An Evaluation of Several Controller Synthesis Methodologies Using a Rotating Flexible Beam as a Test Bed

The objective of this study is to assess the effectiveness of a number of control system synthesis methodologies as practical design tools. The effectiveness is measured by the extent to which a controller obtained by a specific methodology has to be tuned for it to work in a real implementation. For this purpose we consider as a test bed a highly flexible beam attached to a d.c. motor driven rigid hub. Included in the study are five synthesis methodologies. They are (i) classical PD control, (ii) the LQR technique, (iii) robust servomechanism theory, (iv) the Lyapunov method, and (v) Quantitative Feedback Theory (QFT). Used are extensive computer simulations and actual experiments with each of the controllers synthesized using these methodologies. Each of the compensators performed satisfactorily in simulations. In actual implementation, however, some of the controllers did not work as predicted by simulations. The higher the d.c. gain and the bandwidth of the synthesized controller it is less likely to work in reality. This was clearly observed with the LQR controller, the servo controller and the Lyapunov based controllers. The QFT controller is the only one that accounted for the bandwidth limit at the synthesis stage. The other controllers require much fine tuning by trial and error for satisfying actual physical limits including the bandwidth. It is established that controllers designed using methodologies which incorporate real practical considerations such as modeling uncertainties, bandwidth limitations and input saturations need very little tuning whereas the others yield controllers which after tuning are quite different from the synthesized ones.