Modeling and Control of Dynamical Effects Due to Impact on Flexible Structures
Abstract
In the first part of this dissertation, the author considers modeling and approximation of impact dynamics on flexible structures. A nonlinear model is developed through the Hertz law of impact in conjunction with the dynamic equation of the flexible structure. The author analyzes this nonlinear model and establishes the existence and uniqueness of solutions of the nonlinear equation. A numerical method is developed based on the contraction mapping principle. By utilizing the fact that impact interval is very short in general, one may approximate the transfer functions of the systems to which the impacting bodies belong by Taylor polynomials of low order. The author has developed the first and second order approximations. The first order approximation yields a special function that can be used for analytical and computational purposes. The second order approximation leads to a two-parameter family of ordinary differential equations of which the solutions exhibit universal features of impact problems. Simulation results of various examples demonstrate the usefulness of the developed numerical method and approximation methods. The second part of the dissertation is devoted to control of impact dynamics. The author has formulated and studied a control problem in which a linear system is subjected to a series of impact forces. The impact forces are treated as disturbances to the system and modeled as finite duration events using the theory developed in part one. A reasonable control objective is to design a feedback controller to minimize the energy transferred from the disturbances to the controlled outputs in the L2 norm sense. Under the assumption that the disturbance information is known a priori, a (sub)optimal control strategy is derived based on dynamic game theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1994
- Accession Number
- ADA451732
Entities
People
- Qifeng Wei
Organizations
- University of Maryland