A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators

The control of lightweight flexible manipulators moving along predefined paths is the focus of this work. The flexible manipulator dynamics is derived on the basis of a Lagrangian-assumed modes method. The full order flexible dynamic system does not allow the determination of a tracking control as for rigid ma~ipulators, since there are not as many control inputs as output variables. Thi~ drawback is overcome by accomplishing a model order reduction, based on a singular perturbation strategy, where the perturbation parameter can be identified as the ratio of speeds of the slow versus the fast dynamics. A composite control is adopted. First a slow control is designed with the purpose to track the trajectory in the joint space as accurately as possible. A quasi steady-state trajectory is then determined for the fast variables, and a fast control is in charge of stabilizing them along that trajectory. The one link flexible arm prototype in the Flexible Automation Laboratory at Georgia Tech is chosen for developing a case study. Extensive simulation results are illustrated. State-of-the-art design of mechanical arms results in a high ratio of arm weight to payload weight. The use of lightweight arms certainly represents one successful strategy to achieve benefits like lower arm cost, higher motion speeds, better energy efficiency, safer operation and improved mobility. These issues and others have been addressed by Book (1984 (August)). In this scenario control is one of the crucial points to an effective use of lighter arms. As a matter of fact the price to pay is the much more complex dynamics involved by the flexibility distributed along a lightweight. .. me c han i cal s t r u ct u r e. Con s eq u en t 1 Y the con t r 0 lob j e c t i ve for f 1 ex i b 1 e manipulators is to be properly reformulated, at least as compared to the case of today's industrial manipulators, whose links and drives are purposely made stiff to obtain higher precision, even if at the expenses of lower speed and higher drive power. In fact not only is a flexible manipulator required to execute some. motion, so as a rigid manipulator is, but also it is desired to stabil ize the vibration?, which are naturally excited, along the motion and daf\lp them out as fast as possible at the terminal point. The dynamic interaction …