Abstract
The purpose of this research is to design robust control for a flexible arm via the deterministic approach. This approach represents a new development in control theory and allows dealing with uncertain elements; which every dynamical system may contain, as well as with unknown or imperfectly known inputs and state measurement errors. The obtained controller will guarantee that all possible responses of the system behave in a desired fashion. The controllers, designed via this approach, are called "robust" or "deterministic". The deterministic or robust principle of control is successfully applied to SIMO (single input multiple-output) system with a system matrix as large as 6 × 6 (in the case of one link flexible arm). Two different controllers are designed. The uncertain parameters appear here as a set of the natural frequencies of the system. The procedure for the design performed here, can also be applied (with some modification) to MIMO (multi-input multi-output system), e.g., to a manipulator with several flexible links. Theoretical proof that the robust control may be applied to MIMO systems is available. A computer-controlled manipulator represents a mechanical device whose end effector equipped with a gripper or tool can be made to follow a prescribed trajectory in its workspace and then to stay at a commanded location in order to perform a required task. A manipulator is generally built as a chain of structurally rigid links connected by rotary or sliding joints, each driven by its own actuator. The control algorithms, which can drive the manipulators with the flexible links, are not available at the present time, so the industrial manipulators must have very rigid (and very heavy) links to perform their tasks with required precision.
Published Version
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