Title page for ETD etd-10302012-133755

Type of Document

Dissertation

Author

Guzzardo, Carla Ann

Author's Email Address

cguzzard@tigers.lsu.edu, carla.guzzardo@gmail.com

URN

etd-10302012-133755

Title

Optimal Actuation in Active Vibration Control Using Pole-Placement

Degree

Doctor of Philosophy (Ph.D.)

Department

Mechanical Engineering

Advisory Committee

Advisor Name	Title
Pang, Su-Seng	Committee Co-Chair
Ram, Yitshak M.	Committee Co-Chair
de Queiroz, Marcio	Committee Member
Li, Guoqiang	Committee Member
de Hoop, Cornelis	Dean's Representative

Keywords

vibration
state feedback control
pole assignment
partial pole placement
resonance avoidance
minimization of control effort
optimal actuation
active vibration control

Date of Defense

2012-10-10

Availability

unrestricted

Abstract

The purpose of this study was to find and demonstrate a method of optimal actuation in a
mechanical system to control its vibration response. The overall aim is to develop an active
vibration control method with a minimum control effort, allowing the smallest actuators and
lowest control input.
Mechanical systems were approximated by discrete masses connected with springs and
dampers. Both numerical and analytical methods were used to determine the optimum force
selection vector, or input vector, to accomplish the pole placement, finding the optimal location
of actuators and their relative gain so that the control effort is minimized. The problem was of
finding the optimal input vector of unit norm that minimizes the norm of the control gain vector.
The methods of pole placement and partial pole placement were introduced, and used to
solve various problems, including the active natural frequency modification problem associated
with resonance avoidance in undamped systems, and the single-input-multiple-output pole
assignment problem for second order systems. Both full and limited controllability were
addressed.
During the numerical analysis, it was discovered that the system is uncontrollable if a
control input vector is chosen that is mathematically orthogonal to an eigenvector associated with a reassigned eigenvalue. Conversely, the optimal input vector was discovered to be mathematically parallel to an eigenvector. This was proven analytically through mathematical proofs and demonstrated with various examples. Simulations were performed in MATLAB and
Maple to verify the results numerically.
An example using realistic units was developed to show the order of magnitude improvement expected by using this method of optimization. All initial conditions and system
parameters were held the same, but the input vector was changed. The optimal input vector
provided an order of magnitude improvement over an evenly distributed input vector.
The principal conclusion was that by choosing a state feedback input vector that is
mathematically parallel to the eigenvector associated with the open-loop eigenvalue to be
reassigned, or in the case of multiple assignments, in the subspace of the eigenvectors, the control effort to accomplish pole placement can be reduced to its minimal value.

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