Delayed Model Approximation and Control Design for Under-Damped Systems

The presented paper introduces a simple methodology to obtain a reduced-order approximation to high-order systems with oscillating dynamics. The reduction is based on the frequency domain characteristics of the under-damped high-order process. Classic control theory tools are used in order to obtain an accurate model reduction. Time-delay term plays an important role at the low-order model since it allows to hold the phase characteristics of the original system. Finally, a simple PID tuning methodology has been proposed in order to obtain the controller gains from the reduced model. Some numerical simulations are presented obtaining a similar performance when the PID controller applied to the high-order plant.