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UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

COURSE TITLE : ENGINEERING LABORATORY VI (BDA 37101)

TOPIC : RECTILINEAR CONTROL SYSTEM TO COMPARE THE

DIFFERENT STIFFNESS OF THE SPRING

1. INTRODUCTION

A control system is an interconnection of components forming a system

configuration that will provide a desired system response. In control system, the

relationship between the input and output represents the cause and effect relationship

of the process. The control system requires us to understand and modelled the

systems. There are two types of control systems, which open-loop control system and

closed-loop control system. An open-loop control system utilizes an actuating device

to control the process directly without using feedback. Meanwhile a closed-loop

control system uses a measurement of the output and feedback of this signal to

compare it with the desired output (reference or command).

The transfer function of a linear system is a mathematical representation of the

system which defined as the ratio of the Laplace transform of the output variable to

the Laplace transform of the input variable, with all conditions equal to zero. This

transfer function represents the relationship describing the dynamics of the system

under consideration. By using transfer function we can calculate the system with

several parameters that can be measured. This technique uses the experimental

approach to get the transfer function of a system is known as system identification.

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

2. OBJECTIVES

The objectives of this experiment are:

I. To learn how to analyse control system through simulation using rectilinear

plant system.

II. To compare the result obtained from the experiment by using different

parameters of rectilinear plant system.

III. To study the effect of different position of spring and number of encoder of

the rectilinear plant system.

3. LEARNING OUTCOMES

At the end of this experiment, students should be able to:

I. To develop skills for working with others in an experimental environment.

II. To know how to relate the experiment in real application.

4. SCOPE

I. Analyse the parameter by using two springs which 400 N/m and 800 N/m.

II. Analyse the result by using three encoders with and without damper.

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

5. THEORY

In control theory, a controller is a device which monitors and affects the

operational conditions of a given dynamical system. The operational conditions are

typically referred to us output variables of the system that can be effected by adjusting

certain input variable.

Figure 1: Schematic view of rectilinear system

Schematic of model:

2 masses/inertia ,

Each have a positioning freedom : 2DOF system

Connected via spring element ,

Model damping : a viscous damping ,

Input u ; F to output y : =

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

Much smaller amplitude response become dominated by nonlinear friction effects and

do not reflect the salient system dynamic. Divide the number of cycles by the time taken to

complete them. Sure to take beginning and end times from the same phase of the respective

cycles. Convert the resulting frequency in Hz to radian/sec. This damped frequency ,

approximates the natural frequency, according to :

f = ……………………. (1)

= ………………………… (2)

= ………………… (3)

Measure the initial cycle amplitude and the last cycle amplitude for the n cycle

measured. Using relationships associated with the logarithmic decrement.

= ln ) ..…………….(4)

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

6. APPARATUS

Figure 2 shows the equipment used for this experiment. The equipment consists

of:

a. Electromechanical plant

b. System interface software

c. Real-time controller & I/O

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

7. PROCEDURES

7.1 IDENTIFYING THE PLANT PARAMETER

This procedure is to identify the plant parameters applicable to the equation in

theory (5). The approach will be to indirectly measure the mass, spring, and

damping parameters by making measurements of the plant while set up in a pair of

classical spring-mass configurations.

1. Setup all three carriages. Clamp the first carriage to prevent the first

carriage from moving. Verify the stiffness of the spring that is medium

stiffness (400 N/m) and high stiffness (800 N/m).

2. The medium spring (400 N/m) is connecting to the first carriage and the

second carriage. Meanwhile a high stiffness spring (800 N/m) is

connecting to the second and third carriage.

3. Secure four 500g masses on the second and third mass carriage.

4. With the controller powered up, enter the control Algorithm box via the set

up menu and set Ts=0.00442. Enter the command menu, go to Trajectory

and select step, step-up. Select Open Loop Step and input a step size of

zero a duration of 3000 ms and 1 repetition. Exit to the background screen

by consecutively selecting OK. This put the controller in a mode for

acquiring 6 second of data on command but without driving the actuator.

This procedure may be repeated and the duration adjusted to vary the data

acquisition period.

5. Go to Set Up Data Acquisition in the Data Menu and select Encoder #2

and Encoder #3 as data to acquired and specify data sampling every 2(two)

servo cycles. Select OK to exit. Select zero position from the Utility Menu

to zero the encoder positions.

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

6. Click on Command, Execute. Prepare to manually compress the third

carriage approximately 2.5 cm. Then, click Run from the Execute box and

release the carriage after one second. Wait while the encoder data is

collected to record the response. Select OK after data is uploaded.

7. Choose several consecutive cycles (say~4) in the amplitude range between

5500 and 1000 counts. This is representative of oscillation amplitudes

during later closed loop control maneuvers. Much smaller amplitude

responses become dominated by nonlinear friction effects and do not

reflect the salient system dynamics. Divide the number of cycles by the

time taken to complete them. Be sure to take beginning and end time from

the same phase of the respective cycles. Convert the resulting frequency in

Hz to radian/sec.

8. Remove all the masses from the second carriage and third carriage and

repeat step 4 until 7 to obtain data for unloaded carriage. If necessary,

repeat step 4 to reduce the execution duration.

9. Next, attach the damper to the third carriage. Repeat step 4 until step 7 to

obtain the data with damper in the system.

10. Measure the initial cycle amplitude X0 and the last cycle amplitude Xn for

the n cycles measured in step 7.

11. Repeat step 4 until step 10 for the opposite position of spring. The high

stiffness spring (800 N/m) is connecting the first and second carriage.

While medium stiffness spring (400 N/m) is connecting the second and

third carriage.

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

8. OBSERVATION

1. When the medium stiffness spring (400 N/m) is attached between carriage 2 and

carriage 3, the time taken for mass carriages to stop moving after it have been apply

force is shorter.

2. When load (2kg mass) involved in the system, the time taken for carriages to stop

moving are longer compare to system without load.

3. The attachment of damper in the system also cause the time taken for carriages to stop

moving become shorter compare to system that unattached to damper.

4. When the high stiffness spring (800 N/m) is attached between carriage 2 and

carriage 3, the time taken for mass carriages to stop moving after it have been apply

force is longer.

5. When load (2kg mass) involved in the system, the time taken for carriages to stop

moving are also shorter compare to system without load.

6. The attachment of damper in the system also causes the time taken for carriages to

stop moving become longer compare to system that unattached to damper.

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

9. CALCULATION

Spring 400 N/m with load (Encoder 2)

(Graph 1)

f =

=

= 1.293 Hz

=

= 2

= 8.124 rad/s

= ln )

ln )

= 0.040

=

=

= 8.131 rad/s

800 N/m Encoder 3

f =

=

= 1.293 Hz

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=

= 2

= 8.124 rad/s

= ln )

ln )

= 0.042

=

=

= 8.131 rad/s

Spring 400 N/m without load (Encoder 2)

(Graph 2)

f =

=

= 2.459 Hz

=

= 2

= 15.450 rad/s

= ln )

ln )

= 0.0504

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

=

=

= 15.469 rad/s

Spring 800 N/m (Encoder 3)

f =

=

= 2.459 Hz

=

= 2

= 15.450 rad/s

= ln )

ln )

= 0.0553

=

=

= 15.47 rad/s

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

Spring 400 N/m with load with damper (Encoder 2)

(Graph 3)

f =

=

= 2.222 Hz

=

= 2

= 13.961 rad/s

= ln )

ln )

= 0.0739

=

=

= 13.999 rad/s

Spring 800 N/m (Encoder 3)

f =

=

= 2.273 Hz

=

= 2

= 14.28 rad/s

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

= ln )

ln )

= 0.094

=

=

= 14.344 rad/s

Spring 400 N/m without loaded with damper ( Encoder 2)

Graph 4

f =

=

= 2.127 Hz

=

= 2

= 13.364 rad/s

= ln )

ln )

= 0.349

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

=

=

= 14.264 rad/s

Spring 800 N/m (Encoder 3)

f =

=

= 2.127 Hz

=

= 2

= 13.364 rad/s

= ln )

ln )

= 0.4283

=

=

= 14.789 rad/s

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

Spring 400 N/m with load ( Encoder 2)

Graph 5

f =

=

= 1.363 Hz

=

= 2

= 8.567 rad/s

= ln )

ln )

= 0.033

=

=

= 8.571 rad/s

Spring 800 N/m ( Encoder 3)

f =

=

= 1.4285 Hz

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

=

= 2

= 8.975 rad/s

= ln )

ln )

= 0.026

=

=

= 8.983 rad/s

Spring 800 N/m without load ( Encoder 2)

Graph 6

f =

=

= 3 Hz

=

= 2

= 18.849 rad/s

= ln )

ln )

= 0.0617 rad/s

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=

=

= 18.885 rad/s

Spring 400 N/m ( Encoder 3)

f =

=

= 3 Hz

=

= 2

= 18.849 rad/s

= ln )

ln )

= 0.0533 rad/s

=

=

= 18.875 rad/s

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Spring 800 N/m with load with damper ( Encoder 2)

Graph 7

f =

=

= 1.4084 Hz

=

= 2

= 8.8492 rad/s

= ln )

ln )

= 0.2041 rad/s

=

=

= 9.0394 rad/s

Spring 400 N/m ( Encoder 3)

f =

=

= 1.4925 Hz

=

= 2

= 9.3776 rad/s

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= ln )

ln )

= 0.1281 rad/s

=

=

= 9.4555 rad/s

Spring 800 N/m without load with damper ( Encoder 2)

Graph 8

f =

=

= 2.5 Hz

=

= 2

= 15.707 rad/s

= ln )

ln )

= 0.0109 rad/s

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

=

=

= 15.7079 rad/s

Spring 400 N/m (Encoder 3)

f =

=

= 3.5714 Hz

=

= 2

= 22.439 rad/s

= ln )

ln )

= 0.3665

=

=

= 24.117 rad/s

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10. RESULT

Encoder #2

400N/m

Encoder #3

800N/m

Damper

Encoder #2 Encoder #3

load unloaded load unloaded load unloaded load unloaded

f (Hz) 1.293 2.459 1.293 2.459 2.222 2.127 2.273 2.127

8.124 15.450 8.124 15.450 13.961 13.364 14.28 13.364

0.040 0.0504 0.042 0.0553 0.0739 0.3497 0.094 0.4283

8.131 15.469 8.1312 15.47 13.999 14.264 14.344 14.789

0.76431 0.76431 52.331 31.741

k (N/m) 182.443 182.443 9346.13 5668.83

Table 1 : Low stiffness spring k = 400 N/m and 800 N/m

Encoder #2

400N/m

Encoder #3

800N/m

Damper

Encoder #2 Encoder #3

load unloaded load unloaded load unloaded load unloaded

f (Hz) 1.363 3 1.4285 3 1.4084 2.500 1.4925 3.571

8.567 18.849 8.975 18.849 8.8492 15.707 9.3776 22.439

0.033 0.0617 0.026 0.0533 0.2041 0.0109 0.1281 0.3665

8.571 18.885 8.983 18.875 9.0394 15.708 9.456 24.117

0.5188 0.5856 0.9903 0.3633

k (N/m) 184.321 208.054 244.30 182.924

Table 2 : Low stiffness spring k = 800 N/m and 400 N/m

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11. DISCUSSION

Different spring between 400 and 800

Used 3 encoders with spring in front of 400 and at the back 800, attach damper at

encoder 3.

At the open loop step graph, we can see different of time between with load and

without load, which is with load the result we had , the motion stopped at 2.7 second

and without load , it is stopped at 1 second.

Stiffness for result 5668.83 n/m.

Different spring between 400 and 800.

q

Used of 3 encoder with spring in front of 400 and at the back 800 N/m.

Without load the time we had is 2.6 second, without load 4.6 second.

Stiffness = 182.443 n/m

Damper

Encoder 1 Encoder 2 Encoder 3

Encoder 1 Encoder 2 Encoder 3

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Different spring between 800 and 400 with damper.

3 encoder , connected 800 spring at infront and 400 spring at back and attach

damper.

With load = 2.7 second , without load 1.3 second.

Stiffness = 182.924 n/m.

Different spring between 800 and 400.

3 encoder , connected 800 spring at infront and 400 spring at back.

With load = 5.1 second , and without loud 2.7 second.

Stiffness = 184.421 n/m (encoder 2 ) and stiffness = 208.054 n/m (encoder 3 ).

Encoder 1 Encoder 2 Encoder 3

Encoder 1 Encoder 2 Encoder 3

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

DISCUSSION FOR PREVIOUS EXPERIMENTAL.

Low stiffness spring, k = 400 n/m attach with damper.

Used of 2 encoder with attach 1 spring 400 n/m.

Stiffness = 72.878 n/m.

Damping ratio = with load 0.22 and without load 0.857.

Mass carriage 0.1154 kg.

High stiffness spring, k = 800 n/m attach with damper.

Used of 2 encoder with attach 1 spring 800 n/m.

Stiffness = -691.6937 n/m.

Damping ratio = with load 0.146 and without load 0.0883.

Mass carriage = -25.293kg.

12. CONCLUSION

This experiment was done by combination of 2 springs which is 400N/m and

800N/m on different position .Our group have completely done this experiment on fix

given period of time. By referring the objective, our group members have successfully

achieve the goal of this experiment. We also able find the parameter by the previous

calculation formula.

This proved that, even our group have changed the way to do this experiment

without changing the original theory on this experiment. This experiment also done

by some human error which will affect the overall result for this experiment, such as

the hand speed did not synchronize with the computer speed when press the compute

button.

As the conclusion, the application for the spring in a system must suitable with

the maximum force or loads that have been used. So, that the spring can fully support

the loads and the whole systems without any failures.

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FACULTY OF MECHANICAL AND MANUFACTURING ENGINEERING

13. REFERENCES

1) J. Dart. (1990). Modern Control Engineering. Addison Wesley Publishing.

2) Zainal Anuar. (1989). Asas Kejuruteraan Kawalan. Unit Penerbitan UTM.

3) N.S.Nise. (1994). Control System Engineering 2nd

Edition. The Benjamin

Cummings Publishing Co. Inc.