lab11a_servo trainer 3 proportional control of servo trainer speed

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

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Servo Trainer SpeedServo Trainer SpeedServo Trainer SpeedServo Trainer Speed

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Due Date:

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Instructor

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ME 413: System Dynamics and Control Lab Manual

Servo Trainer (3): Proportional Control of Servo Trainer Speed 1

SERVO TRAINER (3)

PROPORTIONAL CONTROL OF

SERVO TRAINER SPEED

OBJECTIVES

The objective of this experiment is to implement a proportional controller of the Servo

Trainer speed and to investigate the closed transient response, and the steady state

errors.

THEORY

The block diagram representation of the configuration for this experiment is shown in

Figure 1.

pk 1

1τ +

G

s

Error Signal,

( )E sPID Controller block

Motor Input

CE110 Servo system

Speed sensor output

( )ωY s

Reference input,

( )rY s

Figure 1 Block diagram representation

The closed loop transfer function may be given by

( )

( )

1

1

1 1

1

11

1

ω

τ + = =

τ + + +

τ +

pp

r pp

Gk

k GY s sGY s s k Gks

(1)

Equation (1) can be written in standard first order system as

( )

( )

1 1

1

11

1

ω = =τ + τ

+ +

p p

r cl

p

k G k GY s

Y s ss

k G

(2)



where

11

ττ =

+cl

pk G

(3)

is the theoretical closed loop time constant. On the other hand, the error signal ( )E s can be expressed as

( ) ( ) ( )ω

= −r

E s Y s Y s (4)

Substituting ( )ωY s from Equation (1) into Equation (4) gives

( ) ( ) ( )

( )

1

11

ω

= −τ + +

��

p

r r

p

Y s

k GE s Y s Y s

s k G (5)

Simplifying the above equation gives

( ) ( )

1

1

1

τ +=

τ + + r

p

sE s Y s

s k G (6)

The steady state error

sse is given by

( )[ ] ( )0 0

1

1

1→ →

τ += =

τ + + ss r

s sp

se lim sE s lim s Y s

s k G (7)

For a constant reference signal (step input) of magnitude

ry , the steady state error

sse may be written as

( )[ ]0 0→ →

= =ss

s se lim sE s lim s

1

1

1

τ + τ + +

r

p

s y

s k G s1

1

=

+

r

p

y

k G (8)

APPARATUS

• CE110 Servo Trainer

• CE120 Controller

• Chart Recorder



PROCEDURE

Part 1: Steady State Errors

► Connections

Connect the equipment as shown in Figure 2(E3.1) that corresponds to the block

diagram of Figure 1.

Figure 2(E3.1)

► Initial Controller settings:

CE 110 Servo Trainer

• Clutch disengaged.

• Large inertial load installed.



• Rear access door firmly closed.

CE 120 Controller

• Potentiometer turned fully anti-clockwise (i.e., set to 0V output)

• PID Controller: Proportional gain set to 10 and switched in,

while Derivative and Integral blocks switched out.

► Steps:

• Investigate whether the steady state error is proportional to the reference signal,

ry .

• Increase the reference speed as given by the potentiometer

output in steps of 1V from 2V to 10 V and record the

corresponding errors signals in Table E3.1.

• Use Equation (8), the value of =pk 10 and

1=G 1 to calculate

the theoretical values of sse for various values of

ry and enter

the results in Table E3.1.

• Investigate whether the steady state error is inversely

proportional to the controller gain pk .

• Set the potentiometer to give a reference speed signal, ry , of

5V.

• Vary the controller gain from 1 to 10 in steps of 1 and record

the corresponding error signal reading in Table E3.2.

• Use Equation (8) to calculate the theoretical values of sse for

each value of pk and enter the results in Table E3.2.

Table E3.1 Steady state errors for various reference speeds

(Clutch disengaged)

Potentiometer Setting (Reference Speed

ry )

(V)

Measured Steady

State Error Signal

(V)

Theoretical sse

11

=+

r

ss

p

ye

k G

[ =pk 10 and

1=G 1]

(V)

2

3

4

5

6

7

8

9

10



Table E3.2 Steady state errors for various controller gains

(Clutch disengaged)

Potentiometer Setting

Controller gain, pk

Measured Steady

State Error Signal

(V)

Theoretical sse

11

=+

r

ss

p

ye

k G

[ =ry 5 and

1=G 1]

(V)

1

2

3

4

5

6

7

8

9

10

Part 2: Transient Response

► Connections

Connect the equipment as shown in Figure 3(E3.3), this corresponds to the block

diagram of Figure 4.

► Initial Control settings:

CE 110 Servo-Trainer

• Clutch disengaged.

• Large inertial load installed.

• Rear access door firmly closed.

CE 120 Controller

• Potentiometer set to 5V.

• Function Generator set to: square wave.

• Frequency 0.05 Hz offset 0V, and level 1V.

• PID Controller: Proportional Controller 1=pk , integral and

derivative blocks switched out.

► Steps:

In this part of the experiment we investigate how the transient response of the Servo

Trainer is affected by the proportional controller gain pk .

• Use the square wave output to generate a series of step

changes in reference speed and plot the corresponding speed



response using the chart recorder (suggested time base 10

mm/sec) for proportional gains =pk 0.5, 1, 2, 4.

• Calculate the closed loop time constant, τcl, from the graph and

compare the results with the theoretical values obtained using

equation (3).

• Enter the results in Table E3.3.

• Notice that for the large inertial load the following approximate

values may be used; τ=1.5 and 1G =1.

Figure 3(E3.3)



pk 1

1τ +

G

s

Figure 4

Table E3.3 Comparison of Measured Closed Loop Time Constants with

Theoretical Values

(Clutch disengaged)

Controller gain, pk

Measured Closed

Loop Time

Constant

(sec)

Theoretical sse

11

ττ =

+cl

pk G

[ τ = 1.5 and 1

=G 1]

(sec)

0.5

1

2

4



REQUIREMENTS

1. Enter the results into the appropriate tables.

2. For Part 1: Discuss the steady state error results and in particular give reasons for any sufficient differences between the measured and the

theoretical values of steady state errors.

3. For Part 2: Calculate the closed loop time constant, τ

cl, from the graph and

compare the results with the theoretical values obtained using equation (3).

4. Discuss the step response results and the differences between the measured and theoretical closed-loop time constants.

References

[1] CE110 Servo Trainer Manual, TQ Education and Training Ltd

lab11a_servo trainer 3 proportional control of servo trainer speed

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