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Unformatted text preview: 1 A design of the DC motor control circuit Abstract: The phase compensation method is applied in the control system design, the speed of DC motor is controlled by using the feedback of both armature current and tachometer voltage. 1. Modeling a DC motor The symbols used in the modeling is defined as follows: L : armature inductance ] [ H a R : armature resistance ] [ Ω i : armature current ] [ A e : applied armature voltage ] [ V e K : back electromotive force constant ] sec/ [ rad V t K : torque constant [ A Nm / ] m J : rotor momentum of inertia [ 2 kgm ] w : rotor speed sec] / [ rad l J : load momentum of inertia [ 2 kgm ] l B : viscous friction coefficient sec] / / [ rad Nm f t : disturbance torque ] [ Nm . In this case the electrical equation is given as w e a K e i R dt di L = + (1.1) and for the mechanical part of the system the torque equation is described as follows: ( 29 f m i K B dt d J J t w w t = + + l l . (1.2) It is often possible to neglect them on the design of a DC motor control system, because the effect of both the inductance L of Eq. (1.1) and the viscous torque w l B of Eq. (1.2) is very slight. The following block diagram for the design of a DC motor control system can be obtained. e i t 1 R K t f t 1 J s K e w Fig. 1 The block diagram for the design of a DC motor control system. The transfer function to the motor speed w from the applied armature voltage e in Fig. 1 is described as s T K s e s m + = 1 ) ( ) ( w , (1.3) where the time constant m T and the gain K are the following formulation: e a m m K K R J J T t ) ( l + = e K K 1 = . (1.4) 2 2. Torque control by means of armature current feedback In case of detection of the large current, a eddy current sensor is often used. It is detected by inserting the small resistance i R in the armature circuit, because the motor current is not so large in this system. Here, let us use the symbol i e as the current reference value. Then, i G is the transfer function of the current amplifier. Moreover, when i K is the feedback ratio of the motor current, the block diagram of the torque control system is shown by the following Fig. 2. e i t 1 R K t f t 1 Js K e w G i e e i K i R i K p Fig. 2 The block diagram of the torque control system. 2.1 The construction of the current amplifier The two typical current amplifiers shown by the following transfer function are considered: A) Amplifier of the first order delay type: Ts K G i + = 1 11 (2.1) B) Amplifier of the integral type: s Ts K G i ) 1 ( 11 + = (2.2) 2.2 The case of using amplifier of the first order delay type The transfer function to the motor speed w from the current reference value i e in Fig. 2 is described as e e i i p p i K K s T K K R K K JK JR JRTs K K K s e s t t t w + + + + = ) ( ) ( ) ( 11 2 11 , (2.3) where J and R are given by the following relation: l m J J J + = , i a R R R + = . (2.4) In addition, the block diagram of the torque control system in the condition that the rotor was locked is shown by Fig. 3. Fig....
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This note was uploaded on 02/06/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.
 Fall '07
 Chen
 Volt

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