Minimum positioning-time for mechatronic systems

Abstract

The paper considers a method for transferring the state of a dynamic system to a specified state for minimum positioning time (positioning servo systems, manipulators, walking robots). The system under consideration is described by a sampled-data model based on a first-order hold element. It is a first-designed feed-forward controller using a special case of an optimal linear system based on a quadratic performance index. When the final state is fixed (final-state control), the result is open-loop control. Owing to the fact that all mechanical systems have resonant modes at high frequencies, the output of a given feed-forward controller must be converted to a smooth reference signal. For that, we use a lowpass filter implemented as an integrator. In the real system, various disturbance sources (disturbances, parameter uncertainty) exist. For such systems, a two-degree-of-freedom control strategy is proposed. In that case, in the paper, a feedback controller is designed using the superstability concept, and the solution is based on linear programming. The main contributions of the paper are: (i) design of a feedforward controller for sampled-data systems with a first-order hold element, based on optimal control theory; (ii) design of a low-pass filter for the above system; (iii) design of two-degree-of-freedom control systems where the feedback controller is based on the super-stability theory of systems.