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.