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Rotary inverted pendulum: trajectory tracking via nonlinear control techniques. (English) Zbl 1265.93138
Summary: The nonlinear control techniques are applied to the model of rotary inverted pendulum. The model has two degrees of freedom and is not exactly linearizable. The goal is to control output trajectory of the rotary inverted pendulum asymptotically along a desired reference. Moreover, the designed controller should be robust with respect to specified perturbations and parameters uncertainties. A combination of techniques based on nonlinear normal forms, output regulation and sliding mode approach is used here. As a specific feature, the approximate solution of the so-called regulator equation is used. The reason is that its exact analytic solution can not be, in general, expressed in closed form. Though the approximate solution does not give asymptotically decaying tracking error, it provides a reasonable bounded error. The performance of the designed feedback regulator is successfully tested via computer simulations.

MSC:
93C10 Nonlinear systems in control theory
93B35 Sensitivity (robustness)
70Q05 Control of mechanical systems
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References:
[1] Castillo B., Castro-Linares: On robust regulation via sliding mode for nonlinear system. Systems Control Lett. 24 (1995), 361-371 · Zbl 0877.93018
[2] Čelikovský S., Huang, Jie: Continuous feedback asymptotic output regulation for a class of nonlinear systems having nonstabilizable linearization. Proc. 37th IEEE Conference on Decision and Control, Tampa 1998, pp. 3087-3092
[3] Priscoli F. Delli, Isidori A.: Robust tracking for a class on nonlinear systems. 1st European Control Conference, Grenoble 1991, pp. 1814-1818
[4] Huang J., Rugh W. J.: On a nonlinear multivariable servomechanism problem. Automatica 26 (1990), 963-972 · Zbl 0717.93019
[5] Huang J., Rugh W. J.: An approximation method for the nonlinear servomechanism problem. IEEE Trans. Automat. Control 37 (1992), 1395-1398 · Zbl 0767.93034
[6] Isidori A., Byrnes C. I.: Output regulation of nonlinear systems. IEEE Trans. Automat. Control 35 (1990), 131-140 · Zbl 0704.93034
[7] Krener A. J.: The construction of optimal linear and nonlinear regulators. Systems, Models and Feedback (A. Isidori and T. J. Tarn, Birkhäuser, Basel 1992, pp. 301-322 · Zbl 0778.49024
[8] Kwatny H. G., Kim H.: Variable structure regulation of partially linearizable dynamics. Systems Control Lett. 10 (1990), 67-80 · Zbl 0704.93009
[9] Sira-Ramírez H.: A dynamical variable structure control strategy in asymptotic output tracking problems. IEEE Trans. Automat. Control 38 (1993), 615-620 · Zbl 0782.93026
[10] Slotine J. J., Hedrick K.: Robust input-output feedback linearization. Internat. J. Control 57 (1993), 1133-1139 · Zbl 0772.93033
[11] Spong M. W., Vidyasagar M.: Robot Dynamics and Control. Wiley, New York 1989
[12] Utkin V. I.: Sliding Modes in Control and Optimization. Springer-Verlag, Berlin 1992 · Zbl 0748.93044
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