrani, A., Rejection of harmonic disturbances at the controller input via hybrid adaptive external models, Automatica, 42, 11, 1977-1985, (2006) · Zbl 1130.93369
[26] Wu, B.; Bodson, M., Direct adaptive cancellation of periodic disturbances for multivariable plants, IEEE trans speech audio process, 11, 6, 538-548, (2003)
[27] Zarikian, G.; Serrani, A., Harmonic disturbance rejection in tracking control of Euler-Lagrange systems: an external model approach, IEEE trans control syst technol, 15, 1, 118-129, (2007)
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