Title page for ETD etd-06112009-075955


Type of Document Dissertation
Author Singh, Akshay Nareshraj
URN etd-06112009-075955
Title State Feedback Control with Time Delay
Degree Doctor of Philosophy (Ph.D.)
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Yitshak M. Ram Committee Chair
Marcio de Queiroz Committee Member
Peter Wolenski Committee Member
Su-Seng Pang Committee Member
Steve Cai Dean's Representative
Keywords
  • time delay
  • state reconstruction
  • vibration
  • state feedback control
  • stability
  • state estimation
  • receptance
  • pole assignment
  • eigenstructure assignment
  • observer design
  • dynamic system
Date of Defense 2009-04-29
Availability unrestricted
Abstract
In this thesis we start with an introduction to the theory of vibration control. We broadly classify the control methods into passive and active schemes. We introduce the problem of state feedback control and provide the classical solution in the form of Ackermann formula. We then identify the limitations of the classical approach and present the more elegant solution of partial pole assignment without spillover. We highlight the problem with model uncertainties and describe the method of pole assignment using data from measured receptances. This approach is extended for pole assignment for a linear vibrating system by using state feedback control delayed in time. This approach is significantly advantageous over various conventional state-space approaches which need to use information of , and matrices. Since the method relies solely on measured receptances, it negates the need to know , and matrices. It is shown that for a system with degrees of freedom, we may assign eigenvalues. Assigning eigenvalues in a time delayed system does not necessarily regulate the dynamics of the system or guarantee its stability. We separate the eigenvalues into two groups, primary and secondary, and propose method of a posteriori analysis to ensure that the primary eigenvalues have been assigned. The method is demonstrated by various examples.

For state feedback control, the control is achieved by measuring the states of the system and feeding them back into the system after multiplying them with appropriate control gain. This makes it imperative to measure all the states of the system. In practical control applications, all states are not accessible for measurement. We address the problem of inaccessibility of states making it difficult to implement the state feedback control. We introduce the theory of linear state estimation also called observer design. We identify the limitations of this approach and introduce the concept of state reconstruction by delayed action. We develop a method to reconstruct the inaccessible states by introducing delay in the system and using information from accessible states. The results are demonstrated by examples.

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