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CONTROL SYSTEM FOR

ADJUSTABLE HEIGHT

ROSTRUM

KOK CHEN LIONG KEM 09001

SHARIFF MOHAMAD FAIRUZ KEM 090051PARISA AKHTARI ZAVAREH KEM 08070

IBRAHIM MOHD GHAZALI KEM

MOHD SABREE ABDULLAH KEM

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Introduction

A rostrum [noun] is; 1. any platform, stage, or dais on which

public speakers stand to address an

audience 2. a platform or dais in front of an

orchestra on which the conductor stands.It has been used by speakers to convey

messages and to address to a crowd. It isstill used and continuously upgraded tokeep up with the need of the market.

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Objective

To design a controllerthat meets the desired

performance Ts, Tp,

%OS. Require the usage of:

a. MATLAB

b. Simulink and;c. Control System

Toolbox

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Literature Review

To explain the block diagram, each block contains:

Potentiometer, as to control the voltage difference and work as a switch

Voltage amplifier, work to increase the difference of the voltage

Motor, in this case we use DC motor

Sensors, linear displacement.

Gear (rack and pinion)

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Modelling

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Schematic Diagram

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Generate Formula

+ + = ()

()

()=

+

+

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= +

+

= + +

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where,

()()

=

+1

+

= +

+ (

)

= + + (

)

Thus, we substitute to the main equation

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Constant ValueConstant Value

Constant value for angular displacement

potentiometer, 2.549 V/radConstant value for linear displacement

potentiometer, 2.549 V/cm

Constant value for the voltage amplifier,

15

Inertia Load (kg/m3) 500Radius Gear and Pinion, r (m) 0.02

Damping constant load, Da 200Damping constant rostrum, DL 30

Number of teeth for the first gear, N1 16Number of teeth for the second gear,N2 15

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Motor

Item ValueRated Voltage, Ea (V) 38

Rated Output Torque,Tm(Nm)

3.2

Torque Constant, Kt(Nm/A)

2.92

BEMF Constant, Kb

(V.s/rad)0.3

Armature Inertia (kgm2) 21.6 x 10-3Armature Damping

(Nms/rad)0.3342

Armature Resistance ()

2.7

The motor that we use is RH 14D 6002 DC Servo Motor.

Below is the constant value of the motor.

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Thus, we get the equation for the motor,

= 4.1762( + 3.1261)

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=.

+ . + .

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Step response

%OS=0.7%

TS=2.24S

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Bode diagram

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Pole/Zero Map

Presents the zero and poles Find the stability

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Design of compensator

Compensator design by SISOTool

Compensator design manually

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Simulink

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SISO Design

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Manually

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Simulation with Compensator 1 (fromSISOTool)

The simulation result is shown in the step inputis applied at t=1s and steady state is achieved atabout t=4s, which the settling time = 2.5s (nearerto our desired settling time). The percentovershoot is negligible.

Simulation with Compensator 2 (from manualcalculation)

The simulation result is shown in the step input

is applied at t=1s and steady state is achieved atabout t=7s, which the settling time = 5.5s andpercent overshoot is negligible.

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Chapter 4

Design

Natural frequency and damping ratio are acquired

from the system

Acquired root is -1.5630+0.989j and -1.5630-0.989j

-Settling time =2.24s

-%OS =0.699%

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Compared with desired

performance

Root is -3.9298j+20.576j and -3.9298-

20.576j

%OS =0.5%

Settling time =1 second

For every increment of 6cm in height

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Root Locus Testing

Desired root is being tested whether itis on the root locus.

Results show that the desired root isnot on the root locus , angles formed

are not(2k+1)180 degree .

Thus a compensator has to be used.

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Root Locus testing

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Lead Compensator

Lead compensator to reduce the settlingtime and %OS

Arbitrarily set compensated zero=-2.5

Find the angle of deficiency=angle ofcompensated pole

Lead compensator with compensated zero

and pole located at -2.5 and -7.2161 Since p>z, the compensation is accepted

and verified in Simulink

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Compensated system

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THANK YOU