L. B. Freidovich
Saint-Petersburg State Technical University,
Department of Mechanics and Control Processes,
29 Politehnicheskaja str., 195251 St.-Petersburg, RUSSIA,
A. A. Pervozvanski
Saint-Petersburg State Technical University,
Department of Mechanics and Control Processes,
29 Politehnicheskaja str., 195251 St.-Petersburg, RUSSIA,
The astatism is a notion extensively used in the classical linear theory. Astatic systems have zero steady-state error if disturbances are constant or tend to constants. For linear systems the astatism ensures a bounded reaction under any unbounded disturbances with bounded derivatives. In the linear case the astatism conditions are very simple: a linear system is astatic if and only if the transfer function is stable with numerator having a zero root. The following questions are of prime practical interest: What is a nonlinear astatic system? What are conditions ensuring the astatism? Do properties of linear astatic systems hold in the nonlinear case? In the paper we give answers to these questions. The notion of astatism widely used in the classical linear control theory is extended to nonlinear systems. Some basic assertions concerning properties of astatic systems are presented. A special attention is paid to robust control problems of Lagrangian systems and robotics manipulators as a particular case. The PID control is shown to ensure robust stabilization of a desired position and tracking with a bounded error if the desired velocities are small. Moreover, we show that general results can be applied for explanation of the robustness of PID feedback in non-linear Lagrangian systems and in the robotics.