Speed

ME2142-2 SPEED/POSITION CONTROL OF A DC MOTOR

SEMESTER 5

2012/2013

Department of Mechanical EngineeringNational University of Singapore

1. OBJECTIVES

To become familiar with the operation of an armature-controlled DC motor. To study the transient and steady state response of a closed-loop speed control

system. To study the transient response of a closed-loop position control system.

2. EQUIPMENT

The major items of equipment needed are:

(i) The MS 150 Modular Servo system comprising the following

OU150A Operational AmplifierAU150B Attenuator UnitPA150C Pre-amplifier UnitSA150D Servo AmplifierPS150E Power SupplyMT150F Motor-Tachogenerator UnitIP150H Input PotentiometerOP150K Output Potentiometer

(ii) Function generator

(iii) DC Power Supply

(iv) Dual-trace oscilloscope

3. THEORY OF OPERATION

3.1 The Armature-Controlled DC Motor3.2

The armature-controlled DC motor shown on the right has a constant field excitation. Control of the motor is achieved by changing the armature voltage va

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Relevant system equations are:

(1) va a a aa

m= R i + Ldidt + e

(2) em = Ke m

(3) T ia= K t

(4) T m m= I + b m

Where va = applied voltage ia = armature currentem = motor back emf Ke = motor voltage constantKt = motor torque constant T = torque generated by motorIm = equivalent moment of inertia reflected at the motor shaftb = equivalent viscous coefficient reflected at the motor shaft

Using Laplace transform, equations (1) to (4) can be written as

V s I s sI s sa a a( ) ( ) ( ) ( ) = R + L + Ea a m

E s s sm m( ) ( ) = Ke

T(s I sa) ( ) = K t

T(s s s sm) ( ) ( ) = I + bsm m2

Combining, we can write

V sb

Ks s s s s sa

ta m m m( ) ( ) ( ) =

R + Ka

e 1 1

Where a =L

Ra

a

and m =I

bm are the armature and the motor time constants respectively. The

transfer function for the armature-controlled DC motor is then

m

a

a

ae t

a

s

V s

R b

s sK KR b

( )

( )=

K

s + +1

t

m m a 2

The armature time constant a is normally small compared to the motor time constant m and the transfer function can be written as

m

a

s

V s

( )

( )=

K

s( s +1) or

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It can be noted that for the armature-controlled DC motor, the transfer function between the output speed and the applied voltage is of first order, that is when a step voltage is applied to the motor, its speed will rise exponentially to a steady state value. For angular position, however, the transfer function between the output position and the applied voltage is of 2nd order.

3.2 Closed loop speed control system

Even though the steady output speed of the armature-controlled DC motor is proportional to the applied voltage in the open loop, the speed obtained may vary with applied load torques. To achieve better speed regulation, that is to be able to maintain the same speed in the face of fluctuating loads, and to achieve a faster response, a closed loop speed control system can be used.

The schematic diagram of an armature-controlled DC motor speed/position control system is shown in Fig. 1. Closed-loop speed control is achieved when switch S1 is closed. A voltage proportional to the negative of the output speed, vf, is obtained through a tachogenerator. This is subtracted from the input vi using an operational amplifier connected as a summer. The error is amplified by a servo-amplifier whose output is used to drive the motor.

The servo-amplifier is required to give the necessary output power, that is both voltage and current, to drive the motor. Viscous load is obtained from the generation of eddy currents through the permanent magnet arrangement which gives a load torque approximately proportional to the speed of the disc. This system is of first order and is stable with the output always lagging behind the command input.

3.3 Closed-loop position control system

By taking the output shaft position and feeding it back to the input, a closed-loop position control system is obtained. This is indicated in Fig. 1 with switch S2 closed. In the figure, if switch S1 is also closed, an inner velocity feedback loop is also present in addition to the outer position feedback loop.

It can be shown that the closed-loop position control system using the armature-controlled DC motor, with or without the inner velocity feedback loop, is of 2nd order and is always stable. (Unless, of course, the viscous damping is zero in which case it will be critically stable).

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Switch S1 and Switch S2 both open :- Open loop speed control systemSwitch S1 closed, and Switch S2 open :- Closed loop speed control systemSwitch S1 open, and Switch S2 closed :- Closed loop position control system without

inner velocity feedback loop.Switch S1 and Switch S2 both closed :- Closed loop position control system with

inner velocity feedback loop.

Fig. 1. Armature-controlled DC motor in speed and position control.

4. PROCEDURE

4.1 Speed Control System

4.1.1 The system has been connected up as shown in Fig. 2. Note that the op.amp.gain is 0.1 with a 10 k resistor in the feedback path of the op.amp.(OU 150A). Carefully check the circuit before switching on the system.

4.1.2 Open-loop operation

4.1.2.1 Disconnect both the position feedback and the velocity feedback signals. (That is, remove the two lines marked position feedback and speed feedback in Fig. 2.)

4.1.2.2 Swing the viscous brake clear of the disc. Make sure that the position of the whole brake assembly relative to the disc is not changed throughout the experiment. Otherwise, the readings obtained at various steps for the same brake scale setting may be inconsistent.

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4.1.2.3 Turn the input potentiometer (IP 150H) to zero position on the scale.

4.1.2.4 Check that as you turn the input potentiometer clockwise, the motor runs such that the output shaft dial turns clockwise. Familiarise yourself with the use of the non-contact tachometer to measure the motor speed. This is done by aiming the sensing beam of light from the tachometer at the small white tag pasted on the disc attached to the output shaft to the motor.

Fig. 2. Wiring diagram of DC motor speed/position control system

Tacho-generator Calibration

4.1.2.5 Set the input potentiometer such that the motor runs at approximately 400 rpm.

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Measure the actual speed and both the tacho-generator voltage vf and the input vo to the servo-amplifier and fill out Table 1 and 2 below.

Table 1

Motor Speed (rpm)

Tacho output (volts)

4.1.2.6 Repeat Step 4.1.2.5 for speeds of approximately 800, 1200, 1600, and 2000 rpm.

4.1.2.7 Plot the tacho-generator calibration curve of tacho-generator output voltage against motor speed.

Motor open-loop characteristics

4.1.2.8 Plot the open-loop motor characteristics of motor speed (Y-axis) against input voltage, vo(X-axis) for brake setting of 0.

4.1.2.9 For brake scale settings of 2 and 4, repeat Step 4.1.2.5 and 4.1.2.6 but this time recording only the input voltage, 0. Check that the tacho-generator output voltage f depends only on the motor speed and is not affected by the brake setting. For each setting of input voltage in 4.1.2.8, set the brake at 0, 2 and 4 and record the corresponding speeds.

Table 2

Volts

motor speed for brake setting 0



4.1.2.10 Plot the open-loop motor characteristics as in Step 4.1.2.8 for brake settings of 2 and 4 on the same graph.

Motor load regulation

4.1.2.11 With the brake scale setting at 0, adjust the input potentiometer to set the motor speed at 1000 rpm.

4.1.2.12 Move the brake scale setting to 2, 4, 6, 8, and 10 and record the motor speed at each setting.

Fill out Table 3 and plot motor speed against brake scale setting.

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Table 3

Brake Scale Setting 0 2 4 6 8 10

Motor Speed, rpm

4.1.3 Closed-loop operation

4.1.3.1 Re-connect the speed feedback signal. Set brake scale setting to 0.

4.1.3.2 Set input potentiometer for a motor speed of approximately 1000 rpm.

4.1.3.3 Move the brake scale setting 2, 4, 6, 8, and 10 and record the motor speed at each setting as in Table 3. Note that it is possible that current limiting will occur in the servo-amplifier power supply (PS 150E). This is indicated when the ammeter will not further increase its reading. Record the point at which this occurs.

4.1.3.4 Repeat Steps 4.1.3.1 to 4.1.3.3 for op.amp. gains of 0.01 and 0.05 (by replacing the op.amp. feedback resistor to 1 k and 5 k respectively). For each gain setting, plot the motor speed against brake scale settings on the same graph as that for Step 4.1.2.12. When completed, this graph will then show the speed characteristics for open-loop and closed loop (3 gain settings).

4.1.4 Transient Response

4.1.4.1 For the closed-loop speed control system, remove the input speed command signal (that is, the input 1 to the op.amp. from the input potentiometer). Set the op.amp. gain to 0.05 (5 k feedback resistor).

4.1.4.2 Generate a 0V to -8V square wave signal at a frequency of 0.5 HZ using the function generator and use this as the input command speed signal (input 1 to op.amp.). Observe the transient response of the output speed on the oscilloscope provided for brake scale settings of 5 and 10.

4.1.4.3 Repeat Step 4.1.4.2 for op.amp. gains of 0.01 and 0.1.

4.2 Closed-loop Position Control System

4.2.1 Connect the position feedback signal to give a position feedback control system.

4.2.2 Set the op.amp. gain to 0.1 (10 k feedback resistor) and the brake scale to 5. Check that as you rotate the input potentiometer, the output disc follows accordingly.

4.2.3 Disconnect the position command input signal (input 1 to the op.amp from the input potentiometer is now the input position command signal). Using the function generator, generate a square wave of frequency 0.2 Hz and 1V peak-to-peak and use this as the position command input. Display and observe both the input

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command position and the output position signal on the oscilloscope and note the overshoot of the output.

4.2.4 Repeat Step 4.2.3 with op.amp. gain setting of 0.01 (feedback resistor 1 k respectively).

4.2.5 Disconnect the speed feedback signal. The position feedback system now has no inner velocity feedback loop. Repeat Steps 4.2.3 and 4.2.4 for op.amp. gains of 0.1 and 0.01.

4.3 Phenomenon of Instability

4.3.1 Interchange the connections to terminals 1 and 2 of the output potentiometer. Now terminal 1 will be connected to -15V and terminal 2 to +15V. The system now has positive feedback. Observe that the system is now unstable.

5. DISCUSSIONS

Discuss the differences in open-loop and closed loop control in achieving a speed control system and the effects of loop gain and load on the output speed.

Discuss the effect of loop gain and brake scale settings on the transient response of the closed-loop speed control system.

Discuss the effect of loop gain and velocity feedback on the response of the closed loop position control system.

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Speed

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