Abstract
Stabilization of physical systems by shaping their energy function is a well-established technique whose roots date back to the work of Lagrange and Legendre. Potential energy shaping for fully actuated mechanical systems was first introduced in Takegaki and Arimoto (Trans ASME J Dyn Syst Meas Control 12:119–125, 1981) more than 30 years ago. In Ortega and Spong (Automatica 25(6):877–888, 1989) it was proved that passivity was the key property underlying the stabilization mechanism of these designs, and the, now widely popular, term of passivity-based control was coined. In this chapter we summarize the basic principles and some of the main developments of this controller design technique.
Bibliography
Bloch A, Leonard N, Marsden J (2000) Controlled Lagrangians and the stabilization of mechanical systems I: the first matching theorem. IEEE Trans Autom Control 45(12):2253–2270
Byrnes CI, Isidori A, Willems JC (1991) Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear systems. IEEE Trans Autom Control 36:1228–1240
Fujimoto K, Sugie T (2001) Canonical transformations and stabilization of generalized Hamiltonian systems. Syst Control Lett 42(3):217–227
Hill D, Moylan P (1980) Dissipative dynamical systems: basic input-output and state properties. J Frankl Inst 309:327–357
Monshizadeh N, Monshizadeh P, Ortega R, van der Schaft A (2019) Conditions on shifted passivity of port-Hamiltonian systems. Syst Control Lett 123:55–61
Ortega R, Spong M (1989) Adaptive motion control of rigid robots: a tutorial. Automatica 25(6):877–888
Ortega R, van der Schaft A, Mareels I, Maschke B (2001) Putting energy back in control. IEEE Control Syst Mag 21(2):18–33
Ortega R, van der Schaft A, Maschke B, Escobar G (2002a) Interconnection and damping assignment passivity-based control of port-controlled hamiltonian systems. Automatica 38(4):585–596
Ortega R, Spong MW, Gomez F, Blankenstein G (2002b) Stabilization of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans Autom Control 47(8):1218–1233
Ortega R, Loria A, Nicklasson PJ, Sira-Ramirez H (2013) Passivity-based control of Euler-Lagrange systems, 3rd edn. Springer, Berlin, Communications and Control Engineering
Slotine J, Li W (1988) Adaptive manipulator control: a case study. IEEE Trans Autom Control 33(11):995–1003
Takegaki M, Arimoto S (1981) A new feedback for dynamic control of manipulators. Trans ASME J Dyn Syst Meas Control 12:119–125
van der Schaft A (2016) L2–gain and passivity techniques in nonlinear control, 3rd edn. Springer, Berlin
Zhang M, Borja P, Ortega R, Liu Z, Su H (2018) PID passivity–based control of port-Hamiltonian systems. IEEE Trans Autom Control 63(4):1032–1044
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Ortega, R., Borja, P. (2020). Passivity-Based Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_100072-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_100072-1
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