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Journal of Electrical and Electronics Engineering 7 _______________________________________________________________________________________________ Control of Separately Excited Dc Motor ALIM Abdul1 and ABUBOKAR Talukdar2 1 University of Chittagong, Department of Applied Physics, Electronics & Communication Engineering, Chittagong-4331, Bangladesh. E-mail: [email protected] 2 Chittagong University of Engineering & Technology (CUET), Dept. of Electrical & Electronic Engineering, Bangladesh. Email: [email protected] Abstract – Speed control of separately excited DC motor and performance analysis by software simulation has been done. The objective of this paper is to describe the principle of DC motor speed control using nonlinear combined control (armature voltage and field current) and proportional integral- derivative (PID) controller for DC motor drives. In the field control mode, the armature voltage is held constant and an adjustable voltage is applied to the field. Simulation models of separately excited DC motor have been developed using MATLAB/Simulink. Keywords: Separately excited DC motor, armature voltage and field current control, performance analysis, simulation. I. INTRODUCTION Direct current (DC) motors have been widely used in many industrial applications such as electric vehicles, steel rolling mills, electric cranes, and robotic manipulators due to precise, wide, simple, and continuous control characteristics. Traditionally rheostat armature control method was widely used for the speed control of low power dc motors. One method of speed control is applicable for speeds below rated or base speed by Controlling Terminal Voltage VT and keeping If or Φ constant at rated value. Another method of speed control is applicable for speeds below rated speed by Controlling (reducing) Field Current If or Φ and keeping VT at rated value [2, 3]. The desired torque-speed characteristics could be achieved by the use of conventional proportional integral- derivative (PID) controllers. As PID controllers require exact mathematical modeling, the performance of the system is questionable if there is parameter variation [1, 5]. This paper lies in the application of PID controller for the speed control of separately excited dc motor. Simulation results demonstrate the successful application of PID controller to control the speed of a separately excited dc motor. MATLAB/SIMULINK is used because of the short learning curve that most students require to start using it, its wide distribution, and its general-purpose nature . This will demonstrate the advantages of using MATLAB for analyzing power system steady state behavior and its capabilities for simulating transients in power systems and power electronics and control system dynamic behavior. II. IMPLEMENTATION Voltage speed control of a separately excited DC motor: The field current, If is constant (and hence the flux density B is constant), and the armature voltage is varied. A constant field current is obtained by separately exciting the field from a fixed dc source. The flux is produced by the field current, therefore, essentials constant. Thus the torque is proportional only to the armature current . Field speed control of a separately excited dc motor: We can also control the dc motor, which is varying its speed by varying the field flux. The method of control is generally used when the motor has to run above its rated speed. To understand the operations of field control suppose that the dc motor running at a constant speed. If the field current is reduced by reducing the voltage across the field coil, the flux density will be reduced. This will reduce the back emf instantaneously and will cause armature current to increase resulting in the motor speed increasing. Consequently the back emf will increase and a new equilibrium will be established at a higher speed. With field control one can achieve as high a speed as five times the rated speed [1, 2]. The armature current, Ia, is kept constant and the flux density B is varied by varying I f. Combined armature and field control of separately excited DC motor: The speed of a separately excited dc motor could be varied from zero to rated speed mainly by varying armature voltage in the constant torque region. Whereas in the constant power region, field flux should be reduced to achieve speed above the rated speed. Torque and limitations in combined armature voltage and field control can be shown in Figure 1. 8 Volume 4, Number 1, May 2011 _______________________________________________________________________________________________ This is followed by a transformer which is then fed into a “6-Pulse Rectifier” which produces a directed voltage and current [1, 7]. This is connected across the motor. To simplify the design, the armature resistance and inductance has been shown as one impedance. A PID Speed Controller was used, where the following figures elaborate on the design. The speed of a separately excited dc motor could be varied from zero to rated speed mainly by varying armature voltage in the constant torque region. Whereas in the constant power region, field flux should be reduced to achieve speed above the rated speed . The specifications of the dc motor are detailed in the Table1. Fig. 1: Combined armature voltage and field current control. Proportional integral- derivative (PID) controller for DC motor drives: DC Motors of different genres abound. They are used abundantly across different industries including paper mills, robotics, guided vehicles, and conveyors. As can be noted the voltage source is AC. The following diagram shows the basic DC motor design. TABLE 1: Parameter values Parameter Ra La Kp Ki Kd Kα Ke Km B J Fig.2: Basic DC Motor Design TL Vm Pm ωm Vs Label Armature Resistance Armature Inductance Voltage to Speed correction parameter Voltage to Speed correction parameter Voltage to Speed correction parameter Phase Angle to Voltage correction parameter Motor Torque to Motor Current proportionality constant Motor EMF to Speed proportionality constant Motor Viscosity Motor Moment of Inertia Load Torque Rated Voltage Rated Power Rated Speed Transformer Secondary Voltage Value 0.139Ω 0.045H 5.262 26.586 0.3498 0.2 1.91 1.91 0.6Nms 3.5Nms2 200 + ωm + 0.05ωm2 240V 40kW 1150 rpm 240V (L-L) Mathematical modeling: Using Kirchoff’s Voltage Law in Figure 2, the following equation can be derived. (1) V m = I m R a + L a di m / dt + E m Fig. 3: MATLAB/SimPowerSystems model of separately excited dc motor speed control Where, Vm is the input voltage to the motor, Im is the motor current, Em is the voltage left for the motor, not affected by its impedance. Using Newton’s Second Law, the following equation can be derived. Journal of Electrical and Electronics Engineering 9 _______________________________________________________________________________________________ T m = T e − Jd ω m / dt + B ω m (2) III. SIMULATION RESULTS 300.00 250.00 EMF Torque (Nm) Where, Tm is the Motor Torque and Te is the torque produced by the voltage not accounting the losses. EMF Torque 350.00 Simulation is carried out in Matlab-Simulink. The inputs of the controller are the reference speed and the actual speed and the output is the driving voltage to the motor. From Table 1 that TL = 200 + ωm + 0.05ωm2, the following plot can be made. 200.00 150.00 100.00 50.00 0.00 0 2 4 6 8 10 12 14 16 18 Time (s) Fig. 6: Plot of Induced EMF Torque VS Time The inertial torque can be defined as Tacc = J dωm/dt. We know ωm = 120.4sin (0.628t) and J = 3.5Nms2.This implies that dωm/dt. = 75.6112cos (0.628t), so Tacc=3.5(75.6112cos (0.628t)). Finally, Tacc = 264.64cos (0.628t), the following graph show its plot. Inertial Torque VS Time 300 200 Inertial Torque (Nm) 100 Fig. 4: Plot of Angular Speed VS Torque Load 0 0 2 4 6 8 10 12 14 16 18 20 -100 It can be noted that there is a positive relationship between the torque load and angular speed. As one increase, so does the other. According to reference , for such parameters Te = 50 + ω + 0.0115ω2. According to references  and  we can assume sinusoidal speed variation. With ωref = 120.4 rad/s. So let’s assume ωm= 120.4sin (0.628t). This would generate the following graph of ωref vs time. -200 -300 Time (s) Fig. 7: Plot of Inertial Torque VS Time Also the damping torque Tb = Bωm, but since B = 0.6Nms and ωm = 120.4sin (0.628t). This means Tb = 0.6(120.4sin (0.628t)). The following graph depicts this. Reference Angular Speed VS Time Damping Torque VS Time 1.500 80 1.000 0.500 40 0.000 0 2 4 6 8 10 12 14 16 18 -0.500 -1.000 Damping Torque (Nm) Ref. Angular Speed (rad/s) 60 20 0 0 2 4 6 8 10 12 14 16 18 -20 -40 -60 -1.500 Time (s) -80 Time (s) Fig. 5: Plot of Reference Angular Speed VS Time Fig. 8: Plot of Damping Torque VS Time Bearing in mind that Te = 50 + ωm + 0.0115ωm2, the following graph can be plotted. Using equation (2), note that Tm = Te – Tacc – Tb. This is 10 Volume 4, Number 1, May 2011 _______________________________________________________________________________________________ plotted on the following graph. IV. CONCLUSION AND DISCUSSION MotorTorque 400.00 300.00 Motor Torque (Nm) 200.00 100.00 0.00 0 2 4 6 8 10 12 14 18 16 -100.00 -200.00 -300.00 Time (s) Fig. 9: Plot of Motor Torque VS Time Recall, Te = 50 + ωm + 0.0115ωm2. Also Te = keIm. From table 1, ke = 1.91. This means Im = (1/1.91) (50 + ωm + 0.0115ωm2) ==> dim/dt = (1/1.91) (dωm/dt + 2(0.0115)ωm dωm/dt) Also recall, Vm = ImRa + Ladim/dt + Em . Also Em = kmωm. Using parameters from table 1 it can be written Vm = 0.139Im + 0.045 dim/dt + 1.91ωm. Knowing ωm = 120.4sin (0.628t) and dωm/dt. = 75.6112cos (0.628t), plot variations in Vm, Im & Tm. Motor Voltage VS Current Non-linearity of the combined field and armature control system has been studied and carried out using Matlab/Simulink. A DC motor drive for the armature and associated field winding of the motor includes an armature feedback loop responsive to the current flow in the armature, an input command signal such as a speed control signal, and the actual speed of the armature for providing a control of the current supplied by a DC source means to the armature to thereby provide speed control of the motor. A field feedback loop control is also provided and includes means responsive to the voltage across the armature and to the line voltage supplied to the armature for providing a control of the field intensity to assure that the back EMF of the armature is always less than the available DC voltage supplied to the armature. This dual feedback control provides for a faster response time of the armature throughout its total speed range together with the feature of a constant torque for different speeds. V. ACKNOWLEDGMENT The authors would like to acknowledge the Dept. of Electrical & Electronic Engineering, CUET for giving lab facilities and supports to accomplish this work. 300 REFERENCES 200 Motor Voltage (V) 100 0 0 20 40 60 80 100 120 140 160 180 -100 -200 -300 Current (A) Fig. 10: Plot of Motor Voltage VS Current Motor Torque VS Current 400.00 300.00 Motor Torque (Nm) 200.00 100.00 0.00 0 20 40 60 80 100 120 140 160 -100.00 -200.00 -300.00 Current (A) Fig. 11: Plot of Motor Torque VS Current View publication stats 180  Michael A., Mohammad, H.: PID Control, New Identification and Design Methods 2006.  Moleykutty George, “Speed Control of Separately Excited DC Motor.” American Journal of Applied Sciences 5 (3): 227-233, 2008, ISSN 1546-9239.  Zuo L., Fang L., Muhammad H.: Speed Nonlinear Control of DC Motor Drive with Field Weakening. IEEE. Ind. Applications. Vol. 39(2), March 2003.  J. Santana, J. L. Naredo, F. Sandoval, I. Grout, and O. J. 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