The aim of this project is to investigate the potential
use of multivariable control theory in multi-channel dynamic
structural testing. The ideal behaviour of a control system
for dynamic testing is analysed and this is used to provide
the specifications for control schemes for both sinusoidally
derived and random loadings. The need for an integrated
multivariable control system approach is shown.
An experimental test rig is used to test the
applicability of multivariable control methods to dynamic
testing. The rig consists of a cantilever beam which can be
excited into vibration by two electrodynamic shakers. The
displacement on two locations on the beam is measured by
Linear Variable Displacement Transducers (LVDTs). The rig is
configured to provide the worst possible cross-coupling
between different input-output pairs. Analytical modelling of the test is accomplished by
regarding the cantilever beam as continuous elastic body.
The order of the models, which can be either in state-space
or in transfer function matrix form, is a function of the
frequency range over which accurate modelling is required.
The output variable can be displacement, velocity or force.
The analytical modelling led to programs for the
simulation of the beam for any given input time series and
for a varying number of vibrators and output measurement
transducers. The locations of both shakers and output
sensors can be varied at will by a procedure which is
transparent to the user.
The multivariable control methods used for controller
design are the characteristic locus and the Nyquist array
method with recent extensions. Emphasis waS given during the
design process to producing robust performance and stability.Both the characteristic locus and the Nyquist
array designs were assessed using singular value
decomposition analysis and were found to perform
satisfactorily. The merits of both designs are analysed and
In the initial stages of the project a considerable
amount of time was devoted to developing a C.A.D. package
for multivariable control. The features of this package are
described. Also software development based on the MATLAB
package is discussed.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.