The Research Of Pole Assignment In Uncertain Parametric Structures

The multiple frequencies system and the closely frequencies system with uncertain parameters will convert to each other due to the uncertainty of structural physical parameters,and the conversion is more common among the multiple frequencies systems.In the transformation,the main mode vector may jump because of the uncertainty of the structure parameters,and the main mode vector is linearly independent and become linearly dependent.The reason for this phenomenon is that in the case of multiple eigenvalues and close eigenvalues,the selection of the main mode vector of multiple frequency system and the close spaced system is arbitrary.There is orthogonality between any vector corresponding to multiple eigenvalues and close eigenvalues and the vector corresponding to non-close isolated eigenvalues other than multiple eigenvalues and close eigenvalues.But there is no orthogonality between any two of the infinitely many vectors of main modes corresponding to multiple eigenvalues and close eigenvalues.Just as in plane,a unit circle has infinitely many radii.Two radii of any choice are not necessarily perpendicular to each other.Moreover,two radii that are perpendicular to each other will also have weak coupling due to uncertainty,turning linear independence into linear dependence.And even for the uncertain systems with non-close isolated eigenvalues,the modal controller has poor robustness when the representation of the uncertain dynamic system and the actual model have large errors.The quantitative representation of uncertainty is the key to the design of structural modal controllers.In this paper,the uncertainties obtained from the physical parameters of the structure and the control matrix are considered,and all the values of the uncertainties are contained in a bounded convex set.For the uncertainty of external effects,such as interference or measurement noise.Too much knowledge of signal processing is involved,so it is not considered for the moment.The main research is on the iMPact of model uncertainty on eigenvalues and responses.There are probabilistic model,fuzzy model,convex model and interval model.The choice of model for uncertainty analysis depends on the size of the effective value of the known uncertainty information.When the stochastic method is difficult to construct the probability density function due to the lack of effective data,the calculation accuracy is not high.Interval means that the uncertainty is used as a useful supplement to the stochastic method.Effective representation of dynamic systems with uncertain parameters is the core of robust control theory for non-probabilistic convex set models.It is proved that the modal controller based on the interval perturbation method and the finite element method has good robustness.Through the study of a large number of structural vibration control problems with uncertain parameters,some common problems that need to be solved are extracted.It is mainly targeted at local vibration control of structures with uncertain parameters.There are two methods for vibration control:passive modification and active control.Passive modification changes the inherent characteristics of the structure according to the design requirements to avoid resonance,but the conditions of the structure vibration control is that a structure must be controlled,so first explore contains the structure of the uncertain parameters of control.In theory,for the non-close solitary frequency structure,when the control matrix and all the characteristics of the vector is not vertical,a control structure is completely controllable but the executor implementation scope cannot be arbitrarily large due to the effect of various factors.The control force is much larger than the range of the actuator.In this paper,the minimum number of actuators and their optimal positions are obtained by using the control force optimal position configuration method.By the feedback gain matrix calculation method,the eigenvalues of the closed-loop control system are estimated by the interval flexibility method based on the receptance method and the recursive design method of modal controller.Under the controllability condition,the controllability condition of multiple frequency and close frequency structures with uncertain parameters and the condition of mutual transformation of uncertain structure types by active control are studied and we obtained the following conclusions:First,by means of speed feedback control and displacement feedback control,the solitary frequency system is destabilized and linear flutter occurs when the control force is equivalent to circulating force.Second,the solitary frequency structure is converted to the multiple frequency deficit structure when the active damping provided by the control force is non-proportional damping.Third,active control makes the structure convert between solitary frequency structure,multiple frequency structure,solitary frequency and multiple frequency structure.The modal control equations of the multiple frequency structure and the near-loss system are regarded as the perturbations of the multiple frequency complete system and the multiple frequency deficit system respectively.The feedback control of multiple frequency problem is transformed into feedback control of multiple frequency problem by physical method.Since the loss system is similarly diagonalized,the Jordan standard method is often used to design the modal controller.It is concluded that the single-input system makes the partial multiple frequency mode uncontrollable and the control force of the loss-making system far exceed the range of the actuator’s execution force.To solve these two problems,this paper introduces the multi-input control.