Co-existence of multiple attractors in the PWM controlled DC drives

Abstract

DC shunt and series drives are extensively used in the industry. The occurrence of bifurcation and chaos in dc shunt and permanent magnet drives are well known. It is observed that the behavior of the drives not only depends on the value of system parameters but also on the value of initial conditions. Multiple attractors can exist for same parameter value. Different choice of initial conditions gives different periodic behavior of the system. The drive is intended to operate in a parameter range to give period-1 behavior. We report the existence of sub- harmonic oscillations in the period-1 region of the bifurcation diagram along with co-existing attractor with fractal basin boundaries in PWM controlled dc series drives. The series drive is extensively used in electric traction and other applications. The dc drives are run with dc input voltage. This dc voltage may be derived from a dc source or an ac source with a rectifier. The dc series drive shows different bifurcation behavior when different types of input voltage and switching elements are used. The existence of period-1, period-2 and period-4 orbits are observed with different initial conditions in the desired period-1 region of the bifurcation diagram. The dependence of system’s behavior on initial condition may render the system’s behavior unpredictable. These phenomena may have serious implication in performance.