טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentScher Guy
SubjectControl of a Flexible Beam Using Infinite Dimension
Transfer Functions
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Yoram Halevi
Full Thesis textFull thesis text - English Version


Abstract

Motion control and vibration suppression of flexible structures is an important area in control engineering. Practical engineering applications exist in various areas such as the defense, aerospace, biomedical and robotics industries. Many research studies have addressed this control problem using techniques that can be categorized as either passive or active vibration damping, where the latter is also suited for tracking purposes. Whenever the control performance specifications, in bandwidth terms, are close to, or even over, the resonant frequencies of a structure, it is considered flexible. In order to achieve those specifications, the control engineer must take these vibrations into consideration.

This work considers the control of an Euler-Bernoulli beam with various boundary conditions. An exact mathematical model of the system structural dynamics is obtained from the well-known partial differential equation by applying the Laplace transform, thus obtaining an infinite dimension transfer function. Using this model, a control algorithm (compensator) that eliminates the resonant modes of the beam is proposed. It does so by manipulating the boundary condition to match the characteristic impedance of the beam, making it behave like a semi-infinite beam, or alternatively, acting as a wave-absorbing controller. The compensator receives the local deflection and slope as its inputs and controls the force and moment applied at one end. The derived ideal controller is a fractional order controller, i.e. has non-integer powers of the Laplace variable 's'. This work will discuss the theoretical and computational aspects of such controller, and present several techniques of approximation. Closed loop simulations to test the algorithms show the effectiveness of the obtained control law whose performance is similar to what was predicted analytically. Several degenerated cases, where one of the actuators or sensors is missing, are presented, showing satisfactory performance of the controller in these cases as well.