i

Acknowledgement

First of all, I am grateful to my teammate, Tan Li Xiu for the cooperation in completing

this arduous advanced control project.

I wish to express my sincere thanks to Prof. Azlan, lecturer of advanced control subject,

for providing me with all the necessary knowledge. I place on record, my sincere gratitude to Mr

Fauzi and Miss Jarinah. I am indebted to them for their expert, sincere and valuable guidance

extended to me.

I take this opportunity to thank my parents and other course mates for their constant

encouragement.

ii

Contents Acknowledgement ..................................................................................................... i

List of tables ............................................................................................................. iii

List of figures ........................................................................................................... iii

1. Introduction .......................................................................................................... 1

1.1 Biodiesel ........................................................................................................... 1

1.2 CSTR in series with recycle stream .................................................................. 1

2. Literature review .................................................................................................. 4

2.1 Conventional control system ............................................................................ 4

2.2 Cascade control system ..................................................................................... 5

2.3 Adaptive control system ................................................................................... 6

3. Methodology ......................................................................................................10

3.1 Modelling equation .........................................................................................10

3.2 Control system design .....................................................................................11

3.3 Robustness of the system ................................................................................11

3.4 Simulink block diagram ..................................................................................12

4. Results and Discussion ......................................................................................16

4.1 Transfer function and PID gain value .............................................................16

4.2 Performance of various control system ..........................................................16

5. Conclusion .........................................................................................................22

6. References ..........................................................................................................23

7. Appendix ............................................................................................................23

iii

List of tables

Table Description Page

Table 1 Ideal output subjected to various input and operating conditions 3

Table 2 Classification of advanced control system 6

Table 3 Classification of adaptive control system 7

Table 4 Difference between MRAC and STR 7

Table 5 Parameters of adaptive filter 9

Table 6 Robust test for the various control systems 10

Table 7 Calculation result using ZN-method 16

Table 8 Comparison between 3 different control systems 22

List of figures

Figure Description Page

Figure 1 Transesterification reaction of TG with DMC 1

Figure 2 Series of CSTRs 1

Figure 3 Schematic diagram of STR and MRAC system 6

Figure 4 Simulink block diagram for controller and Lyapunov adaptation law 8

Figure 5 Process instrument diagram of the series of CSTR 9

Figure 6 Simulink block diagram for the system without and with conventional

control system

10

Figure 7 Simulink block diagram for subsystem for series of CSTRs 12

Figure 8 Simulink block diagram for 3 advanced control system (cascade,

MRAC and STR)

15

Figure 9 Figure 9: Performance of CSTR, Ca without control system, with

proportional controller at ultimate gain and with PID at ZN tuning

(m=0.0005, Ca0=0.001, β=1 θ=1)

16

Figure 10 Figure 10: Performance of MRAC at different set point (m=0.006,

0.004 and 0.002; Ca0 = 0.005)

17

Figure 11 Figure 11: Performance of STR at different weight (0.1, 0.2 and 0.3

at step size 1) and different step size (1, 100 and 1000 at weight 0.25)

18

Figure 12 Figure 12: Simulink block diagram for the various control systems

(PID, Cascade and STR)

19

Figure 13 Figure 13: Conversion of the product using different control system

(m=0, Ca0=0.005mol/dm3)

19

Figure 14 Performance of various controllers (Test 1 = set point tracking; Test 2

= disturbance rejection; Test 3 = increase of transport delay; Test 4 =

decrease of coolant ratio)

21

Figure 15 Temperature profile of tank 3 at coolant ratio of 0.0003 22

1

1. Introduction

1.1 Biodiesel

Biodiesel is a mixture of fatty acid methyl ester (FAME) produced from triglycerides (TG).

Currently, it is being viewed as the most potential candidate to replace fossil fuel.

Transesterification of palm oil with dimethyl carbonate (DMC) is among the many possible

reactions to produce fatty acid methyl ester (FAME) and glycerol dicarbonate (GDC) as shown

in Figure 1[1]

. The reaction is found to be first-order with respect to the concentration of

triglycerides. Since the reaction is exothermic, a great control has to be done to obtain high yield.

Figure 1: Transesterification reaction of TG with DMC

1.2 CSTR in series with recycle stream

While the rate constant of any reaction is temperature-dependent, the order of the reaction is not.

Since the catalyst present in small amount, CSTR is usually used for such reaction. In this project,

a series of CSTRs are being studied as shown in Figure 2.

Reaction : A (TG) → B (FAME)

Rate of reaction :

Figure 2: Series of CSTRs

2

Product B (FAME) is produced and reactant A (TG) is consumed in each of the three perfectly

mixed reactors by a first-order reaction occurring in the liquid. The inlet stream, q0 consists of

TG and DMC while another stream, qm consists only of TG. The product stream is recycled to

increase the conversion rate. It will be constantly drained from 3rd

tank to prevent accumulation

of reactants in the system.

Several control systems will be used to maintain the concentration of reactant A from tank 3, CA3.

The output from tank 3 must be able to follow the changes in set-point and maintain a constant

value despite fluctuation in inlet concentration CA0. A good control of the stream from tank of

pure A is the key to achieve this objective. It must be noted that high temperature favours the

rate of reaction despite the reaction being exothermic. Thus, a coolant is necessary to maintain

the temperature of the CSTR.

In nominal operating condition, the following assumptions are made:

The liquid volume is constant in each reactor.

No reaction occurs in the pipe.

The resistance in the pipe is negligible.

Density and specific heat of the mixture are constant.

Coolant dynamics are negligible.

The log mean temperature difference is approximated by using an arithmetic mean.

The operating parameters are:

Concentration of inlet, CA0 = 0 to 0.005 mol/m3

Ratio of coolant, β = 0 to 1

Flow rate of pure A, m = 0 to 0.001 m3/min Transport delayed, θ = 0 to 5 min

Volume of each tank, V = 5 m3 Activation energy, E

[1] = 79.1 kJ/mol

Flow rate into 1st tank, F = 0.5 m

3/min Rate law, k

[1] = k0 exp

(-9514/T)

Fraction being recycled, a = 0.10 Density of mixture, ρ [2]

= 0.887 kg/m3

Surface area of the tank, A = 10 m2

Heat of reaction, [2]

= 6828 000

kJ/mol

Temperature of coolant, Tc = 298K Specific heat

capacity, Cp [3]

= 0.130

kJ/mol*K

Feed temperature, Tf = 298K

Rate constant of the

reaction, k0 [1]

= 1.26 x 109 min

-1 Heat transfer coefficient

of steel, U0

= 24 W/m2K

3

Table 1: Ideal output subjected to various input and operating conditions

epic

Concentration of Tank 3 outlet Temperature of the CSTR

0 100 200 300 400 500 600 700 800

0

1

2

3

4

5

6x 10

-3

Time

0 2 4 6 8 10 12 14 16 18 20-3

-2

-1

0

1

2

3

4x 10

-3

Time

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

11x 10

-4

Time

m3

m2

m1

m

beta

White Noise1

White Noise

Transport Delay

Tc Scope

PID

PID Controller

0

No noise

Manual Switch

0.00001

0.001

Gain1

18.33

Final

control element

a1

Concentration

a

Temperature

Ca0

m

Ca0

Tj

beta

Ca1

Ca2

Ca3

T1

T2

T3

CSTRs

Add

m3

m2

m1

m

beta

White Noise1

White Noise

Transport Delay

Tc Scope

PID

PID Controller

0

No noise

Manual Switch

0.00001

0.001

Gain1

18.33

Final

control element

a1

Concentration

a

Temperature

Ca0

m

Ca0

Tj

beta

Ca1

Ca2

Ca3

T1

T2

T3

CSTRs

Add

0 25 50 75 100 125 1501500

1

2

3

4

5

6x 10

-3

Time

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

50

100

150

200

250

300

Time

Inp

ut

Op

erat

ing

co

nd

itio

ns

Idea

l O

utp

ut

Set point

10-3

Disturbance

10-2

Measuring element fluctuations

10-5

Transport delay in measuring element

1 minutes or 2 minutes

Amount of coolant in CSTR

1 or 0.0005

No overshoot

Minimum

response time

Minimum

fluctuations

Stable

temperature

4

2. Literature review

2.1 Conventional control system

Conventional control system utilized the feedback mechanism with PID controller. A major

disadvantage of feedback control is that it can cause oscillatory responses. If the oscillation has

small amplitude and damps out quickly, then the control system performance is generally

considered to be satisfactory. However, under most circumstances, the oscillations may be un-

damped or even have amplitude that increases with time until a physical limit is reached, such as

a control valve being fully open or completely shut. In these situations, the closed-loop system is

said to be unstable. Besides, it is unsatisfactory for processes with significant dead time.

There are three types of conventional controller commonly used which are P, PI and

PID controllers. The selection of controller type and its parameters are based on the model of the

process to be controlled. PID controllers use a 3 basic behaviour types or modes: P

(proportional), I (integrative) and D (derivative). The proportional controller produces an

overshoot followed by an oscillatory response [4]

. It has an output signal which does not equal to

set point and proportional to an error, ɛ. The time domain model is:

where

= Output signal from controller

= Proportional gain / sensitivity

= Error (set point – measured variable)

= Constant (bias value)

The proportional-integral controller produces a smaller overshoot but larger period of oscillation.

One major advantage of the integral action is the elimination of offset after a long settling time.

The time domain model is:

where

= Proportional gain / sensitivity

= Integral time

= Error (set point – measured variable)

5

The proportional-integral-derivative controller produces a smallest overshoot and quickest to

return to set point. However, it is very difficult to tune because of 3 parameters being involved. It

is necessary for process of higher order and offset is not tolerable. The time domain model is:

where

= Proportional gain / sensitivity

= Integral time

= Derivative time

This case study is tune using Ziegler and Nicholos (ZN) method. This is because it is more

popular and achieve satisfactory control as compared to Cohen-Coon (CC) method. Both method

is a heuristic PID tuning rule that used to determine good values for the PID gain parameters.

The steps of tuning by using Z-N method are:

1 The integral and derivative modes of controller are removed, leaving only proportional

controller

2 A value of proportional gain, Kc for disturbing the system is selected and the transient

response is observed. The value of Kc is increased in small steps until the system achieve a

response with oscillation of constant amplitue. At this point, the value of gain and

period of oscillation are corresponded to ultimate gain, Kcu and ultimate period, Pu

respectively.

3 From the values of Kcu and Pu obtained from previous step, the controller’s

parameters can be determined by the ZN rules.

2.2 Cascade control system

Conventional control system can never achieve satisfactory response in real processes especially

when it deals with non-linear system. Thus, various advanced control system is introduced as

shown in Table 1. A cascade control system consists of two feedback controllers and two

measuring elements. The primary controller is known as master controller and the secondary

controller is known as slave controller. The output of primary controller changes the set point of

secondary controller before it finally adjusts the valve (actuator). The secondary controller is

usually a proportional controller with high value of gain. This is to simplify the tuning and any

6

offset associated with proportional control of the inner loop can be eliminated by the integral

action of the primary controller. Thus, primary controller is usually a PID controller.

Cascade controller is better than conventional PID controller because it take measurement before

it enters the final tank. Since disturbance affects the intermediate process output, the secondary

controller limits this effect but the error between the input of tank 3 and the set point. It also

limits the effect of actuator or process gain variations on the control system performance.

Table 2: Classification of advanced control system

Category Sub-category Example

Classical - Cascade, ratio, feed forward and time delay

Modern Adaptive Model reference adaptive control (MRAC) and self-tuning regulator

(STR)

Model-based Model predictive controller (MPC), Global linearizing controller (GLC),

Generic model controller (GMC) and Inverse model controller (IMC)

Artificial

intelligence

Neural network (NN), Fuzzy logic and genetic algorithm

2.3 Adaptive control system

Adaptive control system is defined as control system that monitors its own performance and

adjusts its control mechanism in the direction of improved performance [5]

. Ever since it was

introduced back in 1957 by Drenick and Shahbender, adaptive control has evolved into multiple

different forms as shown in Table 2. All adaptive control system composed of inner loop and

outer loop.

Most of the research carried out focused on two adaptive control system: Model-reference

adaptive control (MRAC) and Self-tuning regulator (STR). Although both are adaptive control

system with almost similar performance, they have a lot of difference as shown in Table 3 and

Figure 3. They are proposed as a method to adaptively stabilize a non-linear system with

unknown model. MRAC manipulate the controller based on a proposed model. The model output

and the actual process output are compared to adjust the parameters of the controller. Thus, a

good reference model is required for the system to behave ideally. On the other hand, STR does

not need a model. It utilizes computation to obtain estimated parameters and adjustment

mechanism.

7

Table 3: Classification of adaptive control system

Category Details

Adaptive

behaviour Passive adaptation

Input signal adaptation

System variable adaptation

System characteristic adaptation

Extremum adaptation

Algorithms Direct system: parameters updated directly in direct system (implicit self tuning)

Indirect system: controller parameters are obtained via design procedure

(explicit self tuning).

Adaptive

scheme Gain scheduling

Self-tuning regulator (STR)

Model-reference adaptive control

(MRAC)

Design

method Minimum variance

Linear quadratic (LQ)

Pole placement

Model following.

Estimator Least square (LS)

Extended and generalized least

square

Stochastic approximation

Instrumental variable

Maximum likelihood

.

Table 4: Difference between MRAC and STR

System MRAC STR

Application Deterministic servo problem Stochastic regulation problem

Analysis Continuous time system Discrete time system

Algorithm Direct approach Indirect approach

Component Reference model and adaptation

mechanism

Parameter estimator and adjustment

mechanism

Model Required No

Weight No Required

Design MIT rule or Lyapunov rule LMS filter or Kalman filter

Figure 3: Schematic diagram of STR and MRAC system

8

In MRAC, the adaptation law is the adaptation mechanism used to find the controller parameters

(θ1 and θ2). Common laws are gradient method (MIT rules) and Lyapunow stability theory. In

Lyapunov theory, a first order system equation is used to simplify the derivation of differential

equation for the error [6]

. The process model given is

The Lyapunov function candidate has the following equation:

In order for the equation to be zero, then it will be as shown in Figure 4.

Figure 4: Simulink block diagram for controller and Lyapunov adaptation law

1

Uc

Product2

Product1

4

Ca3

3

Q1

2

m

1

Q2

2

Q1

1

Q2Product2

Product1

Product

1

s

Integrator1

1

s

Integrator

1

Gain1

-1

Gain

4

Ca3

3

error

2

m

1

adaptation rate

dQ1/dtgamma_e_u

gamma_y _e dQ2/dt

9

The reference model is governed by the maximum overshoot (Mp) and settling time (Ts).

In STR, the series of CSTR can be modeled single-input-single-output system (SISO).

It can be rewritten as

where

In adaptive filter, there are several operating parameters that can be used in this case study as

shown in Table 4. However, the two most important operating parameters are the step size and

filter weight. There are various algorithms available such as least-mean-squared (LMS) method,

normalized LMS, sign-error LMS, sign-data LMS and sign-sign LMS. Filter length is set at

minimum 4, leakage factor of 1 with adaptation.

Table 5: Parameters of adaptive filter

Parameters Description Parameters Description

Algorithm LMS Leakage factor 0 or 1

Filter length 4 Filter weights 0.04

Step size 1000 Adapt port 0 or 1

10

3. Methodology

3.1 Modelling equation

From mass balance, rate of accumulation = rate of flow in – rate of flow out – rate of

consumption

For tank 1, rate of accumulation of CA = Stream in (F) + Stream in (m) – Outlet stream – rate of

reaction

From energy balance for coolant,

From energy balance for the reactor, rate of accumulation of heat = rate of heat flow in – rate of

heat flow out + rate of heat released from reaction – rate of heat lost by cooling jacket

Similarly for tank 2 and tank 3:

11

3.2 Control system design

Manipulated variable : Flow rate of Pure A tank, m (mol/min)

Disturbance variable : Concentration of q0 stream, CA0 and inlet temperature, Tf

Controlled variable : Concentration of tank 3 outlet, CA3 and outlet temperature, T3

Figure 5: Process instrument diagram of the series of CSTR

The measuring element (sensors and transmitters) converts the concentration of A to an

electronic signal. Specifically, the output of the measuring element varies from 4 to 20 mA as the

concentration of A varies from 0.01 to 0.06 mol/m3 of A. The concentration measuring device is

linear. The flow of A through the control valve varies linearly from 0 to 1 m3/min as the valve-

top pressure varies from 3 to 15 psig. The time constant of valve is small compared with other

time constants in the system that its dynamics can be neglected.

3.3 Robustness of the system

Tuning is the adjustment of controller parameters to achieve a satisfactory control. Several

different control system will be subjected to various conditions as shown in Table 5. There are

several criterias where a system can be defined to be ‘good’ or ‘satisfactory’. The observable

criteria in the response are rise time, decay ratio and response time (+-5%). In term of error, it

can be compared using the equation below.

12

Table 6: Robust test for the various control systems

System Category Selected

Conventional - PID

Advanced Classical Cascade

Modern MRAC & STR

Condition m (mol/dm3) CA0 (mol/dm

3) Measuring element θ (min) β

1 0 to 0.005 0.005 No noise 1 1

2 0.005 0 to 0.005 (noise) No noise 1 1

3 0.0005 0.005 With noise 2 1

4 0.0005 0.005 No noise 1 0.0005

3.4 Simulink block diagram

From all those equations above, a block diagram is generated using Simulink as shown in Figure

5. The 4 manipulated variables are concentration of inlet (CA0), concentration of pure A (m), feed

temperature (Tf) and temperature of coolant (Tc). Since the reaction is exothermic, controlling

the concentration of the reactant can control both the reaction rate and temperature. Conventional

control system is shown in Figure 6 with its detailed process shown in Figure 7. Figure 8 and 9

showed the advanced control system used in this project.

Figure 6: Simulink block diagram for the system without and with conventional control system

Ca3

m setpoint

m3

m2

m1

m

beta

White Noise

Tc

Manual Switch

0.001

Gain1

Concentration

Temperature

Ca0

m

Ca0

Tj

beta

Ca1

Ca2

Ca3

T1

T2

T3

CSTRs

Add

m3

m2

m1

m

beta

White Noise1

White Noise

Transport Delay

Tc

PID

PID Controller

0

No noise

Manual Switch

0.00001

0.001

Gain1

18.33

Final

control element

Concentration

Temperature

Ca0

m

Ca0

Tj

beta

Ca1

Ca2

Ca3

T1

T2

T3

CSTRs

Add

13

T36

T3

5

T2

4

T1

3

Ca3

2

Ca2

1

Ca1

1.26e9

k2

1.26e9

k1

1.26e9

k0

aF(Ca3)

0.05

aF

Tf - T

T3 - T2

T2 - T3

T1 - T2

T - Tj2

T - Tj1

T - Tj

Product3

Product2

Product1

Product

1

s

Integrator5

1

s

1

s

Integrator3

1

s

1

s

Integrator1

1

s

-C-

H / pCp2

-C-

H / pCp1

-C-

H / pCp

0.5

F2

0.5

F1

F+m3

F+m1

F+m

F+aF+m

0.55

F+aF

0.5

F

eu

eu

eu

6.103

Display1

-6.105

Display

0

Constant2

0

Constant1

0

Constant

Add7

Add6

Add5

Add3

Add1

0.2

1/V5

0.2

1/V4

0.2

1/V3

0.2

1/V2

0.2

1/V1

0.2

1/V

-9514

-Ea2

-9514

-Ea1

-9514

-Ea

(F+m+aF)(Ca2)

(F+m)Ca1_1

(F+m)Ca1_0

-C-

UA / pCpV2

-C-

UA / pCpV1

-C-

UA / pCpV

298

Tf

2

1

(UA / pCpV)*(T - Tj)2

(UA / pCpV)*(T - Tj)1

(UA / pCpV)*(T - Tj)

4

beta

3

Tj

2

Ca0

1

m

Ca1

T1- (UA / pCpV)*(T - Tj)

Ca2

T2

- (UA / pCpV)*(T - Tj)

Ca3

- (UA / pCpV)*(T - Tj)

Tank 1

Tank 2

14

T36

T3

5

T2

4

T1

3

Ca3

2

Ca2

1

Ca1

1.26e9

k2

1.26e9

k1

1.26e9

k0

aF(Ca3)

0.05

aF

Tf - T

T3 - T2

T2 - T3

T1 - T2

T - Tj2

T - Tj1

T - Tj

Product3

Product2

Product1

Product

1

s

Integrator5

1

s

1

s

Integrator3

1

s

1

s

Integrator1

1

s

-C-

H / pCp2

-C-

H / pCp1

-C-

H / pCp

0.5

F2

0.5

F1

F+m3

F+m1

F+m

F+aF+m

0.55

F+aF

0.5

F

eu

eu

eu

6.103

Display1

-6.105

Display

0

Constant2

0

Constant1

0

Constant

Add7

Add6

Add5

Add3

Add1

0.2

1/V5

0.2

1/V4

0.2

1/V3

0.2

1/V2

0.2

1/V1

0.2

1/V

-9514

-Ea2

-9514

-Ea1

-9514

-Ea

(F+m+aF)(Ca2)

(F+m)Ca1_1

(F+m)Ca1_0

-C-

UA / pCpV2

-C-

UA / pCpV1

-C-

UA / pCpV

298

Tf

2

1

(UA / pCpV)*(T - Tj)2

(UA / pCpV)*(T - Tj)1

(UA / pCpV)*(T - Tj)

4

beta

3

Tj

2

Ca0

1

m

Ca1

T1- (UA / pCpV)*(T - Tj)

Ca2

T2

- (UA / pCpV)*(T - Tj)

Ca3

- (UA / pCpV)*(T - Tj)

Figure 7: Simulink block diagram for subsystem for series of CSTRs

Tank 3

15

Figure 8: Simulink block diagram for 3 advanced control system (cascade, MRAC and STR)

m3

m2

m1

m

beta

White Noise1

White Noise

Transport Delay1

Transport Delay

Tc

PID

PID Controller1

PID

PID Controller

0

No noise

Manual Switch

0.00001

0.001

Gain1

-K- Final

control element

Concentration

Temperature

Ca0

m

Ca0

Tj

beta

Ca1

Ca2

Ca3

T1

T2

T3

CSTRs

Add

m3

m2

m1

m

beta

White Noise1

White Noise

Tc

418.8

s +60s+418.82

Uc

Ca0

Tc

beta

Noise

Ca3

T3

PID

0

No noiseManual Switch1

Manual Switch

-K-

Gain2

0.001

Gain1

model

Q2

m

Q1

Ca3

Uc

Controller

10

Constant

Ca0

Add

adaptation rate

m

error

Ca3

Q2

Q1

Adaptive Law

m3

m2

m1

m

beta

White Noise1

White Noise

Transport Delay

Tc

PID

PID Controller

0

No noise

Manual Switch2

Manual Switch

LMS

Input

Desired

AdaptAdaptAdapt

Output

Error

Wts

LMS Filter

0.00001

0.001

Gain1

18.33

Final

control element

Concentration

Weight

Error

Temperature

0

1

Ca0

m

Ca0

Tj

beta

Ca1

Ca2

Ca3

T1

T2

T3

CSTRs

Add

16

4. Results and Discussion

4.1 Transfer function and PID gain value

Table 7: Calculation result using ZN-method

Controller Type

P 0.50Ku = 0.090 - - 0.090 - -

PI 0.45Ku = 0.081 Pu/1.2 = 32.5 - 0.081 0.0308 -

PID 0.60Ku = 0.108 Pu/2.0 = 19.5 Pu/8.0 = 4.875 0.108 0.0513 4.875

4.2 Performance of various control system

Figure 9: Performance of CSTR, Ca without control system, with proportional controller at

ultimate gain and with PID at ZN tuning (m=0.0005, Ca0=0.001, β=1 θ=1)

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

x 10-3

Time

0 100 200 300 400 500 600 7000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10

-3

Time

17

The performances of the tanks without any control system achieve 0.006mol/dm3 in all 3 CSTRs.

This is obviously unacceptable because large concentration of Ca indicates that only small

amount of Cb (product) is formed at the end of the reaction. After utilizing ZN tuning, it is found

that the conventional system has ultimate gain of 0.180 and ultimate period of 39 minutes as

shown in Figure 10. However, it still has long response time (667 minutes) and large decay ratio

(0.727). With adaptation rate of 20, when Mp = 2 and Ts = 3.398, then

Figure 10: Performance of MRAC at different set point (m=0.006, 0.004 and 0.002; Ca0 = 0.005)

It is found that the performance of MRAC is only ideal when the set point, m is greater than that

of disturbance (Ca0). Otherwise, a large adaptation rate is required. This may sometimes exceed

the amount that can be calculated in Matlab (1099

). This then managed to maintain the

concentration of the outlet of Tank 3, Ca3 to be stable and similar to that of the set point. At this

performance, all the reactant from feed, F will be converted into product. However, this is not

economically feasible because large amount of pure A is required to maintain the concentration

of the product. The performance of the control system begins to decrease when m decreases.

There is a large offset at m = 0.0002mol/dm3. In fact, the performance of conventional PID

controller is found to be even better at lower concentration of pure A, m. Since MRAC cannot

handle set point lower than those of disturbance, cascade and STR control systems are then used

to improve the performance of the system.

0 100 200 300 400 500 600 700-1

0

1

2

3

4

5

6

7x 10

-3

Time

18

The operating condition for cascade controller is similar to that of conventional PID controller.

In addition to that, the secondary controller is a proportional controller with Kc = 1 for a fastest

response. If Kc>1, the system is found to be unstable although an even faster response is

achieved.

On the other hand, the performance of STR is observed at different weight and step size as

shown in Figure 11. It is notable that increasing weight decreases the rise time but at the expense

of higher overshoot initially. Thus, there is an optimum weight where the system achieves

minimum overshoot and offset. Increasing step size makes the system responds even faster.

Desirable performance is achieved at optimum weight of 0.25 and highest step size of 1000.

Figure 11: Performance of STR at different weight (0.1, 0.2 and 0.3 at step size 1) and different

step size (1, 100 and 1000 at weight 0.25)

0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-3

Time

weight = 0.1

weight = 0.2

weight = 0.3

set point

0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

1.2x 10

-3

Time

step size = 1

step size = 100

step size = 1000

set point

19

The ideal operating conditions for cascade and STR control system are incorporated to improve

the performance of conventional PID controller as shown in Figure 12. Among the 3 different

control systems, the performance of STR is found to be ideal in set point tracking. The

conversion of the product achieved 1.00 at steady-state for all controllers as shown in Figure 13.

However, under various robust tests, there are some remarkable characteristics shown by

different control system in Figure 14.

Figure 12: Simulink block diagram for the various control systems (PID, Cascade and STR)

Figure 13: Conversion of the product using different control system (m=0, Ca0=0.005mol/dm3)

F

m3

m2

m1

m

beta

White Noise1

Tc

m

Ca0

Tc

beta

Noise

Ca3

T3

PID

0

No noiseManual Switch1

LMS

Input

Desired

AdaptAdaptAdapt

Output

Error

Wts

LMS Filter

-K-

Gain1

-K- Gain

Temperature

Cb

Weight

Error

Concentration

0.5

0

1

m

Ca0

Tc

beta

Noise1

Ca3

T3

Cascade

Ca0

20 40 60 80 100 120 140 160 180 2000.97

0.975

0.98

0.985

0.99

0.995

1

1.005

Time

PID

Cascade

STR

20

0 100 200 300 400 500 600 700 800 900 1000-2

0

2

4

6

8

10

12

14

16x 10

-4

Time

PID

Cascade

STR

set point

500 550 600 650 700 750 800 850 900 950 1000

4.6

4.8

5

5.2

5.4

5.6

x 10-4

Time

PID

Cascade

STR

set point

0 10 20 30 40 50 60 70 80-2

0

2

4

6

8

10

12x 10

-4

Time

PID

Cascade

STR

set point

Tes

t 1

T

est

2

Tes

t 3

21

Figure 14: Performance of various controllers (Test 1 = set point tracking; Test 2 = disturbance

rejection; Test 3 = increase of transport delay; Test 4 = decrease of coolant ratio)

In all 4 robust tests, cascade control system found to have lower overshoot and response time as

compared to PID controller. This is done at the expense of 2 measuring elements and 2

controllers. Thus, cascade control can be unstable when the transport delayed increased as in

Test 3. STR has the best performance in Test 1, Test 2 and Test 3 with minimum overshoot,

shortest response time and better disturbance rejection.

Under careful inspection, STR also has its own flaws. In Test 1, STR has little overshoot when

the set point increase from 0 to 0.0005mol/dm3 but large overshoot (similar to PID) when the set

point decreases from 0.00075 to 0.00025mol/dm3 at time 400 to 600 minutes. In between that

period, the response is not that satisfactory although it maintains below the set point. In Test 4,

the performance of STR dropped drastically when the coolant ratio decreases from 1 to 0.0005.

Further investigation from the temperature profile has shown that the reactor cannot maintain the

temperature of the reaction when amount of coolant dropped as shown in Figure 15.

This justify that certain minimum amount of coolant is required to maintain the temperature of

all the CSTRs since the reaction is exothermic. Controlling the temperature of the reactor is

unnecessary and difficult because thermometer has large transport delay. As long as the amount

of coolant is above that of minimum, all the temperature of CSTRs shall be maintained at 298K

(room temperature). This can be compensated by installing a low-level alarm and amount of

coolant must be at least twice the amount of minimum requirement.

0 50 100 150 200 250 300 350 400 450 5000

1

2

3

4

5

6

7

8

9x 10

-4

Time

PID

Cascade

STR

set point

Tes

t 4

22

Figure 15: Temperature profile of tank 3 at coolant ratio of 0.0003.

Table 8: Comparison between 3 different control systems

Operating condition PID Cascade STR

Proportional gain (primary) 0.1080 0.1080 0.1080

Integral gain 0.0513 0.0513 0.0513

Derivative gain 4.875 4.875 4.875

Proportional gain (secondary) - 1.0000 -

Weight - - 0.25

Step size - - 5000

Performance (500 minutes for set point tracking, m = 0.0005)

Rise time (minutes) 20 21 15

Decay ratio 0.727 0.467 0.400

Period (minutes) 63 66 60

Response time (minutes) 667 302 257

Disturbance rejection (%) 10 6 0.8

ITAE 6.685 2.364 0.5166

IAE 0.04201 0.02315 0.004859

ISE 6.412 x 10-6

3.220 x 10-6

3.187 x 10-7

5. Conclusion

Self-tuning regulator adaptive control is found to be the best control system as compared to

classic advanced control system (cascade) and conventional control system (PID). It improves

the performance of the system in set-point tracking and disturbance rejection with significant

lower rise time and response time. Unlike cascade controller, it can be used despite large

transport delayed is present in the measuring element. Since it is heavily dependent on the flow

rate of coolant, further improvement can be made by incorporating artificial intelligence

advanced control system on its algorithm.

0 5 10 15 20 25 30 35 40 450

50

100

150

200

250

300

350

400

450

Time

PID

Cascade

Coolant

Ideal temperature Increased infinitely

23

6. References

1. Zhang, L., et al., Kinetics of transesterification of palm oil and dimethyl carbonate for

biodiesel production at the catalysis of heterogeneous base catalyst. Bioresource technology,

2010. 101(21): p. 8144-8150.

2. Fabbri, D., et al., Properties of a potential biofuel obtained from soybean oil by

transmethylation with dimethyl carbonate. Fuel, 2007. 86(5): p. 690-697.

3. Zhou, Y., J. Wu, and E.W. Lemmon, Thermodynamic Properties of Dimethyl Carbonate.

Journal of Physical and Chemical Reference Data, 2011. 40(4): p. 043106-043106-11.

4. Coughanowr, D.R. and L.B. Koppel, Process systems analysis and control. Vol. 3. 1965:

McGraw-Hill New York.

5. Kokotovic, P., Foundations of Adaptive Control, volume 160 of Lecture Notes in Control

and Information Sciences. 1991, Springer-Verlag.

6. Yimam, A., Adaptive Control Design for a MIMO Chemical Reactor. 2004, Addis Ababa

University.

7. Appendix

*Important reference are attached for the details in designing the CSTRs.