Bifurcation and Chaos in Current Mode Controlled DC Drives In Continuous and Discontinuous Conduction Mode of Operation Biswarup Basak Department of Electrical Engineering Bengal Engineering and Science University, Shibpur Howrah-711103 Email: biswarup basak@yahoo.com Sukanya Parui Department of Electrical Engineering Bengal Engineering and Science University, Shibpur Howrah-711103 Email: sp 74107@yahoo.com Abstract—This paper simulates a current mode controlled separately excited dc motor in continuous conduction mode as well as in discontinuous conduction mode. The bifurcation phenomena have been explored with input voltage and speed error amplifier gain as bifurcation parameter. The study is helpful in selecting the range and combination of parameters if the mode of operation of the motor needs to be restricted in a particular operating mode. The study has been conducted with three different sets of motor data. I. I NTRODUCTION Power electronic circuits exhibit nonlinerity due to the inherent feedback controlled switching action. An investigation into the nonlinear phenomena like bifurcation and chaos in power electronic circuits have started in late 1980s. A review of work carried out in this area is available in [1]. Most research works on bifurcation and chaos have been conducted on dc-dc converter circuits operating in continuous conduction mode (CCM) [2], [3], [4], [5]. Some studies reported on the converters operating in discontinuous conduction mode (DCM) [6] and bifurcations taking place in CCM-DCM transition [7], [8], [9]. Though substantial amount of research work has been carried out in dc-dc converter ciruits, the study of nonlienar phenomena in industrial drive circuits are really few in comparison with it. In [10], the authors have explored the bifurcation phenomena in an induction motor drive system. In [11], the author has demostrated the open-loop dynamic characteristics, strange attractors of a smooth-airgap brushless dc motor. In [12], bifurcation and chaos have been explored in a voltage mode controlled dc drive system. The authors have derived a generalised two-dimensional map that describes the second order dc drive operating in continuous conduc- tion mode. In [13], the authors have used the delayed self- controlling feedback technique to stabilize chaos in a voltage mode drive. In [14], the analysis of bifurcation and chaos have been conducted for a current mode controlled dc drive system. All the literatures on dc drive simulate the system in continuous conduction mode. During DCM, the output torque pulsation and speed fluctuation take place which may not be desirable for the smooth operation of a dc drive. If the system behaviour in DCM is well explained or predicted, the parameters can be chosen accordingly so that the system can be engineered to achieve desired system performance. So the knowledge of the operation of the industrial drives in discontinuous conduction mode and the phenomena that take place during CCM to DCM transition are also important. This paper develops the map of a currnet mode controlled dc drive and explores the bifurcation and chaos in CCM as well as in DCM. II. SYSTEM DESCRIPTION AND DERIVATION OF THE SYSTEM MODEL A current mode controlled dc drive system has been consid- ered in this paper. The dc motor is fed from a buck-chopper. The schematic diagram and the equivalent circuit model of the system have been shown in Fig. 1. The speed of the motor, ω(t), is sensed and compared with a reference speed ω ref . The armature current of the motor i(t) is also sensed. If g ω and g i are the speed error amplifier gain and current amplifier gain respectively, the control signals for speed and current v ω (t) and v i (t) can be expressed as: v ω (t) = g ω (ω ref − ω(t)) (1) v i (t) = g i i(t) (2) The switch is controlled by an R-S latch. A clock pulse of period T sets the latch at the beginning of every cycle. Once the latch is set by the clock, switch is turned on and the diode D is off. A comparator compares v i and v ω . The switch remains closed until v i exceeds v ω . When v i exceeds v ω , the latch is reset, the switch is turned off and the diode conducts (in continuous conduction mode). The switch again turns on at the beginning of next clock pulse. In the discontinuous conduction mode both S and D are off and the armature current is zero. Armature current i and the speed ω are the state variables of the system and they are expressed by the following set of differential equations: 978–1–4244–4547–9/09/$26.00 c  2010 IEEE TENCON 2009