study and simulation of the predictive …

STUDY AND SIMULATION OF THE PREDICTIVE

PROPORTIONAL INTEGRAL CONTROLLER IN COMPARISON

WITH PROPORTIONAL INTEGRAL DERIVATIVE

CONTROLLERS FOR A TWO-ZONE HEATER SYSTEM

by

DEEPA THOMAS MANNATH, B.E.

A THESIS

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty

of Texas Tech University in Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

ELECTRICAL ENGINEERING

Approved

December, 2002

ACKNOWLEDGEMENTS

The compilation of this thesis required many consultations and rigorous,

methodical application. Dr. HenrykTemkin and Dr. Siqing Lu of Applied Materials, to

whom I express my sincerest appreciation for their patient support and invaluable

guidance, graciously accepted these. It was a pleasure to work under them and my

experience holds me in good stead for the future.

Deep appreciation is also extended to Yehuda Demayo, my manager at Applied

Materials, who gave me the opportunity to work on this project and has been a

source of constant support and inspiration since. His insight has been valuable and

has gone a long way into making this project a successful one.

I am grateful to Dr. Mark Holtz and Dr. Tim Dallas for their detailed insights of this

thesis.

Many thanks to Ms. Barbi Dickensheet for reviewing this document when it was

in its incipient stages. Such patience is indeed rare and is much appreciated. Finally,

I would like to thank all of my peers and colleagues in the Department of Electrical

Engineering at Texas Tech University, and in the CPI Division at Applied Materials

for their support and advice.

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

ABSTRACT vi

LIST OF TABLES vii

LIST OF FIGURES viii

CHAPTER

1. INTRODUCTION 1

1.1 PI D control 1

1.2 Introduction to Proportional-lntegral-Derivative (PID)

control algorithm 2

1.2.1 Proportional control 2

1.2.2 Overshoot and temperature cycling 2

1.2.3 Eliminating offset 3

1.2.4 Integral action (sometimes called automatic reset) 3

1.2.5 Definition of integral time 4

1.2.6 Integral windup 5

1.2.7 Derivative action (sometimes called rate action) 5

1.2.8 Definition of derivative time 6

1.3 Variations of the PID algorithm 6

1.4 PID control with Feedforward: A special case of PID6 10

1.5 Thesis Outline 10

2. DESCRIPTION OF THE SYSTEM AND THE PROBLEM 12

2.1 Description of the System 12

2.1.1 The SiNgen Centura 300 process chamber 13

2.1.2 Dual Zone Heater Assembly 15

2.1.3 Schematic of the control system 17

2.2 Problems with the existing system 18

2.2.1 Variations in inner and outer zone voltages 18

2.2.2 Disturbances due to change in control algorithm 18

2.3 Goals to be achieved by making necessary changes in the control algorithm 18

3. DESCRIPTION OF THE FUNDAMENTALS AND

THEORY OF PPI CONTROL 20

3.1 Model-based Predictive Control 20

3.2 Predictive PI Controller 22

3.3 Specification of Heater Control 25

3.3.1 Phase I: Overshoot Reduction and Bumpless Transfer 25

3.3.1.1 Current Algorithm 25

3.3.2 Phase II: Total Power Control 26


3.3.2.2 Total Power Control Algorithm 28

3.3.3 Phase III: Autotune of PID parameters 29

3.3.3.1 Current Algorithm 29 3.3.3.2 Relationship of PID Parameters in Gain-Type and

Standard Algorithms 30

3.3.3.3 Autotuning Algorithms 31

3.3.4 Phase IV: Replace PID with PPI 33


3.3.4.2 PPI Algorithms 34

4. MODELING OF THE HEATER 36

4.1 Experimental Data 36

4.1.1 Heater Characteristics 36

4.2 Modeling of the Various Blocks 37

4.3 Simulink For Modeling 38

5. SIMULATIONS AND TUNING 40

5.1 Simulations of The Algorithms 40

5.2 Tuning 44

5.2.1 Tuning of PID 44

5.2.2 Tuning PID: An Example 45

5.2.3 Tuning of PPI 46

5.3 Performance Indices 47

5.4 Simulation Results 48

6. CONCLUSIONS 49

LIST OF REFERENCES 50

ABSTRACT

The PID algorithm is the most popular feedback controller used within the

process industries. This is the algorithm that is currently used on a System in the

DSM (Dielectric Systems and Modules) and the CMD (Contact Metal Deposition)

groups at Applied Materials Inc. The current Algorithm which controls the Ceramic

heater in the LPCVD (Low Pressure Chemical Vapor Deposition) and TTN (Titanium

TiNitride) chambers, had problems, which lead to non-uniform heating. After

examining and listing the problems, it has been concluded that the Predictive

Proportional Integral (PPI) mode of control would provide adequate solutions. In this

project we have studied the heater systems, modeled them and carried out

simulations in Simulink. The results of the simulation were then used to place

Software Requests so that necessary software changes in the Control Algorithm

could be made.

LIST OF TABLES

5.1 Controller settings from Gy and Pu 44

5.2 Example of PID Tuning 45

5.3 Tuning PPI 46

5.4 Results 48

VII

LIST OF FIGURES

1.1 Simplified Block Diagram of a Control System 1

1.2 Response of a PI algorithm to a step in error 4

1.3 Control system with a PID Controller 6

1.4 PI D with Feedforward 10

2.1 SiNgen Chambers on Centura 300 Mainframe 12

2.2 The SiNgen Centura 300 process chamber 13

2.3 SiNgen chamber overview 14

2.4 Dual Zone Heater Assembly 16

2.5 Control System Schematic 17

3.1 Model Predictive Controller (MPC) 21

3.2 Model Predictive Controller (MPC) 22

3.3 Predictive PI control 22

3.4 The Unrealizable Controller 23

3.5 The realizable PPI implementation 24

3.6 Current Algorithm 25

3.7 Cun-ent Algorithm in Current mode 27

3.8 Auto tuning 32

4.1 Power Temperature Curve 36

4.2 Inner Zone Resistance versus Voltage Ratio 37

4.3 Outer Zone Resistance versus Voltage Ratio 37

4.4 Output plots of Various Ordered Systems 38

4.5Simulink Model 39

5.1 Simulink Model for PID1 40





VIII


5.7 Simulink Model for PPI 43

5.8 Ziegler Nichols Ultimate Cycle method 44

5.9 Pu From Steady Oscillations 45

5.10 Response of a second order system with PID1 46

5.11 Perfonnance Indices for Controllers 47

CHAPTER 1

INTRODUCTION

1.1 PID control

The PID algorithm is the most popular feedback controller used within the

process industries. It has been successfully used for over 50 years. It is a robust and

easily understood algorithm that can provide excellent control perfonnance despite

the varied dynamic characteristics of process plants. Figure 1.1 shows the simplified

block diagram of a control system.

This section attempts to:

• introduce Proportional-lntegral-Derivative (PID) control algorithm,

• discuss the role of the three modes of the algorithm,

• introduce variations in the algorithm,

• discuss the PID in the light of the 300mm LPCVD heater controller.

Load _

u Y e Kp Kc Yr

1 u

>^

r Process Kp

C o n t r o l l e r Kc

manipu la ted v a r i a b l e c o n t r o l l e d v a r i a b l e e r r o r ( Y r - Y ) Process ga in C o n t r o l l e r ga in Set Po in t

efi K

Y

^ Yr

Figure 1.1 Simplified Block Diagram of a Control System

1.2 Introduction to Proportional-lntegral-Derivative (PID) control algorithm

1.2.1 Proportional control

For understanding the operation of the three control modes better, the control

modes when applied to a simple heater are considered.

Consider a controller that can throttle back the heater power well ahead of the

temperature reaching set point. That is, make the power shrink in proportion to

distance from set point. The controller now has a chance to anticipate and head off

temperature overshoot and cycling. This action defines it as a proportional controller.

The proportional mode adjusts the output signal in direct proportion to the

controller input (which is the error signal e). The adjustable parameter to be

specified here is the controller gain Kp. The larger the Kpthe more the controller

output would change for a given error. This is proportional control.

Output u = Kp*e + b

where b=bias, e=error.

The size of error needed to make the Proportional Controller deliver 100% power

is called PROPORTIONAL BAND. It is sometimes expressed as a percentage of

the controller range. Therefore, if this controller has a range of say 0 to 1000°, 40°

represents a 4% proportional band. The gain Kp is defined as 100/%PB (100/4 = 25

in this example).

1.2.2 Overshoot and temperature cycling

If the gain is made large enough, the power will throttle back early enough to

avoid overshoot and temperature cycling. If the temperature could reach set point,

the deviation, which is the controller input, would reach zero, therefore, so would the

output. This does not happen. The temperature settles at some temperature below

set point and some intermediate level of output is delivered. This shortfall of

Controller Output below set point is called offset. From the equation for output of a

Proportional Controller, it is seen that the output equals bias when the error is zero.

The bias is fixed at the normal value of output, say 50%, or it can be adjusted

manually to match the load. This is called manual reset. The Proportional Band

could be further reduced (more controller gain) to get more power and to reduce the

offset at the risk of breaking into temperature cycling again. This is called control

loop instability.

1.2.3 Eliminating offset

Due to the proportional relationship between input and output, the error will

change in correspondence with any change in the output. If the output changes to

adjust to a new load, then the error will also change as follows:

Error e=Kp(u-b)/100.

Say the temperature settles at 180°C, i.e., 20°C below the set point of 200°C with

a corresponding power of 50%. The set point could be reset to about 222°C to get

the controlled temperature to come up close to 200°C. Some simple controllers have

a small knob labeled manual reset, which achieves this without it showing as an

extra 22°C on the set point display. This 22°C deviation is amplified into enough

power to heat the zone to about 200°C.

Problem: There may be times when the process needs say, twice that power to

hold 200°C; for example, when there is higher material throughput. To put out twice

the power, the amplifier would need twice the input (about 44°C offset) othenA/ise;

the temperature would head down again towards 180°C.

1.2.4 Integral action (sometimes called automatic reset)

The integral mode corrects for any offset (error) that may occur between the Set

Point and the process output automatically overtime. The adjustable parameter to

be specified is the integral time T of the controller.

Output u=1/T*ledt.

Reset is often used to describe the integral mode. Reset is the time it takes the

integral action to produce the same change in the manipulated variable (u) as the P

mode's initial static change. Figure 1.2 shows the response of a PI controller to a

step input.

Open loop response of a PI c o n t r o l l e r to a s tep 1 n e

I n i t i a l s tep due to P

T i Time

Figure 1.2 Response of a PI algorithm to a step in error

Now coming to our example of the heater it is not feasible to keep resetting the

keep resetting the set point and waiting around every time the heat demand

changes. What is needed is an automatic and continuous watch on the temperature

and automatic power adjustments, aimed at keeping the deviation at zero. So, let

the controller do this as a second job. Let it watch the deviation and so long as it

persists let the controller put out a gently increasing contribution until there is just

enough power to make the deviation e = 0.

The controller is designed to make the rate of output power growth proportional

to deviation. Therefore, when temperature is close to set point the power is changing

very slowly until at set point the power stops growing and holds at just the level

needed to hold the temperature at set point. For deviations above set point, the

power decays to achieve zero deviation.

This is called integral action. This is a PI (Proportional + Integral) controller.

1.2.5 Definition of integral time

The strength of integral action is expressed in terms of integral time, usually seconds

or minutes. If the deviation = one Proportional Band, the contribution of integral

action will grow to 100% power in one INTEGRAL TIME T. Note that a short integral

time brings a fast growth of power and an eager corrective action.

1.2.6 Integral windup

When a controller that possesses integral action receives an error signal for

significant periods, the integral term of the controller will increase at a rate governed

by the integral time of the controller. This will eventually cause the manipulated

variable to reach 100% (or 0%) of its scale, i.e., its maximum or minimum limits. This

is known as integral windup. A sustained error can occur due to a number of

scenarios, one of the more common being control system override. Override occurs

when another controller takes over control of a particular loop, e.g., because of

safety reasons. The original controller is not switched off, so it still receives an en-or

signal, which through time "SA/inds-up" the integral component unless something is

done to stop this occurring. Many techniques may be used to stop this happening.

One method is known as "external reset feedback." Here the signal of the control

valve is also sent to the controller. The controller possesses logic that enables it to

integrate the error when its signal is going to the control valve, but breaks the loop if

the override controller is manipulating the valve.

1.2.7 Derivative action (sometimes called rate action)

The derivative action anticipates where the process is heading by looking at

the time rate of change of the controlled variable (its derivative). Td is the rate

time and this characterizes the derivative action (with units of minutes). In

theory, derivative action should always improve dynamic response and it does in

many loops. In others, however, the problem of noisy signals makes the use of

derivative action undesirable (differentiating noisy signals translate into

excessive movement of the manipulated variable). Derivative action depends on

the slope of the error, unlike P and I. If the error is constant, derivative action

has no effect.

Now the controller has a third function. It watches for CHANGES of

temperature and puts out a contribution of power that is proportional to RATE

OF CHANGE of temperature, e.g., fast dive, big boost, slow dive gentle boost,

fast rises, big throttle-back, etc. The purpose here is to resist and damp out

unwanted changes and to speed up recovery from temperature disturbances.

This contribution to output power exists only when the temperature is changing.

1.2.8 Definition of derivative time

If the temperature dives at a rate of one proportional band in one DERIVATIVE

TIME Td, the contribution of derivative action is 100% power (and minus 100%

power for temperature climbing).

Output u=Td*de/dt.

This is now a PID (proportional + integral + derivative) controller, also called a 3-

tenn or 3-mode controller.

1.3 Variations of the PID algorithm

In Figure 1.3 a control system with a PID controller is shown.

Yr

.

Y

^ e _

,

u Y e Yr V

PID ^U Driver V Heater

manipulated variable controlled variable error (Yr-Y) Set Point Driver Output

Figure 1.3 Control system with a PID Controller

There can be three representations of the PID control Algorithm

/ Serial: U{s) = K^ 1 \

1 + + V

1

Eis)

Parallel: C/(s) = K Eis) + — E{s) + T,sEis) T.s

Gain : f/(s) = K E{s) + £(5) + /:^5^(5)

where

Kp = proportional gain,

Ti = integral time constant,

Td = derivative time constant,

U(s) = Laplace transformed control signal,

E(s) = Laplace transformed error signal,

K,= 1/T,

K d = 1 / T d .

PID1:

/•

U{s) = K^ 1 \

1 + — + Ts 7T a

Eis)

This is the standard textbook controller. Its value is more academic than

practical as it is not physically realizable. This is due to its relative order, which

is - 1 . It is the most widely used and is known as the non-interacting PID

because the three tuning parameters can be adjusted independently.

PID2:

where

Uis) = K^ / 1 T ^

1 Ts 1 + — + — ^

V - 1 + ^ ^ y Eis)

N = noise filtering constant. It is normally 10, but can be varied depending on

the system.

This is the physically realizable form of PID1 and it has the same

characteristics, but with a noise filtering capability.

PID3:

1 Uis) = K^ 1 + - ^ il + T,s)Eis)

This configuration is usually referred to as the interacting controller. If it is

converted to the PID1 configuration, the effective gain, integral and derivative

actions are functions of the original parameters. This version can be interpreted

as:

Uis) = K^ 1 + 1

V T.s J expr^sEis)

This is a PI controller with a pure predictor term (exp TdS) in which the

prediction horizon is Td. This unrealizable term is approximated as:

expTjs«1-1-TdS.

The proposed controller is actually closely related to this configuration. This

controller is also not realizable because it has a relative order o f - 1 .

PID4:

Uis) = K^ f j X /

1 + -T.s

1 + - "^ 1 + ^ 5

Eis)

PID4 is the same as PID3, but it is physically realizable since it has additional

noise filtering capabilities.

8

PID5:

Uis) = K^ V T.s J \ + -^s

where

Y(s) = Laplace transformed output signal.

This configuration avoids the "derivative kick," which occurs with step

changes in the Set Point (Yr). Consider PID1, a sudden change in the SP

causes the derivative term to become very large and this provides the so-called

"derivative kick" to the final control element. This can be avoided if the derivative

term acts on the measurement and not the error.

PID6:

Uis) = K^ ^Yîs)-Yis) + Êis)--^Yis)

where

P = Proportional kick constant,

Yr(s) = Laplace transformed Set Point.

This is similar to PID5, but here the 'proportional kick' is also accounted for.

The Proportional kick constant, p, is used to reduce the overshoot that can be

caused by sudden changes in the Set Point Yr. p is a fractional number and

when there is a sudden change in Yr, p swings into action and helps reduce the

overshoot.

There are two driving types of PID Control.

/ •

Absolute: C/(s) = ^^ \

1 + — + Ts Ts '

Eis)

1 hicremental: At/(s) = KÂEis) + — AEis) + TsAEis)

Ts

9

1.4 PID control with Feedforward: A special case of PID6

PID with Feedforward is a special case of PID6. Its implementation is outlined

in Figure 1.4.

r r

+

J

| j

y

u Y e V r V

P

F l j

i l"-iT^-i^ 1 \\} ^

J r1ve1 H - a - e r ^

V

tnani PL f a t e d v a r i a b l e CO 11 re l i e d v a r ' a b l s e r r o 1 ( ^ ' - Y i '.^^- K D - n t C r " v e O u i p L t

=ccdforv/Q'c f a c t o r

Figure 1.4 PID with FeedfonA/ard

PID + FeedForward: t/(s) = pY^ is) + K^ 1 + — -{-Ts Ts '

Eis)

This is implemented on the Applied Materials Endura SL 300. The advantage is

that the Feed Forward factor automatically sets the balance point. This reduces the

actual range over which temperature needs to be controlled as the temperature

needs to be controlled only around the balance point.

1.5 Thesis Outline

This thesis documents a project undertaken by the DSM (Dielectric Systems

and Modules) and the CMD (Contact Metal Deposition) groups at Applied

Materials Inc. The project examined the problems of the current PID algorithm,

which controls the Ceramic heater in the LPCVD (Low Pressure Chemical Vapor

10

Deposition) and TTN (Titanium TiNitride) chambers. After examining and listing

the problems, it has been concluded that the Predictive Proportional Integral

(PPI) mode of control would provide adequate solutions. The goals of this

project are outlined in the next chapter. In this project we have studied the

heater systems, modeled them and carried out simulations in Simulink. The

results of the simulation were then used to place Software Requests so that

necessary software changes in the Control Algorithm could be made. Finally, it

summarizes the project and discusses the future actions to be taken to

implement these changes.

11

CHAPTER 2 DESCRIPTION OF THE SYTSEM AND THE PROBLEM

2.1 Description of the System

A Centura System shown in Figure 2.1 can hold up to Four Chambers. The

Chamber is attached to the transfer chamber at any of the four locations. Each

chamber has an individual controller, ac box, and gas panel on its frame, which

allows each chamber to run its own process and maintenance independent of

the system. The Factory Interface (Fl) holds cassettes of wafers, which are fed

from the Fl to the Single Wafer Load Locks (SWLLS) and then to the Transfer

Chamber, and finally the wafer is placed into the SiNgen Process Chamber for

nitride deposition.

FACTORY INTERFACE

'CTIAMBEF^ •CONTF^OLLER

Figure 2.1 SiNgen Chambers on Centura 300 Mainframe

12

2.1.1 The SiNgen Centura 300 process chamber

The SiNgen Centura 300 process chamber shown in Figure 2.2, is a single wafer

process chamber.

Figure 2.2 The SiNgen Centura 300 process chamber

It offers a rapid wafer heatup/cooldown cycle and fast deposition rates. It is

designed for thermal chemical vapor deposition of silicon nitride at >600°C

(750°C TO 800°C). Different applications have different requirements for nitride

film deposition. Film Density, film defects, and surface morphology are critical

applications of thin nitride (<100A) in NO stack for advanced gate application

and ONO film stack for capacitor materials. They are less critical for etch stop

and hard mask applications. Good film conformality (step coverage) is important

in spacer and some etch stop applications, but it is not as critical in other nitride

applications where the topography is much less severe.

The SiNgen chamber is equipped with a remote plasma source for in-situ

periodic chamber cleaning. The RPS mounts on the SiNgen chamber lid. NF3

molecules are dissociated in the remote plasma unit. The generated fluorine

13

radicals are delivered to the chamber to remove chamber deposits. The direct

connection between the RPS unit outlet and chamber lid minimizes the

recombination of fluorine radicals, thus maximizing the clean efficiency of the

chamber deposit. Periodic remote NF3 plasma cleans successfully restore

pristine chamber conditions for nitride deposition. A chamber overview is

depicted in Figure 2.3.

CHAMBER LID

CHAMBER BODY

RPS II (REMOTE PUS MA SOURCE)

WATER MANIFOLD

WAFER/HEATER, LIFT ASSEMBLY

Figure 2.3 SiNgen chamber overview.

14

2.1.2 Dual Zone Heater Assemblv

The heater assembly holds the wafer directly below the perforated plate

(showerhead). The heater plate is made of ceramic (AIN), and is heated by the

heating element embedded inside the heater plate. The heater has two separate

heating zones to provide temperature uniformity. They are located on separate

layers inside the heater plate. The heating element of each zone is made of

molybdenum. The heater is heated by resistive heating. The dual zone heating

compensates for the temperature variance therefore providing the desired

temperature uniformity. A ceramic shaft supports the heater plate. During the

process, the interior of the heater shaft is at atmospheric pressure (see Figure

2.4).

1. Heater Plate. The heater assembly holds the wafer during process. The

heater has low separate heating zones. They are located on separate

layers inside the heater plate. The plate is made up of two layers. The top

one is inner zone control and the bottom one is the outer zone control. It

is heated by resistive heating. The wafer is held in place by a 30-mil deep

pocket milled into the surface of the plate. Material: Ceramic

2. Heater Shaft. A shaft that houses the heating element leads and the

Thermocouple lead supports the heater plate. Material: Aluminum.

3. Heater Shaft Clamp. The heater shaft clamp secures the heater shaft to

the aluminum hub. Material: Aluminum.

4. Heating Element Power Lead Insulators. The heating power lead

insulators insulate the heating element power leads from each other and

from the thermocouple lead. Material: Ceramic

5. Aluminum Hub. The heating element power leads and the thermocouple

leads are mounted to the aluminum hub, which acts as a support so that

the leads do not twist or become damaged.

15

THERMOCOUPLE PROBE

HEATER SHAFT CLAMP

HEATING ELEMENT POVifER LEADS

HEATER PLATE

HEATER SHAFT

HEATING ELEMENT LEAD INSULATORS

ALUMItiUMHUB

VITON 0-RING

Figure 2.4 Dual Zone Heater Assembly

6. Heating Element Power Leads. The heating element power leads supply

the power to heat the heating element. Material: Nickel

7. Thermocouple Insulator. The thermocouple insulator insulates the

thermocouple lead from the heating element power leads. Material:

Ceramic.

8. Thermocouple Probe. A thermocouple (TC) assembly monitors the

temperature of the heater plate. The TC only measures the temperature

16

of the center of the heater. The thermocouple probe is a shielded type-K

metallic thermocouple and contains two independent TC junctions:

• Temperature Measurement,

• Over Temperature Protection.

The thermocouple leads pass through the heater shaft to the back of the

heater plate and sends the thermocouple signal from the heater to the

thermocouple amplifier module located on the TC PCB.

^^>{5?)-^ Controller

SP SCR TC Amp

SCR Heater+

TC? Display

Set Point Si l icon Controlled Rect i f ie r Thermocouple Ampli f i e r

Figure 2.5 Control System Schematic

2.1.3 Schematic of the control system

Figure 2.5 shows the schematic of the heater control system. The Set Point is

the required temperature of the heater surface. It can be entered on the screen

at the Factory Interface (Fl). The input to the Controller is the difference

between the Set Point and the amplified Thermocouple measurement. The

Controller output goes to the SCR, which drives the Heater. The Heater

temperature can also be seen at the Display on the Fl screen.

17

2.2 Problems with the existing system

The existing algorithm that controls the heater in the Centura system is a

Proportional Integral Derivative (PID) algorithm. It is unable to provide adequate

control due to the reasons listed below.

2.2.1 Variation in inner and outer zone voltages

The voltage of the inner zone of the heater controls the PID loop, but the

characteristics of the inner zone and the heater temperature vary greatly due to

changes in any of the following factors:

• Operating Temperature,

• Process Conditions,

• Outer/Inner zone voltage ratio.

2.2.2 Disturbances due to change in control algorithm

There are potentially big disturbances when the control strategy changes in the

following cases:

• From Ramp to PID,

• Change in the Feedforward Factor (KRF ),

• Change in the Voltage Ratio (VR).

2.3 Goals to be achieved by making the necessary changes in the control algorithm

The following goals are to be achieved:

• Common code using PPI control to replace PID control for different heaters like

the Ceramic heater in the LPCVD chamber, and in the TTN chamber;

• Multiple set of PPI parameters at different temperature bands;

18

Bumpless transfer between control modes or bands to reduce temperature

overshoot at switching;

Built-in model for reference scheduling;

Tuning guidelines for PPI parameters;

Auto tune of PPI parameters;

Manual Control Mode.

19

CHAPTER 3

DESCRIPTION OF THE FUNDAMENTALS AND THEORY OF PPI CONTROL

3.1 Model-based Predictive Control

A model based predictive controller is a controller that uses a process model

in real time for the computation of the control action to be applied on the

process. This model represents the relationship linking the process input(s) to

the process output.

This model has to be identified: the structure of the model and the

parameters of the model are estimated by an identification algorithm, which

exploits the data collected during specific (open loop) experiments. The model is

used to predict the future process output and to compute the control action in

order to satisfy a given target (SP) for the process variable.

The controller design is only a function of the actual state of the system, x.

There is no predictive action based on the process model. In contrast to the

standard feedback design philosophy, the model predictive controller design is

based upon the feedback information that is the difference between the actual

state of the system x, and a predictive state Xp.

Model predictive controllers as shown in Figure 3.1, basically consist of the

same elements:

• The dynamic model,

• A reference trajectory yr(n) which describes the smooth transition of the

target variable from its current value to the future set point profile C within a

prediction horizon Hp that corresponds to the end of the coincidence horizon He.

This trajectory can be interpreted as the desired behavior of the closed loop

system,

• An objective criterion as a function of the future controller error e(n) between

the reference trajectory and the predicted output over a coincidence horizon

[HI, He].

20

• By minimizing the objective function an optimal profile for the future values of

the manipulated variable is calculated for the coincidence horizon that guides

the predicted target variable as close as possible to the reference trajectory,

• A compensation for modeling errors.

dm clu

X

xp Xsp dm di 'u

u e

process s t a t e p r e d i c t e d s t a t e se t p o i n t s t a t e measured process d is tu rbance unmeasured process d i tu rbance c o n t r o l v a r i a b l e s e r r o r between process s t a t e and p red i c ted s t a t e

Figure 3.1 Model Predictive Controller (MPC)

21

Another example of a Model Predictive Controller would be the one in Figure

3.2. The only modification here is that the Set Point is input to the Model. This is

done to facilitate reference scheduling and this is the algorithm used in this

project.

Set Point

I Model

Yr -

— ^ Clrlr u

1

Driver V

Heater y

Figure 3.2 Model Predictive Controller (MPC)

3.2 Predictive PI Controller

The predictive PI controller is a special case of MPC. Figure 3.3 shows a

schematic of the same.

Set Point

1

Model

Vr

PI u

Driver

Transmitter

V ^ Heater y

Figure 3.3 Predictive PI control

The presence of a time delay in the control loop limits the achievable

perfonnance of a control system. It contributes towards its destabilization by adding

a phase lag, and hence forcing a reduction of the gain of the controller. A pure

predictive term, i.e., e^ '', will cancel the effect of time delay by adding a phase lead

22

and will thus speed up the response. Now, e ^ implies pure prediction and is not

realizable.

The Maclaurin series expansion of e ^ is:

Tps _ _ e = 1 + Tr,S + T n S +

2 2 k k T n S +

2!

Ui(s)= e ^^u(s) ,

3,1

3.2

Using (3.1) in (3.2) and taking the inverse Laplace transform would give

2 2 -pk k U ^ ( t ) = U ( t ) + T ^ d [ u ( t ) ] + T p d [ u ( t ) ] + T p d [ u ( t ) ]

c l ( t ) 2! d ( t ) ^ k! d ( t ) ' < 3. 3

Load

E(s)

' ' - ^ ^ (Kp+1 / TiS ) e sTp

Disturbance

C(s) / A(s)

+

Ul(s

e"^^ B(s) / A(s)

as)

Figure 3.4. The Unrealizable Controller

A realizable approximation would be

2 2 U i * ( t ) = U ( t ) + T p d [ L i | ( t j ] + T p d [ U f ( t ) ]

f ^ d ( t ) 2! d ( t ) ^ 3 . 4

23

where

u^(s) = u^(s) 3,5

N ^ where Tpis the prediction horizon,

N is the noise-filtering constant.

The above equations imply that the current derivatives of a continuous time

signal can be used to predict the future developments of that signal. However taking

derivatives of such a signal in the presence of noise is not feasible because of the

side effect of noise amplification. The simplest solution would be to use filtered

derivatives instead of actual derivatives of the signal. Filtered derivatives are

obtained from the state variable filter.

d ' [ U f < t ) ]

d ( t ) '

s*^ u ( t ) f o r i = 1 , . . . , k

M ( s ) 3 . 6

where, the denominator of 3.5 gives M(s). Figure 3.5 shows the realizable

interpretation of the Predictive PI controller. This controller is actually a PI Controller

enhanced with the predictive term.

Approx. P r e d i c t i o n

U(s)

' ^ - • ^ ^> -» f0<pn /T i5 ) ^

Load Disturbance

C(s) / A(s)

e"^%(s)/A(s)

as)

Figure 3.5. The realizable PPI implementation

24

3.3 Specification of Heater Control

3.3.1 Phase I: Overshoot Reduction and Bumpless Transfer

3.3.1.1 Current Algorithm

The current algorithm for PID on Endura SL 300mm WCVD is shown in

Figure 3.6.

Kff

^ TempRefVr'

Eh®—

Bias

Figure 3.6 Current Algorithm

SCR Heater - i

Filter

The algorithm is as follows:

uik) = Kffy^ik)+K^eik) + u.ik-\) + Keik)-K][yik)-yik-l)] + Bik)

where

x(k) and x(k-1) refers to the current sample and the last sample of variable x;

u is voltage of inner-zone driver;

Uj is the history value of integral part;

Kff is feed forward coefficient;

yr is reference of temperature (this may be different from target temperature);

Kp' is gain of proportional term;

Ki' is gain of integral term;

Kd' is gain of derivative term;

e is difference between yr and y;

B is bias. 25

1. Overshoot reduction algorithm

To reduce overshoot, the following algorithm can be used.

uik) = Kj^y^k)- K'yik) + u.ik -1) + K'eik) -K][yik) - yik -1)] + Bik)

Note the difference of proportional term.

2. Bumpless transfer algorithm

By forcing the initial value to history value of integral part ui (k-1), a bump less

transfer can be achieved. This initialization should be done at one of the

following conditions.

Switch from ramp control to PID control;

Change of any SYSCONs including Kff, Kp", Ki', Kd',B.

uXk-\) = uik-\)-{Kj^y^ik)-K\yik) + Keik)-K][yik)-yik-\)] + Bik)}

where x(k-1) refers to the value of x before switch/change and x(k) refers to the

value of x after switch/change.

3.3.2 Phase II: Total Power Control



Figure 3.7. Note that temperature is controlled in current mode.

26

Figure 3.7 Current Algorithm in Current mode


uik) = K^y^ik)+ Keik) + u.ik-\) + K'eik) - K][yik) - yik -1)] + Bik)

where

x(k) and x(k-1) refers to the current sample and the last sample of variable x;

u is total power P required for SCR heater driver;

Ui is the history value of integral part;

I is current required for SCR heater driver, and

lik) = •^Pik)/Rik) for resistance R which is a function of temperature T;

Kff is feedfoHA/ard coefficient;






B is bias.

In the current software, the relationship of resistance R and temperature T is

hard coded for one type of W heater R=0.0128*T+4.75. This should be

27

changed to a generalized function, or at least, implement the two coefficients as

SYSCONs.

3.3.2.2 Total Power Control Algorithm

It is observed that the relationship between total power input to the heater

and temperature output of the heater can be estimated by a linear function.

Therefore, the feedforwad and PID parameters will not change significantly by

using power to control temperature. This is different from using voltage or

current to control temperature, which requires significant change of those

parameters if one of the following factors changes:

• change between voltage mode and current mode SCR driver;

• change between SCR driver and SSR driver;

• change of power ratio of multiple zone heater.

The algorithm for PID control is exactly the same, the difference is the

converter function from power to the input signal to the heater driver.

Current Mode Single-Zone SCR

Iik) = ^Pik)/Rik)

where

Pik) = uik)

and

Rik) = R[Tik)].

Voltage Mode Single-Zone SCR

Vik) = -^Pik)Rik)

where

Pik) = uik)

and

Rik) = R[Tik)].

28

Current Mode Dual-Zone Heater

P,ik) = K^,Pik)

Fik) = i\-K„)Pik)

I,ik)^^P^ik)/R^ik)

F_ik) = ^Pik)/R,ik)

where A,.,, between 0 and 1, is the power fraction of coil 1, and

Pik) = uik)

R,ik) = R^[Tik)]

R,ik) = R,_[Tik)]

Voltage Mode Dual-Zone Heater

P,ik) = K^,Pik)

P,ik) = il-K^,)Pik)

V,ik) = ^P,ik)R,ik)

V,ik) = ^P,ik)R,ik)

where AT ,, between 0 and 1, is the power fraction of coil 1, and

Pik) = uik)

R,ik) = R,[Tik)]

R,ik) = R,[Tik)]

3.3.3 Phase III: Autotune of PID parameters



Figure 3.6. Note that temperature is controlled in current mode.


uik) = K^y^ ik)-\- Keik) + u,ik -1) + Keik) - K] [yik) - yik -1)] + Bik)

where

• x(k) and x(k-1) refers to the current sample and the last sample of variable x;

• u is total power P required for SCR heater driver;

• Ui is the history value of integral part;

29

I is current required for SCR heater driver, and lik) = Pik)IRik) for

resistance R which is a function of temperature T;

Kff is feedfoHA/ard coefficient;






B is bias.




SYSCONs.

3.3.3.2 Relationship of PID Parameters in the Gain-Type and Standard Algorithms.

Most auto-tuning algorithms are based on the ISA standard algorithm as

shown in the following equation:

/ r . . . ,. ^

or u = K^ T dt

V

Uis) = K^ ^ 1 ^

V T.s J Eis)

where

• Kp is proportional gain;

• Ti is integal time in second;

• Td is derivative time in second.

We need to give the relationship between the gain-type algorithm and the

standard type.

30

K=K^TJT,

^'<i=^,TJT^

where Ts is sampling time of the control system, 0.100 second for Endura SL

300mm.

3.3.3.3 Autotuning Algorithms

The auto-tuning algorithm will automatically estimate the optimal PID and

feedforward parameters when the user requests to tune the parameters. This

feature can be implemented in the heater calibration screen. The algorithm will

calculate and override the corresponding SYSCONs when the AUTOTUNE

button is clicked.

Autotuning can only be done at a steady-state condition and not in ramp up

or cold down stage. The actual procedure is as follows.

1. Wait until a steady-state condition is reached;

2. Record the power Um/Pm and temperature Ym at the condition;

3. Switch from PID control mode to RELAY control mode;

4. Set the RELAY control parameters, basically (a) reduce power by h watts if

temperature is over 5 degree C and (b) increase power by h watts if

temperature is below to 5 degree C, which is shown in Figure 3.8

5. Record the power and temperature value for about 10 minutes;

6. Calculate the amplitude d of temperature output y and period Tu of

power/temperature as shown in the figure;

31

Figure 3.8 Auto tuning

7. Assume that the heater's model is a first order lag plus a pure time delay as

described in the equation:

Where Km is the gain, Tm is the time lag of first-order model and Dm is the

pure time delay.

8. Calculate the model parameters as follows:

Y

T„=^^JiKjJ^l

T D = - ^

" 2;r

where

Tta

( K-tan

'2KT?^

V T

32

Calculate the standard PID parameters as follows:

Kff

K ^'p

T. =

T,--

Call

K K-K,

= 1/^',,,

2r„,

^K„.iT„,-

••T„.

-IL 4

-DJ

Dulate gain-type

= ^ .

-KJJT,

= KJJT

where Ts is sampling time of the control system, 0.100 second for Endura SL

300mm.

3.3.4 Phase IV: Replace PID with PPI



Figure 3.7.


uik) = K^y^ ik)+ K\eik) + u. (A: -1) + Keik) - K\ [yik) - yik -1)] + Bik)

where

• x(k) and x(k-1) refers to the current sample and the last sample of variable x;

• u is total power P required for SCR heater driver;

• Ui is the history value of integral part;

• I is current required for SCR heater driver, and lik) = -,JPik)/Rik) for

resistance R which is a function of temperature T;

• Kff is feedforwad coefficient;

• yr is reference of temperature (this may be different from target temperature);

• Kp' is gain of proportional term;

33

• Ki' is gain of integral term;

• Kd' is gain of derivative term;

• e is difference between yr and y;

• B is bias.




SYSCONs.

3.3.4.2 PPI Algorithms

Predictive PI or PPI control has some advantages over standard PID control.

The predictor term in PPI will give a better prediction than the derivative term in

PID. Actually, we can simply use the Predictor to replace the existing 2"' -order

low-pass filter for temperature and then remove the derivative term in the PID.

y,ik) = yik) + yik-\) + ^yik-2)-^y^ik-\)-^y^ik-2) «0 '^0 «0 «0 «0

where

T=TJT^

ao=0.4r'+1.47^+1

a, =-0 .8r '+2 ' r

a, =o.4r'-i.4r+1

&o=4.2r'+3.ir^+i 6i=-8.4r'+2

62=4.2r'-3.ir,+1

• y is temperature;

• yf is the filtered/prective temperature;

• Tp is the predictive time, which is a replacement of derivative time Td;

• Ts is sampling time of the control system, 0.100 second for Endura SL

300mm.

34

The PI control algorithm is then:

uik) = Kj^yîk)-K^yîk) + u.ik-\) + K][yîk)-yîk)] + Bik)

If auto-tuning algorithm is implemented the PI parameters are still the same

as those in PID and Tp can be selected as 1/3-1/2 of pure delay Dm.

35

CHAPTER 4

MODELING OF THE HEATER

The basic objective of this thesis being to study the behavior of the PPI controller,

a lot of stress has not been laid on modeling. This chapter gives a brief overview of

the data collected for modeling and touches upon the systems used for theoretical

modeling.

The system was modeled from the experimental data collected. The following

sets of data were collected.

4.1 Experimental Data

4.1.1 Heater Characteristics

The power supplied to the heater is varied and the temperature is recorded. The

ratio of temperature and total power does not change greatly. This data was used to

define the SYStem CONStants (SYSCONS) in the system computer. The data from

Figure 4.1 is used to define the SYSCON for gain between power input and

temperature output.

Power vs. Temperature

3.5

S 3

^ 2.5 $ O 2

1.5 650 700 750 800

Tern perature (C)

850

Figure 4.1 Power Temperature Curve

The resistance of the heater coil is only a function of temperature and is

independent of the voltage ratio, Vr. The voltage ratio is the ratio of voltage of

the outer coil with respect to that of the inner coil.

36

R e s i s t a n c e v s . V o l t a g e R a t i o for I n n e r Z o n e

1 1 . 5 0) o c re V) U) 0) IT

1 1

10 .5

10 9.5

• T = 6 7 0 C

• T = 7 5 0 C T = 8 0 0 C

1 2

V o l t a g e Ra t io

Figure 4.2 Inner Zone Resistance versus Voltage Ratio

R e s i s t a n c e v s . V o l t a g e Ra t io for O u t e r Z o n e

11 .5

9> 1 1 u

re 10 .5

I 10 K 9.5

9

• m

T = 6 7 0 C

T = 7 5 0 C

T = 8 0 0 C

1 2

V o l t a g e Ra t io

Figure 4.3 Outer Zone Resistance versus Voltage Ratio

Total power (sum of Inner and Outer Zone powers) is considered for the PID

loop, so that Kff, Kp, Ki and Kd will not change greatly with Vr and Temperature.

4.2 Modeling of the Various Blocks

The heater was modeled as a second order system with the Transfer

Function shown in the block below. This is just a theoretical assumption based

on experience with previous systems. A second order system allowed the

modeling of delay that the resistive coils of the heater gave rise to.

Similariy, the Wafer Disturbance was modeled as a second order system and

Thermocouple Dynamics are modeled as a first-order system.

The delay can be modeled better with higher-order systems:

37

u

t i m e

Step I n p u t O u t p u t o f F i r s t - O r d e r System O u t p u t o f Second-Orde r System O u t p u t o f T h i r d - O r d e r System

Figure 4.4 Output plots of Various Ordered Systems

A second-order system with the following Transfer Function was used.

0.75

30s^ +13S + 1

4.3 Simulink For Modeling

Simulink is a software package built on MATLAB for modeling, simulating,

and analyzing dynamical systems. It supports linear and nonlinear systems,

modeled in continuous time, sampled time, or a hybrid of the two. Systems can also

be multirate, i.e., have different parts that are sampled or updated at different rates.

For modeling, Simulink provides a Graphical User Interface (GUI) for building

models as block diagrams, using click-and-drag mouse operations.

38

step PIP C»ntc,>ll«rl

. •

12bitD/A HeaterDrlverSCR Discrete

Transfer Fon

0 75

30E^+13£-I-1

Heiiter

WdferSeq

-'lOs+O.C

5rjs2+15s+1

Wafe(DI:1urbarice

K* ThttmC'COuple Oifnanao:

- ^ - ^

Temp

Figure 4.5 Simulink Model

This is the Simulink System Model into which the various PID algorithm

models and the PPI model are plugged and simulated. This is the topic of

discussion in the following chapter.

39

CHAPTER 5

SIMULATIONS AND TUNING

There are 6 different types of PID algorithms and 1 PPI algorithm explained in

Chapter 1. This Chapter is devoted to evaluating the performance of the

Predictive PI controller. The PPI is simulated along with the PID structures.

Simulations of these algorithms are carried out in Simulink. The system model

developed in Chapter 4 is used here.

5.1 Simulations of the Algorithms

The Simulink simulation for each of the algorithms is as shown in Figure 5.1

to Figure 5.7.

PID1:

( Uis) = K^

\ ^ + ~ + T,s

T,s Eis)

Yr

€> Y

[ — •

+

Sumi

P

b

1 •

ro poitic

Kp

Ti.s

ntegial

njl1

»-»-

Kp"T?^;^^-^

D C

du/dt

>eriv3tivf

• + ->&

Sum

Figure 5.1 Simulink Model for PID1

40

PID2:

( • ' > 1 Yr

Y

b

1 •

+

Sum1

F

k

k

>I0 pontic

Kp

Ti.s

Integial

nal1

' — r

Kp'Td.s

Td/N.s+1

+ + +

Sum

Transfer Fen

-KD


PID3:

^(s) = ^ , V T.sj

i\ + T,s)Eis)

Yi

&

h p k

w

1 +

k P • K P ^

V

^

Piopoitionail

F

Sumi 1

Kp

Ti.s

^tegial

!—• k

+

+

Sum

Td


du/dt

Deiivative • 0

Sum2 -> U

41

PID4:

Uis) = K, '..±" V T.s J

1 + ^^^^ V 1 + ^ s

Eis)


©1

© Y

1 — •

+

um

k

Pr

1

• Kp

oportio

Kp

Ti.s

Integra

nal1

+

+

Sum

h Kp'Td.s+1

Td/N.s+1

Transfer Fen

•r^ u

PID5:

Uis) = K^ f 1 ^

1 + -T^sj

T,s Eis)--^Y is)

1 + Tf5

©1 Yr

&

Sum1

Pioportionall

Kp_

Ti.s

Integral

Kp'Td.s

Td/N.si-1

Transfer Fen


-KD Sum

42

PID6:

(7(s) = A- Plis)-Yis) + ^Eis)-^^Yis) TiS l+'^s

O Yr

© •

Sum1

Reference

^ Kp

ProportionaH

Kp_

Ti.s

Integral

Kp'Td.s

Td/N.s<-1

Transfer Fen


Sum

-K) u

PPI:

Uis) = K^ 1 + -Ts

[(l + TpS + Tp*Tpl 452X1 + 2Tp IN.s + Tp*TplNI N)]Eis)

(ih Yr

&

Proportlonall

Sum1

l<p_

Ti.s

Tp"Tp/4.s2+Tp.s+1

Tp"Tp/N/N.s2+2'Tp/NsH K!) Integral Sum Transfer Fen

Figure 5.7 Simulink Model for PPI

These blocks were plugged into the Controller block of the System Model

developed in Chapter 4 and the PID controllers were tuned using the Ziegler Nichols

method, while a different tuning method, outlined in the next section, was used to

tune the PPI controller.

43

5.2 Tuning

5.2.1 Tuning of PID

The PID controllers are tuned using the Ziegler Nichols Ultimate Cycle

method. Figure 5.8 shows the response of the system at Ultimate Gain. The

classic closed-loop Ziegler Nichols tuning procedure is to advance the gain of

the Proportional only controller until the process is oscillating continuously at

constant amplitude.

10 15 20 25 30 35-nme

Figure 5.8 Ziegler Nichols Ultimate Cycle method

The gain required for achieving this (the ultimate gain, Gu) and the period of

oscillation (the critical period, Pu) provide parameters from which controller

settings are derived as shown in Table 5.1

Table 5.1 Controller settings from Gu and Pu

Controller Type

PI

PID

Kp

Gu/2 _ _

Gu/1.7

Ti

Pu/1.2

Pu/2

Td

Pu/8

44

Note that it is not necessary here to estimate the steady state process gain

as the controller gain, or proportional band, settings are expressed in terms of

that actually set on the controller to make the plant oscillate.

5.2.2 Tuning PID: an example

Increasing only the Proportional gain of PID, ultimate gain Gu, is 10.347 and

substituting in the formula for PID1 in Table 5.1, we have the following values of Kp,

Ti, and Td. The response is as shown in Figure 5.9.

Table 5.2 Example of PID Tuning

Controller Type

PID

Kp

6.086

Ti

10

Td

2.5

3

2

1

CO

^ 0 >-

-1

-J

X Y Plot

Rj

1 \j \i

-

"\ A .

\ 1 V

•

•

50 ICO .< A:<is

15C 200

Figure 5.9 Pu From Steady Oscillations

45

Using these PID values in the PID1 algorithm, the response shown in Figure 5.10 is obtained:

^iXY Graph

2

L5

11-

0.5

< 0 >-

-0.5

-1

-1.5

-2

X Y Plot

A

Unix]

50 100 150 200 250 300 XAxis

Figure 5.10 Response of a second order system with PID1

5.2.3 Tuning of PPI

There are 3 tuning parameters for PPI; therefore we may select a suitable Tp and

tune the PI part by using the Ziegler Nichols Ultimate Cycle method. The following

values of Kp and T , are used, while the best value for Tp is chosen as 5.

Table 5.3 Tuning PPI

Controller Type

PPI

Kp

4.7032

Ti

16.667

Tp

5

46

5.3 Performance Indices

The performance indices shown in the Figure 5.11 are described below.

1,8

1,6

1,4

1 ,2

^ 1.0

° 0 . 8

0 , 6

0 . 4

0 . 2

/ A A r\

/ 1 .

\ 1 \ / ^ B ^

- — 1 1 1 _ J

0 Tr2 4

Time 8 10 12

Figure 5.11 Perfonnance Indices for Controllers

1. Rise time (Yr): The rise time is the time at which the system output first reaches

the desired steady state value.

2. Overshoot (A/B): The overshoot is the ratio of the maximum peak value to the

desired steady state value of the output variable.

3. Integral Square Error (ISE): In order to make it easier to compare all these

designs and comment on the performance of any particular tuning algorithm the

Integral Square Error (ISE) is used as a common performance criterion and a

measure of quality control for all controllers tested.

47

5.4 Simulation Results

The responses of different controllers for unit step input and a wafer disturbance

with an amplitude of 0.5, period of 120s, duty cycle (% of period) of 80 starting at

4000s are examined and tabulated in the following table.

Table 5.4 Results

Kp

T,

Td

P

Tp

Rise time

Max. Over

shoot

ISE

PID1

6.086

10

2.5

108

1.4

10.925

PID2

6.086

10

2.5

108

1.4

8.9921

PID3

6.086

10

2.5

109

1.5

10.525

PID4

6.086

10

2.5

105

1.7

8.1254

PID5

6.086

10

2.5

112

1.5

11.0030

PID6

6.086

10

2.5

0.6

105

1.3

10.6743

PPI

4.7032

16.667

-

-

5

102

1.1

6.3654

48

CHAPTER 6

CONCLUSIONS

In this thesis six PID algorithms and the PPI algorithm were studied and

simulated. The PPI controller is implemented in continuous time and in effect it has

only one tuning parameter (Tp). The PI parameters can be obtained from those of a

first order with time delay approximation of the original high-order system. The

simulations indicate that the controller is robust. It has lesser tuning parameters,

which is an advantage over other PID tuning procedures, since less tuning

parameters imply easier manual or auto tuning. PID controllers are known for their

robustness and it is seen that PPI controllers share the same robustness properties.

The various goals outlined in Chapter 2 have been achieved and implemented

through algorithms for Reference Scheduling, Overshoot Reduction, Bump less

Transfer, Auto tuning. Total Power Control and finally conversion to PPI from PID

control.

It can be concluded that the PPI controller has better performance than the

standard PID tuned by ultimate ZN tuning rules. The results from the simulations are

tabulated in Chapter 5. It can be seen that the critical parameters like Rise Time,

Maximum Overshoot and Integral Square Error are optimum for the PPI case. PPI

gives minimum Rise Time of 102 seconds, least Overshoot of 1.1 and lowest

Integral Square Error of 6.3654.

These results were used to place Software Requests so that necessary software

changes in the Control Algorithm can be made. After these are incorporated into the

System Software, various Test Matrices are proposed to be carried out to test the

practical validity of these results. The most important parameter that will validate the

success of this project would be better thickness uniformity and control of the

deposited films.

49

LIST OF REFERENCES

[I] W. Fred Ramirez, Process Control And Identification, Academic Press, 1994.

U P. P. Kanjilal, Adaptive Prediction and Predictive Control, Peter Peregrinus Ltd., on behalf of IEEE, 1995.

[3] Lennart Ljung, System Identification Theory for the User, Second Edition, PTR Prentice Hall, Upper Saddle River, N.J., 1999.

[4] Wai Lun Lo and A. Besharati Rad, Comparison of Two Auto-Tuning Predictive PI Controllers, International Journal of Modelling and Simulation, Vol. 15, No. 3, 1995.

[5] W. L. Lo, A. B. Rad, K. M. Tsang, Auto-Tuning of Output Predictive PI Controller, ISA Transactions 38 (1999) 25-36.

[6] David Angeli, Alessandro Casavola, Edoardo Mosca, Predictive Pl-control of Linear Plants Under Positional and Incremental Input Saturations, Automatica 36 (2000) 1505-1516.

[7] K. K. Tan, T. H. Lee, F. M. Leu, Predictive PI Versus Smith Control For Dead-Time Compensation, ISA Transactions 40 (2001) 17-29

[8] Frank Allgower, Rolf Findeisen, Zoltan Nagy, Moritz Diehl, Georg Bock, Johannes Schloder, Nonlinear Model Predictive Control for Large Scale Systems, 6' Int. Conf. On Methods and Models in Automation and Robotics, NMAR 2000, pp 43-54, Poland.

[9] A. Besharati Rad and Wai Lun Lo, Predictive PI Controller, Int. J. Control, 1994, Vol. 60, No. 5, 953-975.

[10] John A. Shaw, Process Control Solutions, http://www.iashaw.com/pid/tutorial/

[ I I ] http://www.engin.umich.edu/qroup/ctm/extras/step.html

[12] http://www.che.utexas.edu/~control/sim/pid.htm

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http://www.iashaw.com/pid/tutorial/

http://www.engin.umich.edu/qroup/ctm/extras/step.html

http://www.che.utexas.edu/~control/sim/pid.htm

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