Modeling And Control Of Flexible Multibody Systems

Along with the advances in the area of aerospace,robotics and high-speed vehicles, light-weight flexible material has been widely applied in engineering plants.Traditional modeling and control theory based on rigid multibody dynamics couldn't meet the practical demand of high-speed and high-precision operation.It's necessary to model such plants to be flexible multibody systems,so as to account for the effects of flexible appendages on system dynamics.Modeling and control of flexible multibody systems is one of the hot research topics currently,for which modern flexible spacecrafts and flexible manipulators are practical examples.Flexible multibody systems are characterized with nonlinearity,serious coupling,distributed-parameter and time-varying property.Consequently modeling and controller design is a challenging problem.The research in this field has intensive background in practice and prominent importance in theory.In view of recent advances in the field of multibody system dynamics,this dissertation investigates modeling and control of flexible multibody systems. Throughout the dissertation,flexible multibody systems with the typical hub-beam configuration are selected as an example.The traditional hybrid co-ordinates model, first order approximation coupling(FOAC)model,and the approximately linearized model are investigated and compared.The accuracy and application slope of every model is discussed.Linear control schemes and nonlinear control schemes are proposed, based on the approximately linearized model and the FOAC model respectively.An experimental platform is built,and the designing procedure is given in detail.Finally experimental modeling study is performed on the platform.The coupling between the large rigid motion and the flexible displacement is essentially nonlinear.Currently the hybrid co-ordinates method is the most widely used modeling method,but fails to accord with the "dynamic stiffening" phenomena in experiments when the motion speed is high.Accordingly,the first order approximation modeling theory was proposed recently.Theoretical modeling problem is discussed first in this dissertation.Taking the hub-beam system as an example,traditional co-ordinates method,dynamic stiffening and FOAC modeling theory are depicted respectively.The uniform simplified formulation of the three models is derived.Then modal characteristics and responses to typical excitations are investigated and compared.The accuracy and application slope are discussed. For systems operating at low speed,ignoring the coupling nonlinearities will preserve satisfying accuracy.In Chapter Three linear control schemes are investigated based on the hub-beam system driven by a momentum wheel.Linear dynamic equation is derived,and a H_∞vibration-suppressing tracking scheme is proposed and transformed into a standard H_∞controller synthesis problem.Self-learning assembling control scheme is proposed with actuators introduced for vibration control purpose.The assembling control law and self-learning law are proved.The two schemes are verified through numerical simulations with the presence of residual modes.For systems operating at high speed,coupling nonlinearities is not neglectable.In Chapter Four nonlinear control schemes are investigated.An approach to transforming a class of nonlinear systems into LPV systems by nonlinear state feedback is proposed first.The approach is proved and discussed in detail.The approach is then applied to an FOAC model of hub-beam systems,and linear state feedback is designed for the resultant LPV system.The regionally poles placement problem is converted into a convex optimization problem.with LMI constraints.The FOAC model is revised for the hub-beam system with piezoelectric actuators introduced.Then sliding mode variable structure control law is designed accounting for residual modes.Optimal placement of actuators is discussed.The two schemes are verified through numerical simulations with the presence of residual modes.Theoretical modeling with some modifications according to experimental results is feasible for many cases.If not,identifying the mathematical model from experimental input and output data is an alternative approach.In Chapter Five experimental modeling is investigated.An experimental platform is built first.The designing principles and procedure are given in details.Frequency domain subspace identification for continuous systems is employed,and the preshaping method in multisine signal design stage is proposed.The identified model is validated by control performance.