Modal expansion is adopted to analyze the dynamics model,and the modal truncation method,balanced truncation method and singular perturbation approximation method are used for model reduction,then we can get the low-order model,and the model error by truncation is obtained to provide the reference for the controller design,and the simulation results demonstrate the effectiveness of the method.
To study the effect of modal truncation on tire compliance,a modal testing of a 195/60R14 tire is performed and the modal parameters of first 17 modes are extracted Tire compliance is calculated by using different number of modes acquired by exponential function fitting The error is less than 10% when using first ten modes and will be less than 5% when first twelve modes are used
To avoid the overflow of the control and observation caused by using mode truncation to design controller,the flexible structure model is transformed into the characteristic model described by a second-order difference equation with unknown coefficients,then a direct adaptive fuzzy predictive control method is presented for the flexible structure position holding.
The simulation result shows that the low-order model obtained by using mode norms, which keeps relatively important modes, is the better approximation of the original system than that of direct mode truncation, and is helpful to suppress the vibration of structures better.
This paper deduces the finite element formulation of intelligent plate containing distributed Piezoceramics on its surface using Hamilton principle adopting finite element model of 12 DOF with 2 electrical DOF, and reduces the order of intelligent plate using the following process in turn: Model truncation, Minimal realization, Balancing reduction.