A METHOD FOR PREVIEW VIBRATION CONTROL OF SYSTEMS HAVING FORCING INPUTS AND RAPIDLY-SWITCHED DAMPERS

Abstract

In a variety of applications, especially in large scale dynamic systems, the mechanization of different vibration control elements in different locations would be decided by limitations placed on the modal vibration of the system and the inherent dynamic coupling between its modes. Also, the quality of vibration control to the economy of producing the whole system would be another trade-off leading to a mix of passive, active and semi-active vibration control elements in one system. This termactiveis limited to externally powered vibration control inputs and the termsemi-activeis limited to rapidly switched dampers. In this article, an optimal preview control method is developed for application to dynamic systems having active and semi-active vibration control elements mechanized at different locations in one system. The system is then a piecewise (bilinear) controller in which two independent sets of control inputs appear additively and multiplicatively. Calculus of variations along with the Hamiltonian approach are employed for the derivation of this method. In essence, it requires the active elements to be ideal force generators and the switched dampers to have the property of on-line variation of the damping characteristics to pre-determined limits. As the dampers switch during operation the whole system's structure differs, and then values of the active forcing inputs are adapted to match these rapid changes. Strictly speaking, each rapidly switched damper has pre-known upper and lower damping levels and it can take on any in-between value. This in-between value is to be determined by the method as long as the damper tracks a pre-known fully active control demand. In every damping state of each semi-active damper the method provides the optimal matching values of the active forcing inputs. The method is shown to have the feature of solving simple standard matrix equations to obtain closed form solutions. A comprehensive 9-DOF tractor semi-trailer model is used to demonstrate the effectiveness of the method. Time domain predictions are made to compare performance of ride and tyre-to-road contact in the model for the presented method with those of some other active and semi-active suspension designs.