The Presence of Bifurcation in a Closed-Loop Discrete Control of a Flexible Benchmark Plant analised from the Jury Stability Criterion

Many interesting phenomena occur when the discrete control is applied over a flexible structure like the aliasing and hidden oscillations. In this work a particular phenomenon called our attention because was a bit strange: increasing the sampling period of a discrete proportional plus derivative closed-loop control (by Tustin or Bilinear method) over a harmonic oscillator (our flexible benchmark plant) we noted that happened regions of stability and instability. Initially we imagined that from some high value of sampling period this control system would instable and it stay instable. This work study analytically this phenomenon and show graphically this bifurcation.