principle of control

8/11/2019 Principle of control

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Mahmood Mustafa Control Engineering ID : 2489429 Supervised By : Dr !ari" Sattar

#eport !itle : Investigation of PID control of a digital servo system

$im: The aim is to move the inertial load to a given position in the shortest possible time

with a smooth transient response.

% & $'stra(t The aim of this experiment was to investigate a standard method of control known as PID

(proportional, integral, derivative) on a digital servo system. The effect of variation of PID gains, sampling

interval, and motor p lse width mod lation are f lly investigated with vario s combination of P, PD, PID

methods. These methods are applied to position and speed control exercises. The experiment is to learn

position control with a proportional controller, to learn the simple speed control with a low gain and

steady inp t demand of ! rad"s, to learn the effect of sampling interval, to learn the position control with a

proportional, derivative control. #nd also to learn the tracking position control system and elimination of

tracking error with integral control. To learn the effect of sampling period T on system stability and

acc racy.

2 & Introdu(tion

Digital $ervo %ontrol of a system can be sed in many applications, position control systems are an

important component of many ind strial prod cts. &xamples are fo nd in disk drives, a tomotive prod cts,

robotics, process control and many others. $ome of these applications and the basics of servo control system

have been described. The aim of this digital control of a servo system is to describe in simple terms,

how digital servos are implemented sing a servo controller circ it control system implementation.

The first thing of the experiment a digital servo mechanism for position control of a servo motor sing digital

sensors and direct digital control system sing digital optical position sensors with a special 'ray coded disk

to meas re shaft position and encoder to convert the 'ray code to a binary sing a decoder. The decoder

o tp t to fed directly to an adder or s mmer with the ang lar position digitally coded by detecting the &D s

different colo red lights to know the servo motor position #ef)%*

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The control signal to a servo is a p lse width a repetition fre+ ency of nominally - /. The width of the

p lse determines the position of the servo motors o tp t. It also draws power proportional to the mechanical

load. The amo nt of power applied to the motor is proportional to the distance it needs to travel. $o, if the

shaft needs to t rn a large distance, the motor will r n at f ll speed. If it needs to t rn only a small amo nt,

the motor will r n at a slower speed. This is called proportional control.

This experiment covers the basic principles of the servo motor control system, incl ding both the physics of

the servos, the key feat res of servo motor in partic lar applications of control, the basic characteristics and

the theory and the basic control system was disc ssed in the report.

The controller board designed to be able to control the servo motor. This report will present in detail the aims

and ob0ectives of the experiment and how they were achieved and provide a detailed log progress thro gh

the experiment life.

# $ervo is a small device that has an o tp t shaft. This shaft can be positioned to specific ang lar positions

by sending the servo a coded signal. #s long as the coded signal exists on the inp t line, the servo will

maintain the ang lar position of the shaft. #s the coded signal changes, the ang lar position of the shaft

changes. In practice, servos are sed in radio controlled airplanes to position control s rfaces like the

elevators and r dders. They are also sed in radio controlled cars, p ppets, and of co rse, robots. In a D%

motor, the load affects the speed and c rrent draw #ef)%*

To process the experiment first we have to get the idea of the servo motors and a more practical sol tionfrom the Internet and engineering books to nderstand and eval ate the res lt and finish the experiment. 1ehave to do several exercises.2asic position control systems consist of a servo motor, position sensor and controller is shown below in thefig re *.

Position

3eference

.igure % : ,osition Control System

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$ensor

%ontroller 5otor o"p

6




This investigation is a st dy of a servo system D$* 7 (as shown in fig re 4) that comprises a dc motor,

gear box and load inertia. The aim is to move the inertial load to a given position in the shortest possible

time with a smooth transient response. I will investigate one of the most commonly employed control

systems to do this. This is the three term PID (proportional, integral, and derivative) controller. The

controller is implemented on a microcomp ter and relies on its control action being taken at discrete

intervals of time. The o tp t (position or velocity) of the analog e system is converted to digital word

and passed to the comp ter at a periodic sampling time. The PID control law is implemented in

the microcomp ter and a control signal applied to the servo system at almost the same time. Time histories

of any signal in the microcomp ters memory can be loaded (8ia 3$ 474 serial comm nication) and viewedon a fo r channel oscilloscope program implemented on the P%, a hard copy of the oscilloscope traces can

be obtained on the attached printer. Incremented encoder this mod le gives p lsed signals corresponding to

the ang lar position, velocity and acceleration of the o tp t shaft (load) of the servomechanism.

9 adrat re decoder converts signals from the shaft encoder to position, velocity and acceleration

meas rements.

.igure 2 : Servo system DS%-/





#nalog e o tp t nit this mod le applies the control signal comp ted by the controller to the power

amplifier on the analog e servo system. #lso, any signal in the servo system can be o tp t via a D"#

converter and viewed on an oscilloscope or a chart recorder.

#nalog e o tp t nit this mod le applies the control signal comp ted by the controller to the power

amplifier on the analog e servo system. #lso, any signal in the servo system can be o tp t via a D"#

converter and viewed on an oscilloscope or a chart recorder.

/ & 0'1e(tives

To investigate a standard method of control known as PID (Proportional, Integral, Derivative) on a Digital

$ervo $ystem. The effect of variation of PID gains, sampling interval, and motor p lse width 5od lations

are f lly investigated with vario s combinations of P, PD, and PID methods. These methods are applied to

position and speed control exercises.

4 & Des(ription

# simple servo mechanism system consists of a D% motor and a controller circ it. # servo motor is basically

an electro:mechanical device, which converts electrical p lses into discrete mechanical movements. The

shaft or spindle of a servo motor rotates in discrete step increments when electrical command p lses are

applied to it in the proper se+ ence. The motor rotation has several direct relationships to these applied inp t

p lses. The se+ ence of the applied p lses is directly related to the direction of motor shafts rotation. The

motor shafts rotation is directly related to the width (or d ration) of the inp t p lses and the length of

rotation is directly related to the n mber of inp t p lses applied #ef)2*

- & !e(hni(al Ba( ground $ervo motors are best well:known for their + ick acceleration and deceleration capability which is made

possible by delivering high:peak tor+ e in con0 nction with a high tor+ e:to:inertia ratio. $ervo motors

may be categori/ed by criteria of magnet type (ind ction or permanent), mechanical technology (rotary or

linear) and electrical technology. # standard servo is a motori/ed device that moves its act ator to a position

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specified by a controlling electronic signal. Inside is a complete servo system, a control circ itry and drive

circ it. $everal si/es of servos exist that range from very fast to very powerf l.

# $ervo is a small device that has an o tp t shaft. This shaft can be positioned to specific ang lar positions

by sending the servo a coded signal. #s long as the coded signal exists on the inp t line, the servo will

maintain the ang lar position of the shaft. #s the coded signal changes, the ang lar position of the shaft

changes. The o tp t shaft of the servo is capable of traveling somewhere aro nd *!- degrees. <s ally, it is

somewhere in the 4*- degree range, b t it varies by man fact rer. # normal servo is sed to control an

ang lar motion of between - and *!- degrees. # normal servo is mechanically not capable of t rning any

farther d e to a mechanical stop b ilt on to the main o tp t gear.

3 & $ppli(ations of the Servo Motor

The se of servo systems is extensive in ind stry, with machine tools forming a significant area of

application. In addition to simple motor control, servos allow the precise movement and control of

machinery in pre:determined paths. &xamples incl de aircraft control, robotic arm movement, disk drivers,

a tomotive prod cts, process control and many others #ef )%*

$ervo motors are basically geared down D% motors with positional feedback control, allowing for acc rate

positioning of the rotor with a range of =- degrees. They can also be modified to allow for contin o s

rotation.

# servo control system is one of the most important sed forms of control system. #ny machine or piece of

e+ ipment that has rotating parts will contain one or more servo control systems. The 0ob of the control

system incl des >

8arying the speed of a motor and load according to an externally set programme of val es.

This is called set point ( reference) tracking.

5aintaining the speed of a motor within certain limits, even when the load on the o tp t ofthe motor may vary. This is called reg lation.

? r daily lives depend on servo controllers. #nywhere that there is an electric motor there will be a servo

control system to control it. $ervo control is very important for man fact ring ind stry wo ld cease witho t

servo systems beca se factory prod ction lines co ld not be controlled, transportation wo ld halt beca se





electric traction nits wo ld fail, comp ters wo ld cease beca se disk drivers wo ld not work properly and

comm nications networks wo ld fail beca se network servers se hard disk drivers #ef )%*

3 % Servo Motor Controlling Me(hanism

The ma0ority of servos re+ ire a power s pply between ;.! and @ volts. The higher the voltage, the faster the

servo will move and the more tor+ e it will have. #ll servos have three connections. ?ne is red is a positive

voltage.

The second is bl e or black it is the gro nd or negative. The third one is yellow or white which is the

controlling signal. The servo is controlled by a series of p lses and the length of the p lse indicates which

position to take. The basic motion control system incl des >

• 5otion controller> : the motion controller is the brain of the motion control system.It provides the instr ctions that the servo motor exec tes.

• $ervo motor> : the servo motor is the m scle of the motion control system, converting the

electrical power from the servo drive into the mechanical power that moves the machine

$ervo motor controllers m st be able to make a n mber of decisions and provide a means to

receive signals from external sensors and controls in the system and send signals to host

controllers that may interface with the servo system #ef )/*

3 2 ,ID Control SystemsThe servo motor sed in the pro0ect the amo nt of power applied to it is proportional to the mechanical load,

this is known as proportional control. The integrator amplifier sed the integral relationship between the

inp t and o tp t voltages arise as the res lt of the derivative relationship between voltage across and c rrent

thro gh a capacitor so the PID A %ontroller is the most widely sed control strategy in servos.

hat is a ,ID Controller 5

PID stands for Proportional:Integral:Derivative. This is a type of feedback controller whose o tp t, a control

variable (%8), is generally based on the error (e) between some ser:defined set point ($P) and somemeas red process variable (P8). &ach element of the PID controller refers to a partic lar action taken on theerror> #ef )4*

• Proportional> error m ltiplied by a gain, B p. This is an ad0 stable amplifier. In many systemsB p is responsible for process stability> too low and the P8 can drift awayC too high and the P8can oscillate.

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• Integral> the integral of error m ltiplied by a gain, B i. In many systems B i is responsible fordriving error to /ero, b t to set B i too high is to invite oscillation or instability or integratorwind p or act ator sat ration.

• Derivative> the rate of change of error m ltiplied by a gain, B d . In many systems B d isresponsible for system response> too high and the P8 will oscillateC too low and the P8 will

respond sl ggishly. The designer sho ld also note that derivative action amplifies any noise in the errorsignal.

T ning of a PID involves the ad0 stment of B p, B i, and B d to achieve some ser:defined optimal characterof system response.

a) Proportional Control

Proportional control is a p re gain ad0 stment acting on the error signal to provide the driving inp t to the

process. The P term in the PID controller is sed to ad0 st the speed of the system.

b) Integral Control

Integral control is implemented thro gh the introd ction of an integrator. Integral control is sed to

provide the re+ ired acc racy for the control system.

c) Derivative Control

Derivative action is normally introd ced to increase the damping ratio of the system. The derivative term

also amplifies the existing noise, which can ca se problems incl ding instability #ef )/*

The controller generates step p lses and direction signals for the driver. #nalog e principles are presented in

progression from operational amplifier characteristics thro gh position and velocity feedback. It is a

contin o s feedback loop that keeps the process flowing normally by taking corrective action whenever

there is any deviation from the desired val e (set point) of the process variable rate. The Integral term is most

effective at low fre+ encies, the Proportional term at moderate fre+ encies, and the Differential term at

higher fre+ encies. These fre+ encies are relative to the bandwidth of the servo or process.

The primary benefit from the integral term is the red ction of steady state error, while the differential term

helps improve the responsiveness and stability. In order to disc ss the effects of PID, it is necessary to lookat a basic closed loop servo and the e+ ation for its closed loop response as shown below.

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.igure / : Closed 6oop Servo

The open loop (#) and closed loop #" (* 6#) responses of the servo in relation to fre+ ency. #" (* 6#) is

approximately e+ al to * when # is large and to # when # is small.

3 / 6imitations of ,ID Control

1hile PID controllers are applicable to many control problems, they can perform poorly in some applications.

PID controllers, when sed alone, can give poor performance when the PID loop gains m st be red ced

so that the control system does not overshoot, oscillate or h nt abo t the control setpoint val e.

The control system performance can be improved by combining the feedback (or closed:loop) control of

a PID controller with feed:forward (or open:loop) control. Bnowledge abo t the system (s ch as the desiredacceleration and inertia) can be fed forward and combined with the PID o tp t to improve the overall

system performance. The feed:forward val e alone can often provide the ma0or portion of the controller

o tp t. The PID controller can then be sed primarily to respond to whatever difference or error remains

between the setpoint ($P) and the act al val e of the process variable (P8). $ince the feed:forward

o tp t is not affected by the process feedback, it can never ca se the control system to oscillate, th s

improving the system response and stability #ef )4* For example, in most motion control systems, in order to

accelerate a mechanical load nder control, more force or tor+ e is re+ ired from the prime mover, motor, or

act ator. If a velocity loop PID controller is being sed to control the speed of the load and command the

force or tor+ e being applied by the prime mover, then it is beneficial to take the instantaneo s acceleration

desired for the load, scale that val e appropriately and add it to the o tp t of the PID velocity loop controller.

This means that whenever the load is being accelerated or decelerated, a proportional amo nt of force is

commanded from the prime mover regardless of the feedback val e. The PID loop in this sit ation ses the

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http://en.wikipedia.org/wiki/Feedback

http://en.wikipedia.org/wiki/Feed-forward

http://en.wikipedia.org/wiki/Feedback

http://en.wikipedia.org/wiki/Feed-forward




feedback information to affect any increase or decrease of the combined o tp t in order to red ce the

remaining difference between the process setpoint and the feedback val e. 1orking together, the combined

open:loop feed:forward controller and closed:loop PID controller can provide a more responsive, stable and

reliable control system.

3 4 6oop ,arameter of ,ID Control

Proportional 'ain (Bp)GProportional gain is the system stiffness. It determines the contrib tion of restoring

force directly proportional to the position error. # high proportional gain gives a stiff responsive system b t

can ca se instability from overshooting and oscillation.

Derivative 'ain (Bd)GDerivative gain is the damping effect on the system. It determines the contrib tion

of restoring force proportional to the rate of change (derivative) of position error. This force is m ch like

visco s damping in a damped spring and mass mechanical system.

Increasing derivative gain red ces oscillation at the commanded position, or it rings beca se of high

acceleration.

Integral 'ain (Bi)GIntegral gain is the static tor+ e load on the system. It determines the contrib tion of

restoring force that increases with time, ens ring that the static position error in the servo loop is forced to -.

This restoring force works against constant tor+ e loads to help achieve /ero position error when an axis is

stopped. Integral gain improves positional acc racy. igh static tor+ e loads need integral gains to minimi/e

position error when stopped #ef )-*

!ransfer .un(tion of a ,ID Controller

2y looking at the general transfer f nction of a PID:controller, the three terms can be recogni/ed

as follows>

⋅+⋅

+= S T S T

K S G d i

pC *

*)( HHHH..

2y rearranging the above form la, a more conventional transfer f nction form can be obtained>

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&+ ation @.;.a




++⋅⋅=

⋅

S T

S T S T T K S G

i

id i pC

)*()(

4

HHHH....

1here >

K p > Proportional gain

T i > Integral time constant

T d > Derivative time constant

$ ch a controller has three different ad0 stments ( K p, T i, T d), which interact with each other #ef )/*

7 & E perimental ,ro(edure + #esults analysis

7 % E er(ise ) % * : ,osition Control ith a proportional (ontroller

,ro(edure

$witch on the system. The Display will read D$%* 7 T J *- m$ . Then I P t the controller on:line so that

all controller config rations and parameters can be set by software on the P% by pressing T&35 then

&KT&3 on the keypad. Then I have $elected $&38? from the men and then $&T <P $&38?. Then the

following will be set according to the experimental proced re>T J *- m$ J -a ex

yJP?$K L$elect the position variable from + adrat re decoder as the feedback re+ iredM

kJ@- ex L8al e of proportional gainM

kiJ-- ex LIntegral gain is set to /eroM

kvJ-- ex LDerivative gain is set to /eroM

Kext thing to do is to select a Step inp t as the type of digital inp t Dtype from the signal generator that theo tp t is re+ ired to follow.

d*J---- ex L$et the signal generator to provide a step waveform. $et as fo r

d4J4--- ex hexadecimal digit n mbers. %hanges from - volts to 4. 8oltsM

dcycJ@;-- ex LThe cycle time is dcyc x - ms J 7.4 sM

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&+ ation @.;.b




In order to activate the control and the internal demand generator select Run (this takes the o tp t position to

d*) followed by Input On/Off (this enables the step demand inp t from d* to d4 and back to d* in a cycle

time given by dcyc ). The motor will drive alternately forward and reverse between two positions. ?bserve

the effect of different val es of proportional control on the step response.

#esultsThe following res lts were obtained as shown in figure 4 when the servo has been set p.

.igure 4 : The gain B J 4- in hex (74 in decimal) with proportional (P) controller only.

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%an yo make the response nstable at some val e of kN

Oes the response at the moment is nstable as shown in figure - and the val e of 'ain B is FF in hex J

4 decimal.

.igure - : The val e of 'ain B is FF in hex J4 decimal, with P controller only

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.igure 3 : The gain is set BJ4- h, The Derivative controller is set to Bv J -@ h, so the

system is controlled by Proportional and Derivative.

) See $ppendi $ for more results o'tained for this e er(ise *

7 2 E er(ise ) 2 * : $ simple speed (ontrol ith a lo gain and a steady input demand of 8 rad s

,ro(edure

The ?b0ective of this exercise was to learn that the stability and dynamic response of a digital control system

are affected by the sampling interval as well as by the loop gain. Then the following will be set according to

the experimental proced re>

T J *@msJ*- ex

yJ8elkJ-;

kiJ--

kvJ--

adc> off

dtype> step

d* J 4--- (e+ ivalent to ! rad"s)

d4 J 4;-- (e+ ivalent to = rad"s)

dcyc J @;--

mJ8el

pwm cycle *- ms

RUN will r n a simple speed control with a low gain k J -; and a steady inp t demand of ! rad"s.

# step demand of = rad"s will not commence ntil Input On/Off is pressed.

Kow the val e of k has to be increases by nit steps, noting the meas red speed, ntil the control becomes

nstable, and then I have to se the oscilloscope program to detect instability. The val e of k after which

instability 0 st occ rs is easily fo nd by in0ecting a small step dist rbance after each gain increment. Kote

the critical val e of k .

#esults

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The following res lts were obtained as shown in figure 7 when I have set p the servo.

.igure 7 : The gain BJ -;h, the system is controlled by Proportional only.

The act al speed does not close to the demand val e of kJ-;, beca se the gain which is p shing the demand

val e is too low kJ-;.

1hen the gain has been increased kJ4 the act al speed come closer to the demand val e as shown

in figure 8

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.igure 8 : The gain BJ 4 h, this system is controlled by Proportional only.

) See $ppendi B for more results o'tained for this e er(ise *

1hen the gain has increases kJ;-, then I have p t in some integral gain BiJ- h the act al speed is closer

then ever to the demand val e as shown in figure 9 . #nd the error position is /ero.





.igure 9 : The gain kJ;-h and the integral gain BiJ- h , this system is controlled by

proportional and integral.

Then I have to increase the val e of k by nit steps, noting the meas red speed, ntil the control becomes

nstable, then I have to se the oscilloscope program to detect instability. The val e of B after which

instability 0 st occ rs is easily fo nd by in0ecting a small step dist rbance after each gain increment.

I have noted the critical val e of k . Then the res lt in figure %& was obtained.

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.igure%& : The gain BJ4-h, the system is controlled by Proportional only.

7 / E er(ise ) / * : Effe(t of sampling interval

,ro(edure

The effect of sampling interval with B set to some val e below the critical gainC alter the val e of T from

l@ms to 74ms

Is the system more or less stableN

%ontin e increasing B ntil complete instability res lts. Then I have to Kote the val e of B.

Then the following will be set according to the experimental proced re

T J ;ms

B J a val e below the critical val e

P15 cycle J ;ms

L5akes the p lse width mod lation cycle consistent with the shorter sample interval T M

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3epeat the stability test, varying k pwards ntil instability sets in. Find the critical val e of k and note the

indicated speed for an inp t demand of 4--- hex.

To see the effect of sampling interval with B set to some val e below the critical gain (kJ- h),

I have set the val e of time period T (TJ4-h).

#esults

Then the following res lt was obtained as shown in figure %%. The system was less stable.

.igure%% : The gain BJ- h and with a time period of T J4-h

Then I have contin ed increasing gain B ntil it becomes a complete instability and the res lt was

obtained is shown in figure%2

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.igure%2 : The gain BJ* h and with a time period of T J4- h the system is complete instability.

) See $ppendi C for more results o'tained for this e er(ise *

7 4 E er(ise ) 4 * : ,ID (ontrol

,ro(edure

1e were re+ ired to carry o t an investigation of Proportional, Integral and Derivative (PID) %ontrol

5ethod. PID control is one of the simplest and most widespread types of control. The reason for its

Pop larity is that this method does not re+ ire detailed knowledge of the dynamics of the plant which is to be controlled. # good mathematical model of the controlled system is s ally diffic lt to obtain d e to

ncertainty abo t effects s ch as friction, nonlinearity, and immeas rable dist rbances s ch as random noise.

The PID %ontroller allows an operator to simply t ne three gains on:line ntil s itable control is obtained.

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!he ,roportional; Integral and Derivative <ains are tuned in order to o'tain the three (ontrol o'1e(tives of :

*) 3apid response (variation of ndamped nat ral fre+ ency) and red ction of steady state error by

t ning proportional gain k.

4) Introd ction of damping into the closed:loop system with Derivative gain in order to prevent

oscillation of the system o tp t (controlled variable) abo t the setpoint.

7) 3ed ction of the error to /ero when tracking changing reference inp ts s ch as ramps by t ning

Integral gain.

# schematic of the digital servo system is shown in figure %/

.igure %/ : # schematic of the digital servo system

The feedback signal can be selected to be either ang lar position or velocity. This is compared with a

software generated set point signal v which can be selected to be a step inp t, a ramp inp t or a programmed

tra0ectory which yo wo ld like the o tp t to follow. #n external analog e setpoint can be converted to a

digital signal and added to the software generated signal v b t yo will not do this.The ob0ective of the control system is to red ce the error e between the reference variable v and the system

o tp t y as rapidly as possible .The control system can be patched p easily in software on the P% by choosing $&38? $&T<P from the

men .

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The control signal for the analog e PID controller is given by the e+ ation as follows >

1here J control o tp t

e J v:y error

v J demand"setpoint

y J o tp t (position"velocity or both)

Bp J proportional gain

Bi J integral gain

Bv J derivative gain

Oo will be implementing a digital controller.

7 4 ) i * : ,osition (ontrol ith a proportional (ontroller

,ro(edureet the inp t reference variable v be a step inp t which changes from a position given by d* J ---- hex to

d4 J 4--- hex with a cycle time of dcyc J @;-- hex (which in real time is e+ al to dcyc x - m$) is e+ al to

7.4 $. $et p the system to feedback the position variable i.e. y JP?$K.

et the derivative gain kv and the Integral gain ki be /ero. $et the initial val e of the proportional gain k to

4- hex. $et the sampling period T J -# hex or *- m$ and the P15 cycle J *- m$. The p lse width

mod lation cycle time m st always be the same as the sampling period T. Display the demanded signal v

and the position signal by sing the men $&T <P DI$P #O. Then increase the gain k and notice the effect

on system rise time and overshoot. The aim is to obtain a stable response with the smallest possible rise time.

#esults

1hen I set the initial val e of the proportional gain k to 4- hex. Then the derivative gain kv and

the integral gain ki I have also set to /ero, then the following res lt was obtained as shown in figure %4 .


&+ ation E.;.a




.igure %4 : The gain BJ4- h, with Proportional %ontroller only.

1hen I have increased the gain k and I have to notice the effect on system rise time and overshoot. Then

the following res lt was obtained as shown in figure %-

.igure %- > The gain BJ7- h , with Proportional %ontroller only.





7 4 ) ii * : ,osition (ontrol ith a proportional and derivative ),D* (ontroller

,ro(edure1ith kv and ki /ero increase k to give stable response with the smallest possible rise time. Then increase the

derivative gain kv in small increments ntil all the overshoot is eliminated. The aim is to obtain a fast and

critically damped response.

#esults

Then the following res lt in figure %3 was obtained.

.igure%3 : The gain BJ*-h , with derivative gain k8J- h , this system is %ontrolled by

proportional and derivative.





7 4 ) iii * : $ tra( ing position (ontrol system and elimination of tra( ing

error ith integral (ontrol

,ro(edure

I have to investigate the ability of the proportional controller to track a constantly changing demanded inp t.

This can be done by selecting the demanded inp t to be a 3#5P with the same val es of D*, D4 and cycle

time as in (i). $tart with a P controller only and see if the o tp t signal y ever catches p with the demand v.

If not, then introd ce integral action ntil the error between the two is /ero.

#esults

Then the following res lts were obtained as shown below.

.igure%7 : The gain BJ7- h , with Dtype ramp, this system is %ontrolled by Proportional.

Kow the following res lts were obtained when we have introd ced the derivative gain and integral gain.

Chemi(al + ,ro(ess Engineering %& &- 2&&84;




.igure%8 : The gain (BJ7-h), with derivative gain (k8J- h), this system is controlled

by Proportional and Derivative.





.igure%9 : The gain BJ7 h , with derivative gain k8J- h , with integral gain kiJ- h this system

is controlled by Proportional, Derivative and Integral (PID).

E.; ) iv * : Speed (ontrol ith an input demand of v = 8 rad s

,ro(edure

I have to investigate the speed control. The PID %ontroller can be sed to control the speed of the inertial

load (the position disc). $et the sampling period to be *@ ms (*- hex). %ompare a demanded speed specified

by v with the meas red speed. This of co rse means that the feedback is selected to be y J 8el. The speed

can be changed from a val e given by dl J 4--- hex (! rad"s) to d4 J 4;-- hex (= rad"s) with a cycle time of

dcyc J@;-- hex (7.4 $). The inp t can either be a step or a ramp between the two levels dl and d4. The

control action investigated can be P, PD or PID.

#esults

The following res lts were obtained >

.igure 2& : The gain BJ* h, with a time period of TJ*-h , this system is controlled by Proportional

only. Kow the following res lts were obtained when we have introd ced the derivative gain and

integral gain.

Chemi(al + ,ro(ess Engineering %& &- 2&&84@




.igure 2% : The gain BJ*@h, with a time period of TJ*-h, with derivative gain k8J- h,

this system is controlled by Proportional and Derivative.

) See $ppendi D for more results o'tained for this e er(ise *

Chemi(al + ,ro(ess Engineering %& &- 2&&84E




.igure 22 : The gain BJ*@ h , with a time period of TJ*-h , with derivative gain k8J- h, and

with integral gain kiJ- h this system is controlled by Proportional, Derivative and Integral.

7 4 ) v * : !he effe(t of sampling period ! on system sta'ility and a((ura(y

,ro(edure

I have to set p a speed control system exactly as in (iv) with an inp t demand of 4--- hex and proportional

action only. I also have to Increase the gain k pwards ntil instability res lts. The val e of gain k 0 st below

the val e which ca ses instability is termed the critical gain. The critical gain can be more readily fo nd by

toggling the setpoint between 4--- hex and 4;-- hex. This change in inp t sho ld drive the system into

instability. Kow, with the gain k set at the critical val e, change the sampling period from *@ m$ (*- ex) to

74 m$ (4- ex).

#esults

The following res lts were obtained >

.igure 2/ : The gain (BJ*@h), with a time period of (TJ*-h), with an inp t demand of (D*J4---h),

this system is controlled by Proportional only . Kow is when we increase the gain B and Time

period T pwards ntil instability res lts.

Chemi(al + ,ro(ess Engineering %& &- 2&&84!




The following res lt was obtained as shown in figure 24

.igure 24 : The gain (BJ4 h), with a time period of (TJ4-h), with an inp t demand of (D*J4---h),

this system is controlled by Proportional only

Chemi(al + ,ro(ess Engineering %& &- 2&&84=




8 & #esults $nalysis + Dis(ussion#t the beginning of exercise * I have tested the motor sing proportional and derivative control on the

nit step response. I have tested the motor s ccessf lly and I have driven the motor alternatively

forward and reverse between two positions with o t the motor over shoot and oscillate the final positions.

In exercise 4 I have investigated that a simple speed control with a low gain kJ-;, steady inp t demand

of ! rad"s and step demand of = rad"s. I have tested and r n s ccessf lly a simple speed control with

a low gain, steady inp t demand and step demand to see if the act al speed come closer to the demand

val es. 1hen I have increased the gain kJ;-, then I have p t in some integral gain (BiJ- h), then the

act al speed is closer then ever to the demand val es. In exercise 7 I have investigated that the effect

of sampling interval. To see the effect of sampling interval with B set to some val e below the critical

gain (kJ- h) and I have set the val e of time period T (TJ4-h). Then the system becomes nstable.

Then I have contin ed increasing gain (kJ*Eh) ntil the system it becomes a completely nstable. The first

part of exercise ; is position control with a proportional controller in order to obtain a stable response with

the smallest possible rise time. 1hen I set the initial val e of the proportional gain k to 4- hex. Then

the system has large overshoot. 1hen I have increased the gain k and then I have introd ced derivative

and integral controller, then all the overshoot is eliminated. The second part of exercise ; is a tracking

position control system and elimination of tracking error with integral control. I have started with a

P controller, and then I have introd ced integral action ntil the error between the two it becomes /ero .

The second third part of exercise ; is a $peed control with an inp t demand of v J ! rad"s. the inp t demand

can either be a step or a ramp between the two levels dl and d4. The control action was investigated and

we have sed P, PD and PID. The last part of exercise ; is to see the effect of sampling period T

on system stability and acc racy. I have set p a speed control system exactly as in (iv) with an inp t

Chemi(al + ,ro(ess Engineering %& &- 2&&87-




demand of 4--- hex and proportional action only. Then I have also increased the gain B pwards ntil the

system becomes nstable.

Don t forget appendices Oa mahmood

#eferen(es

Bi'liography

Q7R $heffield hallam niversity. Q?nlineR #vailable from>

http>""www.sh .ac. k"schools"eng"teaching"rw"pidt torial.htmSPage 4-end . Q#ccessed ! #pril 4--ER.

3ef ( 4 ) www.freepatentsonline.com";-= * E.html


http://www.shu.ac.uk/schools/eng/teaching/rw/pidtutorial.htm#Page%20end

http://www.shu.ac.uk/schools/eng/teaching/rw/pidtutorial.htm#Page%20end




Q7R Packaging digest. Q?nlineR #vailable from> http>""www.packagingdigest.com"articles"4--7-!"==.php .

Q#ccessed *- #pril 4--ER.

#ef )4* t(n1 edu >rgraham ,ID?tuning html

#ef )- : Innovative a tomation control. Q?nlineR #vailable form> http>""www.ctc:ontrol.com"c stomer"elearning"servot t"pid.asp

http://www.packagingdigest.com/articles/200308/99.php


http://www.ctc-control.com/customer/elearning/servotut/pid.asp






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