The Well-posedness And Stabilization Of A Single Link Flexible Robot Arm Under Non-collocated Feedback Controls

When modeling a flexible robot arm system mathematically, people usually choose Euler-Bernoulli Beam vabrating system or Timoshenko Beam vabrating system to de-scribe the dynamic motion of the system. However, in this paper, because the surgical robotic arm that we investigated is a type of slender structure, using vibrating string system is more in line with its dynamic characteristics.Unlike the traditional method for non-colloated controller designing, for this kind of flexible robot arm whose dynamic motion is described by vabrating string system, the author designs a non-colloated controller which is located in some point of the arm to stabilize the system. Then we investigat the well-posedness and the stability of the system. Our results show that the system operator A generates a Co-semigroup on the energy state space. By using asymptotic methods, we obtain the conclusion that the asymptotic distribution of the spectrum of the system operator and the completeness of the system operator. Furthermore we conclud that the generalized enginvalues of the system operator A generates a Rizse basis for the state space. So the spectrum determined growth condition is obtained. Based on this conclusion, we analysis the stabilization of the system by using of mathmatical analysis.