Stability Analysis of a Multilink Flexible Manipulator: Nonlinear Observers

As is well known, MLFMs are generally lightweight materials with typically low payload–to–arm weight ratio, so they are of interest in many application fields.1–3 And the modeling of MLFMs has stimulated the interest of many researchers.4–6 Nevertheless, the difficulty of the modeling and control of flexible manipulators (FMs) is aggravated, since the linear effects of flexibility can’t be separated from typical nonlinear effects of multi body rigid dynamics7 and the authors addressed some dynamics problems in view of the structural flexibility of lightweight structures. It should be noted that in the control system of FMs, there was the fact that the number of controlled variables was strictly less than the number of mechanical degrees of freedom. Also, during the high–velocity maneuver of the manipulators, a high degree of elastic vibration was derived. But when the lightweight manipulator was operating at low velocities, a very complicated dynamics was developed from the structural joint friction. Moreover, the dynamic equations of motion were nonlinear and of large dimensions. At many special situations, without some consideration of these dynamics problems in the total control system design, the measurements used for feedback control will often be not adequate enough for acceptable control system performance. However, the relevant robust state estimation (filtering) problem1,8,9 has been studied extensively for nonlinear systems.