lab10a_servo trainer 1 basic tests and transducer calibration

8/18/2019 Lab10a_SERVO TRAINER 1 Basic Tests and Transducer Calibration

1/30

ME 413: System Dynamics & ControlME 413: System Dynamics & ControlME 413: System Dynamics & ControlME 413: System Dynamics & Control

Servo TrainServo TrainServo TrainServo Trainerererer ((((1111))))Basic Tests and Transducer CalibrationBasic Tests and Transducer CalibrationBasic Tests and Transducer CalibrationBasic Tests and Transducer Calibration

__________________________________

__________________________________

__________________________________

__________________________________

__________________________________


2/30

SERVO TRAINER (1)

BASIC TESTS AND TRANSDUCERCALIBRATION

OBJECTIVES

The objective of this experiment is to calibrate the circuits of the Servo Trainer, namelythe input actuator (motor circuit) and also the output sensors (the speed and angular

position sensors).

1. INTRODUCTION

A Servo is a small device that has an output shaft. This shaft can be positioned tospecific angular positions by sending the servo a coded signal. As long as the coded

signal exists on the input line, the servo will maintain the angular position of theshaft. As the coded signal changes, the angular position of the shaft changes. Inpractice, servos are used in radio controlled airplanes to position control surfaces like

the elevators and rudders. They are also used in radio controlled cars, puppets, andof course, robots, Reference [1].

Figure 1 A Futaba S-148 Servo, Reference [1].

Servos are extremely useful in robotics. The motors are small, have built in control

circuitry, and are extremely powerful for their size. A standard servo such as theFutaba S-148 has 42 oz/inches of torque, which is pretty strong for its size. It also

draws power proportional to the mechanical load. A lightly loaded servo, therefore,


3/30

doesn't consume much energy. The guts of a servo motor are shown in Figure 2. You

can see the control circuitry, the motor, a set of gears, and the case. You can alsosee the 3 wires that connect to the outside world. One is for power (+5volts),ground, and the white wire is the control wire, Reference [1].

Figure 2 A servo disassembled, Reference [1].

So, how does a servo work? The servo motor has some control circuits and apotentiometer (a variable resistor, aka pot) that is connected to the output shaft. InFigure 2, the pot can be seen on the right side of the circuit board. This pot allows

the control circuitry to monitor the current angle of the servo motor. If the shaft is at

the correct angle, then the motor shuts off. If the circuit finds that the angle is notcorrect, it will turn the motor the correct direction until the angle is correct. Theoutput shaft of the servo is capable of traveling somewhere around 180o. Usually, it

is somewhere in the 210o range, but it varies by manufacturer. A normal servo isused to control an angular motion of between 0o and 180o. A normal servo ismechanically not capable of turning any farther due to a mechanical stop built on to

the main output gear, Reference [1].

A servo system is one of the most important and widely used forms of controlsystems. Any machine or piece of equipment that has rotating parts will contain one

or more servo control systems. The job of the control system may include:

Maintaining the speed of a motor within certain limits, even when load output

of the motor might vary. This is called regulation.

Varying the speed of a motor and load according to an externally set program

of values. This is called set point (or reference) tracking.

2. SERVO SYSTEM MODELING: SPEED CONTROL SYSTEM

Initially, consider the servo control system with the clutch disengaged. In thisconfiguration the system is a speed control process which can be represented asshown in Figure 3.


4/30

The system model is determined by relating the torque supplied by the motorm

T to

that required to drive the load generator, the flywheel and frictional losses. This canbe expressed by applying Newton’s second law

( )v t

L R

I

( )l v t

ω

Figure 3 Servo control system: Clutch disengaged

d

d

ω=∑T I

t (1)

or

dd

ω= ω + +m l l

T b K v I t

(2)

where b is the friction coefficient of rotating components,l

K is the gain constant of

the load generator and I in the inertia of the flywheel.

The motor electrical circuit is governed by the equation (Apply Kirshhoof VoltageLaw)

( ) = + +bemf

di v t Ri L v

dt

(3)

where ( )v t is the motor input voltage, R is the motor armature resistance, L is

the armature inductance, i is the armature current andbemf

v is the motor back emf.

The back emf and the motor torque can be written in terms of the motor constant

m K , thus

= ω

=

bemf m

m m

v K

T K i (4)


5/30

Combining Equations (2), (3) and (4) by taking Laplace transforms and eliminating

variables yields the transfer function relating the output speed ( )Ω s to the inputvoltage ( )V s and the load voltage ( )l V s

( )

( ) ( )( ) ( )

( ) ( )( )

2 2

+Ω = +

+ + + + + +

m l l

m m

K K sL Rs V s V s sI b sL R K sI b sL R K

(5)

The transfer function simplifies if the inductance L of the armature circuit assumedto be small compared with the inertia of the flywheel. This gives the first ordertransfer function

( ) ( ) ( )

1 1Ω = +

τ + τ +

' '

m l

l

K K s V s V s

s s (6)

where

2

2

2

τ =+

=+

=+

m

' m

m

m

' l

l

m

IR

bR K

K K

bR K

K RK

bR K

(7)

Frequently, we will consider the situation when the servo-control system only has aninertial load. In this case ( ) 0=l V s and Equation (6) simplifies to

( ) ( )

1Ω =

τ +

'

m K

s V s s

(8)

3. SERVO SYSTEM MODELING: POSITION CONTROL SYSTEM

With the electric clutch engaged, the gearbox and output position shaft are

connected to the main shaft as shown in Figure 4.

The output shaft position ( )Θ s , is related to the main shaft velocity ( )Ω s by

( ) ( )1

30Θ = Ωs s

s (9)

where ( )Θ s and ( )Ω s are the Laplace transform of ( )θ t and ( )ω t , respectively.The constant 30 is associated with the 30:1 reduction in speed through the gearbox.Note that the addition of the gearbox load will also change the gain and time

constant characteristics of Equations (6), (7) and (8).


6/30

Equations (6), (7) and (8) are used together to provide the system model for theservo-control system dynamics.

ShaftBearings

LoadGenerator

Motor

( )v t

L R

Flywheel with inertia,I

( )l v t

AngularVelocity, ω

Gearbox

30:1

Positionoutputshaft

AngularPosition, θ

Figure 4 Servo control system: Clutch engaged

4. ACTUATOR AND SENSOR CHARACTERISTICS

When the servo-control system is used as a feedback control system the motor

speed, ( )Ω s , is controlled (or actuated) by adjusting the applied voltage to themotor drive amplifier, ( )V s . Likewise, the shaft speed and angular position aresensed by transducers which produce output voltages ( )

ωY s and ( )

θY s which are

proportional to the shaft velocity, ( )Ω s , and position, ( )Θ s , respectively. Theoverall system may be represented schematically as shown in Figure 5.

( )ω

Y s

1

3 0s

( )θ

Y s ( )V s ( )Θ s ( )Ω s

Figure 5 Schematic representation of a servo control feedback system.

The motor voltage, v , and the shaft speed, ω , are related by a steady stateactuator characteristic which assumed to be linear. The velocity sensor and angularposition sensor also have linear characteristics, as shown in Figures 6, 7,and 8.

Ifi

K ,ω

K andθ

K are the motor, velocity sensor and angle sensor gain constants

respectively, then


7/30

ω ω

θ θ

ω =

= ω

= θ

i K v

y K

y K

(10)

v

ω

Figure 6 Speed versus motor input voltage.

Shaft

Speed, ω

ωy

S l o p

e K ω

Sensor

output

Figure 7 Sensor output versus shaft speed.


8/30

Shaft

position, θ

θy

S l o p

e K θ

Sensor

output

Figure 8 Speed versus motor input voltage.

Notice thati

K is the steady state gain constant that is equal to the gain ' m

K from

Equation (6), obtained for the modeling part. Taking Laplace Transforms of Equation(10) and combining the resulted equations with (8) gives the standard first ordersystem transfer function

( ) ( )1

1ω

=τ +

G Y s V s

s (11)

where1 ω

=i

G K K , is the steady state gain for the transfer function from the input

drive voltage, ( )V s to the sensed shaft position, ( )ωY s . The transfer function

relating the input drive voltage, ( )V s to the sensed shaft position, ( )ω

Y s isshown in Figure 9.

( )ω

Y s ( )V s

1

1τ +

G

s

Figure 9

In addition, the sensed output shaft position ( )θ

Y s is related to the sensed velocity

( )ω

Y s by

( ) ( )2θ ω

= G

Y s Y s s

(12)

where


9/30

2

1

30

θ

ω

=

K G

K (12)

The overall transfer function for the servo-control system can be drawn as in Figure

10 and written thus:

( )

( )( )1 2

1θ

=τ +

G G Y s V s

s s (13)

( )θ

Y s ( )ωY s ( )V s 1

1τ +

G

s 2

G

s

Figure 10 Overall transfer function for the servo control system.


10/30

5. EXPERIMENT

APPARATUS

• CE110 Servo Trainer

• CE120 Controller

Important NoticeImportant NoticeImportant NoticeImportant Notice

Access is gained to the inertial load of the CE110 servo trainer, by a door to therear left of the front panel. When operating the equipment you should ensurethat the selected inertial load is firmly secured by the knurled nut provided and

the access door is firmly closed. The access door has a micro-switch that

prevents the motor turning when the door is open. It is important therefore whenclosing the door to ensure the door is firmly shut and the micro-switch is

engaged.

PROCEDURE

Part 1: Motor Calibration Characteristic

► Connections

Connect the equipment as shown in Figure 11(E1.1).

► Initial Control settings:

CE 110 Servo Trainer

• Clutch disengaged (i.e., position shaft not connected).

• Rear access panel firmly closed (Check micro-switch contact is

made).

• Smallest inertial load installed (No additional discs).

CE 120 Controller

• Potentiometer in center position and reading 0V.

► Steps:

•

Slowly increase the potentiometer voltage (turning thepotentiometer clockwise) until the motor just starts to run. Thisthe size of the positive dead-zone for the motor drive amplifier,enter it into the second row of Table E1.1 provided.

• Increase the potentiometer to 1V; record the correspondingmotor speed from the speed display on the CE110 front panel.

•

Enter your results in Table E1.1.


11/30

• Increase the potentiometer voltage in 1V steps to 10V andrecord the corresponding speed in Table E1.1.

• Repeat the procedure with negative voltages.

• Repeat the above procedure with the clutch disengaged, and

complete Table E1.2.

• Plot the results from Table E1.1 and Table E1.2.

Figure 11(E1.1)


12/30


13/30

Part 2: Speed Sensor Setting

► Connections

Connect the equipment as shown in Figure 12(E1.2)

Figure 12(E1.2)



• Clutch disengaged.

• Rear access panel firmly closed.

•

Smallest inertial load installed (No additional discs).


14/30

CE 120 Controller

• Potentiometer in center position and reading 0V.

► Steps:

• Slowly increase the potentiometer voltage until the speedsensor reads 1V.

• Enter the corresponding speed reading in Table E1.3.

• Repeat the process in steps of 1V for positive and negative

speed sensor reading in the range -9V to +9V.

• Plot the results from Table E1.3.

Table E1.3 Speed Sensor Calibration(Clutch Disengaged)

Motor Speed(rpm)

(positive)

Speed SensorOutput

(V)

Motor Speed(rpm)

(Negative)

Speed SensorOutput

(V)

1 1

2 2

3 3

4 4

5 5

6 6

7 78 8

9 9

Part 3: Angular Position Transducer Calibration

► Connections

Connect the equipment as shown in Figure 13(E1.3)



• Clutch engaged.

• Rear access panel firmly closed.

• Smallest inertial load installed (No additional discs).

CE 120 Controller

• Potentiometer in center position and reading 0V output.


15/30

Figure 13(E1.3)

► Steps:

• Slowly increase the potentiometer voltage until the output shaftbegins to turn.

• Measure the angular position sensor output at angularincrements of 30o starting at -150o and enter your results inTable E1.4. (Hint: with the output shaft rotating at a low butsteady speed, disconnect the potentiometer drive input andposition the output shaft at the desired angle by manuallymaking and breaking the connection to the motor drive).

•

Plot the results from Table E1.4.


16/30

Table E1.4 Speed sensor calibration(Clutch disengaged)

Indicated Angle

(o

)

Position Sensor Output

(V)-150

-120

-90

-60

-30

0

30

60

90

120

150


17/30

REQUIREMENTS

1.

Complete all tables. (i.e., Table E1.1, Table E1.2, Table E1.3, Table E1.4).

2.

Plot the characteristic results from all tables (i.e., Table E1.1, Table E1.2,Table E1.3, and Table E1.4).

3. Are the above characteristic plots linear? If yes find the slope of each one ofthem.

4. Comment on the characteristics plots and discuss why the motor drivecharacteristic differs with the clutch engaged and disengaged.

References

[1] CE110 Servo Trainer Manual, TQ Education and Training Ltd[2] https://reader009.{domain}/reader009/html5/0727/5b5a5aa6a23c4/5b5a5ab49d864.jpg


18/30

APPENDIX A: CE101 SERVO TRAINER

CE110 Servo Trainer

CE120 Controller


19/30


20/30


21/30


22/30


23/30


24/30


25/30


26/30


27/30


28/30


29/30


30/30

lab10a_servo trainer 1 basic tests and transducer calibration

Documents