Abstract:
In this paper, period doubling bifurcation of a Permanent Magnet Direct Current (PMDC) motor is identified mathematically using Poincare map and Floquet theory or Monodromy matrix method. Derivative of the Poincare map gives Jacobian matrix (J-matrix) and Floquet theory calculates Monodromy matrix (M-matrix). The period doubling operation is identified when one of the eigen values of the matrix exceeds unity along the negative real axis. Poincare map identifies the period doubling bifurcation for various parametric conditions and the results obtained agrees with results of the Monodromy matrix method. In this work, calculation of eigen values is performed with J-matrix and compared with M-matrix under various proportional gains, supply voltages and load torques. Also the numerical calculation is verified by means of MATLAB Simulink outputs of speed and current waveform. In order to control the bifurcation behavior, an Extended Time Delay Auto Synchronization (ETDAS) controller is used. This controller controls bifurcation and extends the normal period-1 operation of the drive. This analysis is useful in identifying the stable operating region of the system. Also period doubling operation further leads to chaotic behaviour, the controller helps to avoid such chaos in the operation of the drive system.
