טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentIrit Peled
SubjectModeling and Control of Dynamic Systems with Elements
Governed by the Wave Equation
DepartmentDepartment of Mechanical Engineering
Supervisor Full Professor Halevi Yoram
Full Thesis textFull thesis text - English Version


Abstract

The modeling and control of continuous flexible structures is one of the most challenging problems in control theory. This topic gains more interest with the development of slender space structures or even traditional transmissions that contain flexibilities. In this work the modeling, simulation, and control laws synthesis problems are solved by using infinite dimension, accurate Laplace transfer functions of flexible structures governed by the wave equation.

After some theoretical background, these transfer functions are used to develop new modeling methods for multi-link flexible transmissions with both gear and shaft flexibilities. Two modeling methods are discussed: the feedback approach which gives an intuitive understanding of the nature of wave propagation in the system, and the dynamic stiffness approach.

The “feedback” model leads to new multi-link simulation schemes based on Ordinary Differential Equations rather than the usual Partial Differential Equations. It builds generic links that may be connected in series to produce an accurate simulation of the system using standard software such as Matlab-Simulink.

The next part of the thesis investigates the control related properties of single link systems, such as a single flexible shaft. First a comprehensive analysis of the pole zero locations for different boundary conditions and for collocated and non-collocated systems is presented. This analysis leads to new and interesting results, including interlacing properties and pole-zero configuration in the presence of non-collocation. These results are later used in a Nyquist plot analysis of the system. The Nyquist plot analysis gives intuitive and complete understanding of the stability robustness of a closed loop with Finite Dimension Linear Time Invariant controllers, with and without controller delay, which is missing in previous works. This analysis reveals the stability robustness problems that may arise when using such controllers.

These results lead also to the synthesis of robustly stabilizing controllers. The Absolute Vibration Suppression (AVS) controller, proposed in previous works, is studied and modified accordingly leading to the new Robust AVS control law (RAVS). A novel algorithm for the tuning of this controller is proposed based on this study.

Finally, the AVS controller is compared to existing controllers (for lumped systems) that are based on wave approach, i.e. Wave Based Control and the open loop Input Shaping. These control laws are adjusted for the continuous systems. The investigation shows that for the flexible shaft these three control laws have identical nominal behavior. A comparison between these controllers in the presence of uncertainties is presented.