ME2142-2 Lab MAnual Speed and Position Control

ME2142-2 SPEED/POSITION CONTROL OF A DC MOTOR

SEMESTER 6 2016/2017

Department of Mechanical Engineering National University of Singapore

1.

2.

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

EQUIPMENT

The major items of the equipment needed are: (i) The MS 150 Modular Servo system comprising the following: - OU150A Operational Amplifier - AU150B Attenuator unit - PA150C Pre-amplifier unit - SA150D Servo Amplifier - PS150E Power Supply - MT150F Motor-Tacho-generator unit - IP150H Input Potentiometer - OP150K Output Potentiometer (ii) (iii) (iv)

3.

Function Generator DC Power Supply Dual-trace Oscilloscope

THEORY OF OPERATION 3.1. The Armature-Controlled DC Motor

The armature-controlled DC motor shown in Figure 3.1 has a constant field excitation (constant i f  ); i f  stands for field current. Control of the motor is achieved by changing the armature voltage ( va ).

Figure 3.1. Schematic of DC Motor

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Relevant system equations are: di v a  Ra ia  La a  em   dt 

(1)

em  K e m  

(2)

T   K t ia  

(3)

  b    T   I m  m m

(4)

Where: va = applied voltage to the armature

ia = armature current

em = motor back e.m.f

K e = motor voltage constant

K t  = motor torque constant

T  = torque generated by motor

 I m = equivalent moment of inertia reflected at the motor shaft

b = equivalent viscous coefficient reflected at the motor shaft Using Laplace transform, assuming zero initial conditions, equations (1) to (4) can be written as: V a s    Ra I a s   La sI a s   E m s   

(5)

 E m s   K e s m s   

(6)

T s   K t  I a s   

(7)

T s    I m s 2  m  bs m  

(8)

Combining equations (5) to (8), we can write: V a s  

Where

 a

 Ra b



K t 

 La  Ra

s a s  1 m s  1 m s   K e s m s   

 and

 m



 I m b

(9)

are the armature and the motor time constants respectively.

The transfer function for the armature-controlled DC motor is then:

 m s  V a s 



K t   Ra b

   K  K    2 s  m a s   m   a s   e t   1     Ra b   

The armature time constant

 a  is

 

(10)

normally small compared to the motor time constant

and the transfer function can be written as:  m s   m s  K  K    or   V a s  s s  1 V a s   s  1 Where K  

K t  K e K t   Ra b

  and

 



 m Ra b

K e K t   Ra b 3



(11)  I m Ra K e K t   Ra b

 

(12)

 m

It can be noted that for the armature-controlled DC motor, the transfer function between the output angular speed and the applied voltage is first order. Meanwhile, the transfer function between the output angular position and the applied voltage is second order. 3.2. Closed-loop Speed Control System

Even though the steady state output angular speed of the armature-controller DC motor is  proportional to the applied voltage in the open loop system, the angular speed obtained may vary with applied load torques (through the viscous damping, b ). To achieve better speed regulation, that is to be able to maintain the angular speed of the motor 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 Figure 3.2. Closed-loop speed control is achieved when switch S 1 is closed. A voltage proportional to the negative of the output speed ( v  ) is obtained through a tachogenerator. This is subtracted from the reference voltage ( vr  ) using an operational amplifier connected as a summer. The error ( e  vr   v  ) is amplified by a servo-amplifier whose output is used to drive the motor ( va ). The servo-amplifier is required to give the necessary output power, which 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 angular speed of the motor’s shaft (term b m  in equation (4)). 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’s position and feeding it back to the input, a closed-loop position control system is obtained. This is indicated in Figure 3.2 with switch S 2 closed. In the figure, if switch S 1 is also closed, an inner angular speed 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 angular speed feedback loop, is of 2 nd  order and is always stable.

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Figure 3.2. Armature-controlled DC motor in speed and position control  Notes: Switch S 1 and switch S 2 both open Switch S 1 closed, and switch S 2 open Switch S 1 open, and switch S 2 closed

: Open loop speed control system : Closed loop speed control system : Closed loop position control system without inner angular speed feedback : Closed loop position control system with inner angular speed feedback

Switch S 1 and switch S 2 both closed

4.

PROCEDURE 4.1. Speed Control System

The system has been connected up as shown in Figure 4.1. Note that the operational amplifier (OU 150A) gain is 0.1 with 10 k  resistor in the feedback path of the operational amplifier. Carefully check the circuit before switching the system. For the speed control system experiment, there are four types of experiment that will be done. Following are the experiments and their respective procedures: 4.1.1. Tacho-generator characteristics experiment (closed-loop speed control system)

a. This experiment is done in closed-loop speed control system. Make sure that the cable marked speed feedback is connected to the operational amplifier.  b. This experiment is done without viscous load to the motor. Swing the viscous brake clear of the disc. Set the gain of the attenuator unit to 10. c. Turn the input potentiometer clockwise such that the motor runs at approximately 400 rpm. The angular speed of the motor can be read from the tacho-generator display. After the angular speed of the motor reach 400 rpm, slide the switch beside 5

the tacho-generator display to view the output voltage of the tacho-generator. Repeat this step for angular speed of 800, 1200, 1600 and 2000 rpm and record the data (motor angular speed and output voltage of the tacho-generator) in Table 1 (See Appendix). d. Plot the motor angular speed (rpm) versus the output voltage of the tacho-generator. The slope of the curve is K   .

Figure 4.1. Wiring diagram of DC motor speed/position control

4.1.2. Open-loop speed control system characteristics to variation in loads

With this experiment, we can observe how good the open-loop speed control system maintains the angular speed of the motor with variation in the motor load. a.

 b.

c.

d.

To operate in open-loop speed control system, disconnect the speed feedback signal from the operational amplifier. These are done by removing the cable marked speed feedback. With the gain of the attenuator unit set at 10 and the viscous brake set at 0, turn the input potentiometer clockwise until the angular speed of the motor is approximately 1000 rpm. Without changing the input potentiometer, change t he brake setting to 2,4,6,8 and 10 and record the angular speed of the motor for each brake setting. Fill out Table 2 in the Appendix. Plot the motor angular speed (rpm) versus brake scale setting. Use simple analysis (i.e. equations (11) and (12)) to explain the result.

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4.1.3. Closed-loop speed control system characteristics to variation in loads

With this experiment, we can observe how good the closed-loop speed control system maintains the angular speed of the motor with variation in the motor load. This experiment will be done three times, each with attenuator unit gain setting of 3, 6, and 10. a.  b.

c. d. e.

To operate in closed-loop speed control system, re-connect the speed feedback signal to the operational amplifier. Set the gain of the attenuator unit to 3 and set the brake at 0. Turn the input  potentiometer clockwise until the angular speed of the motor is approximately 1000 rpm. Without changing the input potentiometer, change t he brake setting to 2,4,6,8 and 10 and record the angular speed of the motor for each brake setting. Repeat step c and d for attenuator unit gain of 6 and 10 and fill out Table 3 in the Appendix. Plot the motor angular speed (rpm) versus brake scale setting for the three gains of the attenuator unit. Use simple analysis to explain the effect of attenuator gain setting in the motor angular speed in face of variation of load.

4.1.4. Transient response of closed-loop speed control system

With this experiment, we can observe the effec ts of the attenuator unit gain and the brake scale settings to the transient response characteristics of the system (represented by the time constant). The attenuator gains that will be used are 6 and 10, while the brake scale settings are 0 and 10. This experiment will be done four times with different settings: attenuator gain of 6 with  brake setting 0; attenuator gain of 6 with brake setting 10; attenuator gain of 10 with brake setting 0; and attenuator gain of 10 with brake setting of 10. a.

 b. c. d.

Remove the input signal from the input potentiometer to the operational amplifier. Connect the output signal from the signal generator to the operational amplifier and to the input channel 1 in the oscilloscope. Connect the output signal from the tachogenerator to the input channel 2 in the oscilloscope. Generate a 0V to -4V square wave signal at frequency of 0.5 Hz from the function generator. Observe the transient response of the motor using the oscilloscope. Print out the transient response plot (with the help from lab assistant). Fill out Table 4 in the Appendix and use simple analysis to explain the effect of attenuator gain and brake scale settings to the time constant of the system.

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4.2. Closed-loop Position Control System

With this experiment, we can observe the effects of the attenuator unit gain and the inner angular speed feedback to the transient response characteristics of the system (represented  by the percentage of overshoot, settling time and rise time). The attenuator gains that will  be used are 6 and 10, while the brake scale setting is set to 5. This experiment will be done with attenuator gain of 6 and 10. For each gain, the closedloop position feedback will be done with inner angular speed feedback and without inner angular speed feedback. a. To use both angular speed and position feedback, connect the cables marked position feedback and speed feedback to the operational a mplifier. Then, connect the cable from channel 2 of the oscilloscope to the output potentiometer to read the actual position signal of the motor.  b. Generate a square wave of frequency 0.2 Hz with amplitude of 1V from the function generator. Observe the transient response using the oscilloscope and estimate the % overshoot, settling time (5%) and rise time (90%). c. To carry out the experiment without the angular speed feedback, remove the cable marked speed feedback and repeat the experiment. d. Print out the transient response plot for each experiment. e. Fill out Table 5 in the Appendix and use simple analysis to explain the effect of attenuator gain and angular speed feedback to the transient response of the system. 4.3. Phenomenon of Instability

Interchange the connections to terminals 1 and 2 of the output potentiometer. Now terminal 1 will be connected to -15V while terminal 2 to +15V. The system now has  positive  feedback . Observe that the system is now unstable. 5.

DISCUSSIONS

(1)

(2)

Discuss the points mentioned in 4.1.2.d and 4.1.3.e, and also comment the differences  between open-loop and closed-loop speed control system characteristics in face of variation in motor load (with constant reference voltage). Discuss the points mentioned in 4.1.4.d and 4.2.e

ADDITIONAL NOTES ON ATTENUATOR GAIN

(1) Attenuator unit gain of 10 results in K c  gain of 0.1 (2) Attenuator unit gain of 6 is results in K c  gain of 0.06 (3) The value of K c  is the proportional gain in the feedback loop where v a  K c e  K c v r   v   for the case of closed-loop speed control OR v a  K c e  K c v r   v   v     for the case of closed-loop position control with the inner angular speed feedback applied

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APPENDIX

TABLE 1. Tacho-generator characteristics Speed (rpm) 400 Tacho Outputs (volts)  With speed feedback



800

1200

1600

2000

Attenuator gain = 10; brake setting = 0

TABLE 2. Open-loop load-speed characteristics Brake setting 0 Speed (rpm) 1000  Attenuator gain = 10

2

4

6

8

10

TABLE 3. Closed-loop load-speed characteristics Brake setting Speed (gain = 3) Speed (gain = 6) Speed (gain = 10)

0 1000 1000 1000

2

4

6

8

10

TABLE 4. Transient response of the closed-loop speed control system Brake setting

Brake 0 Time constant (ms)

Brake 10 Time constant (ms)

Gain = 6 Gain = 10  Time constant: time to reach 63.2% of the steady state value from the start of the input step

TABLE 5. Transient response of the closed-loop position control system Brake setting = 5

With speed feedback overshoot settling rise time (%) time (ms) (ms)

Without speed feedback overshoot settling rise time (%) time (ms) (ms)

Gain = 6 Gain = 10  Settling time (5%): time for the response to reach and remain in the region of 5% of the steady state value for the first time. Time is measured from the start of the input step



Rise time: time for the response to reach 90% of the steady state value from the start of the input step

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