An investigation into the use of multivariable control theory in multi-channel structural testing

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 compared. 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.