Research On State Space Modeling Method For Multi-input And Multi-Output Vibration System

The control of multi-input and multiple-output(MIMO)vibration system is a new and high technology which is drawing arising academic and industrial attention.To realize the control of multi-input and multi-output vibration system,a proper approximated model of the vibration system is needed firstly.The state space model is a suitable choice as the description of this model needs no special model parameterization.Then based on the research of the state space modeling method,the modelization of the MIMO vibration system is studied in this thesis.(1)The basic principles and properties of the state space model are elaborated in details.The existing research on the modelisation of the MIMO vibration system by state space modeling methods is reviewed.(2)Current frequency response function fitting method are investigated as well.and it is found that the vector fitting method possesses high accuracy and reliability while fitting the wide frequency band and the dense mode.(3)Then a new state space modeling method for MIMO vibration system inspired by the ideas of minimum realization and reduced order in the modern control theory is proposed.The resulted state space model is both controllable and observable.Compared with the ERA algorithm,it is found that this method has faster running speed and higher modeling precision when dealing with low order vibration system.The ill conditioned problem of the calculation process is improved by using the balance reduction method.(4)In order to verify the feasibility of the method,state space models of a three dimensional spring mass block and a double-input and double-output cantilever beam system are established and analyzed using MATLAB simulations.state space models of three-axis vibration table and double-input and double-output cantilever beam are established based on experimental data.The practicability of the method are then validated.