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On the PID tracking control of robot manipulators. (English) Zbl 0974.93039

Summary: We consider the problem of PID tracking control of robotics manipulators. Our objective is to prove that under classical PID control, semiglobal stability can be assured with arbitrary small output tracking error. This means that, for any given set of initial conditions \(W_{x}\), there exist PID control gains such that all trajectories starting in \(W_{x}\) converge to a residual set of arbitrary size. A novel PID control configuration is developed in terms of a parameter that is directly related with the size of the region of attraction and the size of the residual set. Tuning guidelines are extracted from the stability analysis.

MSC:

93C85 Automated systems (robots, etc.) in control theory
70B15 Kinematics of mechanisms and robots
93B51 Design techniques (robust design, computer-aided design, etc.)
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