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Variable structure control of robotic manipulator with PID sliding surfaces. (English) Zbl 0903.93015

For the classical mathematical model of a rigid robotic manipulator \[ A(q)\ddot q+ C(q,\dot q)\dot q+ G(q)= u+ d \] subject to disturbances bounded in some \(l_p\) norm as \[ \| d\|_p\leq \alpha_1+ \alpha_2\| q\|_p+ \alpha_3\|\dot q\|_p \] four sliding-mode tracking controllers are proposed. A characteristic feature of these controllers is that the sliding surface depends on the tracking error in the PID way, i.e. \[ s= K_Pe+ K_I \int^t_0 edt+\dot e. \] Assuming prescribed bounds for the manipulator’s dynamics and the specified above bounds for allowable disturbances, a globally asymptotically stable sliding-mode control algorithm is derived (Theorem 1). In order to avoid the control chattering phenomenon, an alternative control law is introduced for which the closed loop system remains uniformly ultimately bounded (Theorem 2). In the case when the model bounds are unknown, both control algorithms are supplemented with a suitable parameter adaptation subsystem. Again, either the global asymptotic stability (Theorem 3) or the uniform ultimate boundedness (Theorem 4) of the tracking error is proved.

MSC:

93C85 Automated systems (robots, etc.) in control theory
93B12 Variable structure systems
93B51 Design techniques (robust design, computer-aided design, etc.)
93C40 Adaptive control/observation systems
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