Tracking and disturbance rejection for fully actuated mechanical systems. (English) Zbl 1152.93403

Summary: We solve the tracking and disturbance rejection problem for fully actuated passive mechanical systems. We assume that the reference signal \(r\) and its first two derivatives \(\dot r, \ddot r\) are available to the controller and the disturbance signal \(d\) can be decomposed into a finite superposition of sine waves of arbitrary but known frequencies and an arbitrary \(L^{2}\) signal. We combine the internal model principle with the ideas behind the Slotine-Li adaptive controller. The internal model-based adaptive controller that we propose causes the closed-loop state trajectories to be bounded, and the tracking error and its derivative to converge to zero, without any prior knowledge of the plant parameters. An important part of our results is that we prove the existence and uniqueness of the state trajectories of the closed-loop system.


93C40 Adaptive control/observation systems
70Q05 Control of mechanical systems
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[1] Astolfi, A.; Limebeer, D.J.N.; Melchiorri, C.; Tornambe, A.; Vinter, R.B., Proceedings of the workshop modelling and control of mechanical systems, (1997), Imperial College Press London
[2] Bonivento, C., Gentili, L., & Paoli, A. (2004). Internal model based fault tolerant control of a robot manipulator. In Proc. IEEE CDC 2004 · Zbl 1137.93361
[3] Byrnes, C.I.; Delli Priscoli, F.; Isidori, A., Output regulation of uncertain nonlinear systems, (1997), Birkhäuser Boston · Zbl 0873.93043
[4] Byrnes, C.I.; Isidori, A., Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation, IEEE transactions on automatic control, 48, 1712-1723, (2003) · Zbl 1364.93329
[5] Davison, E.J.; Goldenberg, A., Robust control of a general servomechanism problem: the servo compensator, Automatica, 11, 461-471, (1975) · Zbl 0319.93025
[6] Hara, S.; Yamamoto, Y.; Omata, T.; Nakano, M., Repetitive control system: A new type servo system for periodic exogenous signals, IEEE transactions on automatic control, 33, 659-668, (1988) · Zbl 0662.93027
[7] Huang, J.; Chen, Z., A general framework for tackling the output regulation problem, IEEE transactions on automatic control, 49, 2203-2218, (2004) · Zbl 1365.93446
[8] Isidori, A., Nonlinear control systems, (1995), Springer-Verlag London · Zbl 0569.93034
[9] Jayawardhana, B. (2006). Tracking and disturbance rejection for passive nonlinear systems. Ph.D. thesis, Imperial College London
[10] Jayawardhana, B., & Weiss, G. 2005. Disturbance rejection with LTI internal models for passive nonlinear systems. In Proc. 16th IFAC 2005 world congress
[11] Jayawardhana, B., & Weiss, G. State convergence of passive nonlinear systems with an \(L^2\) input. IEEE Transactions on Automatic Control (in press) · Zbl 1367.93435
[12] Khalil, H.K., Nonlinear systems, (2000), Prentice-Hall Upper Saddle River, NJ · Zbl 0948.93007
[13] Logemann, H.; Ryan, E.P., Asymptotic behavior of nonlinear systems, American mathematical monthly, 111, 864-889, (2004) · Zbl 1187.34068
[14] Ortega, R.; Loría, A.; Nicklasson, P.J.; Sira-Ramírez, H., Passivity-based control of Euler-Lagrange systems, (1998), Springer-Verlag London
[15] Panteley, E.; Ortega, R.; Gäfvert, M, An adaptive friction compensator for global tracking in robot manipulators, Automatica, 33, 307-313, (1998) · Zbl 0902.93048
[16] Delli Priscoli, F., Output regulation with nonlinear internal models, Systems & control letters, 53, 177-185, (2004) · Zbl 1157.93412
[17] Sage, H.G.; de Mathelin, M.F.; Ostertag, E., Robust control of robot manipulators: A survey, International journal of control, 72, 1498-1522, (1999) · Zbl 0941.93501
[18] van der Schaft, A.J., \(L_2\)-gain and passivity techniques in nonlinear control, (2000), Springer-Verlag London · Zbl 0937.93020
[19] Scherpen, J.M.A.; Ortega, R., On nonlinear control of Euler-Lagrange systems: disturbance attenuation properties, Systems & control letters, 30, 49-56, (1997) · Zbl 0901.93041
[20] Serrani, A.; Isidori, A.; Marconi, L., Semiglobal nonlinear output regulation with adaptive internal model, IEEE transactions on automatic control, 46, 1178-1194, (2001) · Zbl 1057.93053
[21] Slotine, J.J.E.; Li, W., Adaptive manipulator control: A case study, IEEE transactions on automatic control, 33, 995-1003, (1988) · Zbl 0664.93045
[22] Slotine, J.J.E.; Li, W., Composite adaptive control of robot manipulators, Automatica, 25, 509-519, (1989) · Zbl 0696.93045
[23] Sontag, E.D., Mathematical control theory: deterministic finite dimensional systems, (1990), Springer-Verlag New York · Zbl 0703.93001
[24] Weiss, G.; Häfele, M., Repetitive control of MIMO systems using \(H^\infty\) design, Automatica, 35, 1185-1199, (1999) · Zbl 0949.93043
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