10.1.1.1039.4745

Advances in Natural and Applied Sciences, 8(22) Special 2014, Pages: 19-27
AENSI Journals
Advances in Natural and Applied Sciences
ISSN:1995-0772 EISSN: 1998-1090
Journal home page: www.aensiweb.com/ANAS
Corresponding Author: Suryakala, S., Assistant Professor, ICE Department, Sri Manakula Vinayagar Engineering College,
Pondicherry, India, 605107.
Self Tuning Regulators for a Liquid Level Process
1
S. Suryakala and 2
Dr. D. Rathikarani
1
Assistant Professor, ICE Department, Sri Manakula Vinayagar Engineering College, Pondicherry, India,605107.
2
Associate Professor, E&I Department, Annamalai University. Chidambaram, India, 608001.
ARTICLE INFO ABSTRACT
Article history:
Received 3 September 2014
Received in revised form 30 October
2014
Accepted 4 November 2014
Keywords:
Level control, Recursive least square,
Self tuning regulator, Pole placement,
model following.
Liquid level control is highly important in industrial applications. Liquid level control
using Self tuning regulator and self tuning pole placement controller is presented in this
paper. As a first step modelling of the process is highly essential for accurate control of
the process. In this paper to estimate the process parameters recursive least square
algorithm is used. Two different self tuning control algorithms using pole placement
technology are designed and implemented to control the process. The objective of this
work also includes a comparative analysis of performances of the chosen system when
implementing these two strategies under different operating regions. The design and
simulation studies are carried out in MATLAB/SIMULINK platform.
© 2014 AENSI Publisher All rights reserved.
To Cite This Article: S. Suryakala and Dr. D. Rathikarani., Self Tuning Regulators for a Liquid Level Process, Aust. J. Basic & Appl. Sci.,
8(22): 19-27, 2014
INTRODUCTION
In many industrial processes, control of liquid level is required. It was reported that about 25% of
emergency shutdowns in the nuclear power plant are caused by poor control of the steam generator water level.
Such shutdowns greatly decrease the plant availability and must be minimized. Liquid level control system is a
very complex system, because of the nonlinearities and uncertainties present in oil refinery plant, overflow of
oil can be hazardous, dangerous and costly. Empty vessels lead to pumps or drain stream processes dry.
Inaccurate measurements in mixtures processes can lead to product defects and higher costs (E.P.Gatzke 2012).
Accurate liquid level is vital in the process industries where inventories, batching and process efficiency are
critical measurements. The majority of processes met in industrial practice have stochastic character.
Traditional controllers with fixed parameters are often unsuited to such processes because their change in
parameters. Parameter changes are caused by changes in the manufacturing process, in the nature of the input
materials, fuel, machinery use (wear) etc. Fixed controllers cannot deal with this.
Adaptive control is a specific type of control, applicable to processes with changing dynamics in normal
operating conditions subjected to stochastic disturbances. Adaptive control is a specific type of control where
the process is controlled in closed loop, and where knowledge about the system characteristics are obtained on-
line while the system is operating (K.Barriljawatha 2012). The self-tuning regulator attempts to automate the
tasks involved in the adaptive control scheme namely modeling, design of a control law, implementation and
validation (Shi Jingzhuo 2011).
I. Process Description:
The piping and instrumentation diagram of real time experimental level process setup is shown in Fig. 1
Pump(P) discharges the water from the Reservoir Tank(RT) to Over Head Tank(OHT). The Process Tank(PT)
receives the water from the OHT. Flow rate is measured with Rotameter (R) at the inlet. An RF capacitance
Level Transmitter(LT) is used to measure the level in the tank (0-20cm). The output current signal (4-20 mA)
from LT is converted to corresponding digital value using a VUDAS100, USB based Data Acquisition card
(DAQ) card which is interfaced with PC as shown in Fig. 4. The digital control algorithm is developed and
configured in the controller which gives appropriate control signal. The controller output is given to digital to
analog converter(DAC) in DAQ card is used to actuate motorized control valve (MCV). The inlet flow is
manipulated by varying the stem position of the control valve in order to maintain the level of water in the
process tank.

20 S. Suryakala and Dr. D. Rathikarani, 2014
Fig. 1: Piping and Instrumentation diagram.
HV-Hand valve; H-Heater; FT-Flow Transmitter; TT-Temperature Transmitter; S-Stirrer; TPC-Thyristor
power control; OHT-Over head tank; R-Rotameter; PT-Process tank; MCV-Motorized control valve; LT-Level
transmitter; RT-Reservoir tank.
Estimation Algorithm:
It is important to estimate the process parameters on-line in adaptive control. When operating regions
changes, the model parameters are to be estimated, so that the controller parameters are tuned accordingly.
A. Process Model:
It is assumed that the process is described by the single-input, single output (SISO) system
)
(
)
(
)
(
)
(
)
( 0
0
1
1
d
k
v
d
k
u
q
B
k
y
q
A 


 

(1)
Where
n
nq
a
q
a
q
A 





 ...
1
)
( 1
1
1
m
mq
b
q
b
q
B 





 ...
1
)
( 1
1
1
with 0
d
n
m 
 . In equation (1) y is the output, u is the input of the system, and v is the disturbance. Here
)
(
),
( 1
1 

q
B
q
A
are the polynomials in the variable
1

q
. For the process taken in this work the structure of the
process is given by
2
2
1
1
2
1
1
0
1
1
)
( 








q
a
q
a
q
b
q
b
q
H
where 0
b , 1
b are the numerator polynomial coefficients and 1
a , 2
a are the denominator polynomial
coefficients.
)
( 1

q
H
is the pulse transfer operator.
B. Least-squares Estimation Algorithm:
The least-square method is commonly used in system identification. (Deepak M.Sajnekar 2013,
M.Chidambaram 2002, Yoan D.Landau 1998). In adaptive control system the observations are obtained
sequentially in real time. Recursive estimation algorithm is desirable. It saves the computation time by using the
results obtained at time k-1 to get the estimates at time k . Hence, the recursive least-square (RLS) estimation
method is implemented. The process model which is given in equation (1) can be rewritten as
)
(
...
)
(
)
(
...
)
2
(
)
1
(
)
( 0
0
0
2
1 m
d
k
u
b
d
k
u
b
n
k
y
a
k
y
a
k
y
a
k
y m
n 












(2)
The model is linear in the parameters and can be written in the vector form as

 )
(
)
( k
k
y T

(3)
where
T
n
m a
a
a
b
b
b ]
,....,
,
,
,..
,
[ 2
1
1
0


 T
n
k
y
k
y
m
d
k
u
d
k
u
k )
(
),..
1
(
),
(
),...,
(
)
( 0
0 








The recursive least-square estimator is given by
)]
1
(
ˆ
)
(
)
(
)[
(
)
1
(
ˆ
)
(
ˆ 



 k
k
k
y
k
K
k
k T




(4)
OHT
Pump
To
R.T
H3
H2
FT
HV4
RT
HV5
HV7
PT
HV6
H1
MCV
HV1
R
HV2
HV3
TPC
LT
TT
S
1

1
))
(
)
1
(
)
(
)(
(
)
1
(
)
( 



 k
k
P
k
I
k
k
P
k
K T


 (5)
)
1
(
)
(
)]
(
)
1
(
)
(
)[
(
)
1
(
)
1
(
)
( 1






 
k
P
k
k
k
P
k
I
k
k
P
k
P
k
P T
T



 (6)
where P(k) is covariance matrix, K(k) is the Gain matrix and
)
(
ˆ k
 is the estimated parameter vector.
II. Self Tuning Regulator:
Self-tuning regulator (c1) is a well-known technique in adaptive control systems. The block diagram of self
tuning regulator is shown in fig. 2. For an adaptive controller the process parameters are to estimated for every
second and the estimated process parameters are 1
0
2
1
ˆ
,
ˆ
,
ˆ
,
ˆ b
b
a
a
and t
r
s
s ˆ
,
ˆ
,
ˆ
,
ˆ 1
1
0 are the adapted controller
parameters for every value of process parameters.
Fig. 2: Block diagram of Self tuning regulator.
A. Control Algorithm:
Linear Controller of General Structure:
The process model is described in equation (1) as
)
(
)
(
)
(
)
(
)
( 0
0
1
1
d
k
v
d
k
u
q
B
k
y
q
A 


 

(7)
Assume that the polynomials
)
( 1

q
A
and
)
( 1

q
B
are co-prime, i.e. they do not have any common factors.
Furthermore,
)
( 1

q
A
is monic. That is, that the coefficient of the highest power is unity.
A general linear controller can be described by
)
(
)
(
)
(
)
(
)
(
)
( 1
1
1
k
y
q
S
k
u
q
T
k
u
q
R c





(8)
where
)
( 1

q
R
,
)
( 1

q
S
and
)
( 1

q
T
are polynomials in the backward shift operator
1

q
. This controller
consists of a feedforward transfer operator
)
(
/
)
( 1
1 

q
R
q
T
and a feedback with the transfer operator
)
(
/
)
( 1
1 

q
R
q
S
. It thus has two degrees of freedom.[Ioan D.Ladue, 2002]
From equations (2) and (8), the following equations for the closed loop system are obtained.
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
( 1
1
1
1
1
1
1
1
1
1
1
1
k
v
q
S
q
B
q
R
q
A
q
R
q
B
k
u
q
S
q
B
q
R
q
A
q
T
q
B
k
y c 















(9)
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
( 1
1
1
1
1
1
1
1
1
1
1
1
k
v
q
S
q
B
q
R
q
A
q
S
q
B
k
u
q
S
q
B
q
R
q
A
q
T
q
A
k
u c 















(10)
Thus, the closed loop characteristic polynomial is (for simplicity, the operator
1

q
is omitted)
BS
AR
Ac 
 (11)
In equation (9)
)
(k
uc is the command signal. The key idea of the controller design is to specify the desired
closed loop characteristic polynomial Ac as a design parameter. By solving the Diophantine equation (11), the
polynomials R and S can be obtained. The closed-loop characteristic polynomial Ac determines the property
and the performance of the closed system. The Diophantine equation (11) always has solutions if the
polynomial A and B are co-prime as required and the solution may be poorly conditioned if the polynomials
have factors that are very close.
t
r
s
s ˆ
,
ˆ
,
ˆ
,
ˆ 1
1
0
Reference
Input Output
Self Tuning Regulator
Process parameters
1
0
2
1
ˆ
,
ˆ
,
ˆ
,
ˆ b
b
a
a
Specification
Controller
Design
Estimator (Recursive least
square Algorithm)
Controller
Process

B. Model Following:
The Diophantine equation (11) determines only the polynomials R and S. Other conditions must be
introduced to calculate the polynomial T in the controller equation (8). To do this, the response from the
command signal to the output follow the model which is represented by equation (12) (Karl Astrom 1998).
)
(
)
( k
u
B
k
y
A c
m
m
m  (12)
From equation (9), the following condition must hold.
m
m
c A
B
A
BT
BS
AR
BT


 (13)
It then follows from the model-following condition represented by equation (13) that the response of the
closed-loop system to command signal is specified by the model equation (12). Equation (13) implies that there
are cancellations of factors of BT and Ac. Factorize the polynomial B as


 B
B
B (14)
where

B is a monic polynomial whose zeros are stable and so well damped that they can be canceled by the
controller and

B corresponds to the unstable or poorly damped factors that cannot be canceled. Since

B
remains unchanged, it thus holds that

B must be a factor of equation (15).
'
m
m B
B
B 

(15)
Since

B is canceled, it must be a factor of c
A . Furthermore, it follows from equation (13) that, m
A is also
a factor of c
A . The closed-loop characteristic polynomial c
A thus can be rewritten as
0
A
A
B
A m
c


(16)
Since c
A and B have the common factor

B , it follows from equation (11) that it must also be a factor
of R . Hence
'
R
B
R 
 (17)
The Diophantine equation (11) then can be simplified as
c
m A
A
A
S
B
AR 

 
0
'
(18)
Substituting equations (14), (15) and (16) into equation (13), equation (19) is obtained.
0
'
A
B
T m

(19)
C. Compatibility Condition:
To have a control law that is causal in the discrete-time case, the following conditions are imposed upon the
polynomials in the control law given by equation (8).
R
S deg
deg  (20)
R
T deg
deg  (21)
In the case of no constraints on the degree of the polynomial, the Diophantine equation (11) can have
many solutions if
*
R and
*
S are two specific solutions, then so are
MB
R
R 
 *
(22)
MA
S
S 
 *
(23)
where M is an arbitrary polynomial with any degree. Since there are so many solutions, it is desirable to seek
the solution that gives a controller with the lowest degree, i.e. the minimum-degree controller. Given deg A>deg
B, it then follows from equation (11) that
A
A
R c deg
deg
deg 
 (24)
From equation (21), the degree of S is at most
1
deg 
A . This is defined as the minimum-degree solution
to the Diophantine equation (11). The condition R
S deg
deg  thus implies that
1
deg
2
deg 
 A
Ac (25)
From equation (19), the condition
R
T deg
deg  implies that
0
deg
deg
deg
deg d
B
A
B
A m
m 


 (26)
It implies that the time delay of the model must be at least as large as the time delay of the process. It is
natural that to get a solution in which the controller has the lowest possible degree. Meanwhile it is reasonable

to require that there is no extra delay in the controller. It means that the polynomials R , S and T have the same
degrees. Then, the following algorithm is implemented.
The RLS estimator computes the model parameters for various operating regions and are tabulated(Table
III). These parameters are used in the design of controllers (Self Tuning Regulator c1 and Self Tuning pole
placement controller c2).
Minimum-degreee Pole Placement (MDPP):
Data: Polynomials A and B .
Specification: Polynomials m
A , m
B and 0
A
.
Compatibility Conditions:
A
Am deg
deg  ;
B
Bm deg
deg 
1
deg
deg
deg 0 

 
B
A
A
'
m
m B
B
B 

Step 1: Decompose B as


 B
B
B
Step 2: Solve the diophantine equation below to get R' and S with
A
S deg
deg  ; m
A
A
S
B
AR 0

 
using R'and Bm', the polynomials R and T are computed
R=B+
R'
T=A0Bm'
using R,S and T polynomials the command signal is computed.
Step 3: From
'
R
B
R 
 and
'
0 m
B
A
T 
, and compute the control signal from the control law
Sy
Tu
Ru c 

D. Model following without zero cancellation:
Let the desired closed loop reference model be
2
2
1
1
1
1
0
1
1
1
1
)
(
)
(
)
( 










q
a
q
a
q
b
b
q
A
q
B
q
H
m
m
m
m
m
m
m
In this work, the self tuning regulator with no zero cancellation is designed and implemented. Since no
process zeros are cancelled,
1


B (27)
1
1
0




 q
b
b
B
B
B
Bm 
 ,where
)
1
(
/
)
1
( B
Am

 , 1
deg
deg 
 A
A and T =βA. Furthermore,
1
deg
deg
deg 0 

 B
A
A
and 0
A
T 
 . The closed loop characteristics polynomial is m
c A
A
A 0

and the Diophantine equation in Step
2 becomes
m
c A
A
A
BS
AR 0


 (28)
It also follows from the compatibility conditions that the model must have the same zero as the process.
The discrete closed loop transfer operator is
2
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
)
( 













q
a
q
a
q
b
b
q
a
q
a
q
b
b
q
H
m
m
m
m
m
m
m 
(29)
where 0
0 b
bm 
 and
1
0
2
1
1
b
b
a
a m
m





which gives unit steady state gain. Here 0
m
b , 1
m
b , 1
m
a , 2
m
a are the refence model parameters. The
Diophantine equation becomes
)
1
)(
1
(
)
)(
(
)
1
)(
1
( 1
0
2
2
1
1
1
1
0
1
1
0
1
1
2
2
1
1

















 q
a
q
a
q
a
q
s
s
q
b
b
q
r
q
a
q
a m
m (30)
Replacing 0
1 /b
b
q 
 and solving for 1
r
2
0
2
1
0
1
2
1
2
1
1
1
0
1
0
1
0
2
2
2
0
2
0
1
1
)
(
)
(
b
a
b
b
a
b
b
a
a
a
b
b
a
a
a
a
b
a
a
r m
m
m
m
c









(31)

Equating coefficients of terms
2
q
and
0
q
in equation
2
0
2
1
0
1
2
1
2
1
2
0
2
1
2
1
0
2
0
2
1
0
1
2
1
0
1
2
2
1
1
1
2
1
0
1
1
0
)
(
)
(
b
a
b
b
a
b
a
a
a
a
a
a
a
a
b
b
a
b
b
a
b
a
a
a
a
a
a
a
a
a
b
s m
m
m
m
m
c














(32)
2
0
2
1
0
1
2
1
1
2
0
1
2
0
2
2
2
2
0
2
0
2
1
0
1
2
1
2
0
2
0
2
1
2
1
1
1
1
)
(
(
b
a
b
b
a
b
a
a
a
a
a
a
a
a
a
b
b
a
b
b
a
b
a
a
a
a
a
a
a
a
b
s m
m
m
m
m
c












(33)
and
)
1
(
)
(
)
( 1
0
1
1 




 q
a
q
A
q
T c 
 (34)
III. Self Tuning Pole Placement Controller:
Self tuning pole placement controller (c2) is a discrete single input single output controller that can be used
to control systems of second and third order processes. Self tuning pole placement controller is designed for the
process with the structure shown below
2
2
1
1
2
1
1
0
1
1
)
( 








q
a
q
a
q
b
q
b
q
H
Controller specific parameters are damping factor ξ and natural frequency ω.
Control law is given by
2
1
2
2
1
1
0 )
1
( 


 




 k
k
k
k
k
k u
u
e
g
e
g
e
g
u 

The controller parameters 2
2
2
1
2
0 ,
, c
c
c g
g
g and 2
c
 are calculated by solving following diophantine equation
)
(
)
(
)
(
)
(
)
( 1
1
1
1
1 





 q
D
q
Q
q
B
q
P
q
A
where polynomials are as follows
2
2
1
1
1
ˆ
ˆ
1
)
( 




 q
a
q
a
q
A
2
1
1
0
1 ˆ
ˆ
)
( 



 q
b
q
b
q
B
)
1
)(
1
(
)
( 1
1
1 




 q
q
q
P 
2
2
2
1
2
1
2
0
1
)
( 




 q
g
q
g
g
q
Q c
c
c
2
2
1
1
1
1
)
( 




 q
d
q
d
q
D
1
for
1
cos
)
exp(
2 2
0
0
1 





 


 


 T
T
d
1
for
1
cosh
)
exp(
2 2
0
0
1 





 


 


 T
T
d
 
0
2 2
exp T
d 


Solving the diophantine equation leads to following relations for controller parameters
2
2
2
2
2
ˆ
ˆ
a
b
g c
c 

; 1
1
2
2
r
s
g c 











 1
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
2
1
1
0
2
2
1
2
2
1
a
a
b
b
g
b
a
g c
c
)
ˆ
1
(
ˆ
1
1
1
1
2
0 



 a
d
b
g c
Where
  
2
0
2
1
0
1
1
0
1
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ b
a
b
b
a
b
b
r 


    
 
1
1
1
2
0
1
0
2
1
1
1
0
2
1
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ b
d
b
d
b
b
b
a
b
a
b
b
a
s 





IV. Simulation Responses:
In this section Self Tuning Regulator(c1) and self tuning pole placement controller(c2) is implemented in
order to obtain the closed loop response of the process. The simulation of the above controllers are performed
using MATLAB/SIMULINK. In this work 0-5cm(R1), 5-10cm(R2), 10-15cm(R3) and 15-20 cm(R4) are the
various operating regions (ORs) considered for the level control. The operating regions are 0-5cm is R1, 5-
10cm is R2, 10-15cm is R3, 15-20cm is R4. R1, R2, R3, R4 are the Region1, Region2, Region3 and Region4
Respectively.

A. Process output and controller output:
The closed loop response of the process with c1 and c2 for various operating regions are shown in Fig. 3. A
disturbance of -1 cm is given at 250 sec at second operating region(R2) and 2 cm is given at 350 sec at third
region(R3).
Fig. 3: Closed loop response of the process with c1 and c2.
For the R3 and R4 ORs, The closed loop servo and regulatory response have lesser overshoot and under
shoot compared to the lower operating regions (R1,R2) and the responses which are presented in fig 3. The
closed loop response of the process with Self Tuning pole placement controller(c2) for various operating
regions have no overshoot and undershoot.
The self tuning regulator(c1) rejects disturbance faster but the self tuning pole placement controller(c2)
takes long time to reject the disturbance. The controller output for c1 and c2 for various operating regions are
shown in fig.4.
Fig. 4: Controller Output of the Self Tuning Regulator.
B. Adaptation of controller parameters:
The adaptation of controller parameters r1c1, s0c1, r1C1, s1c1, tc1 for self tuning regulator and 2
c
 , g0c2, g1c2, g2c2
for self tuning pole placement regulator for various operating regions are listed in table I. Initially at 0 second
the controller parameters are at zero and for every second the controller parameters are updated with the change
in process parameters.
Table I: Adaptation of Controller Parameters For Self Tuning Pole Placement Controller.
Region Self tuning Regulator(c1) Self tuning pole placement controller(c2)
r1c1 s0c1 s1c1 tc1
2
c
 g0c2 g1c2 g2c2
R1 -3.354 -2.405 -0.1607 -2.354 2.999 -3.118 0.6786 0.5478
R2 -3.247 -2.274 -0.1516 -2.247 2.355 -2.372 0.4961 0.01797
R3 -3.156 -2.176 -0.1475 -2.158 2.055 -1.782 0.19 0.1225
R4 -3.123 -2.128 -0.154 -2.123 2.339 -2.266 0.4083 0.2113
The adapted controller parameters r1c1, s0c1, r1C1, s1c1, tc1 for self tuninig regulator(c1) and 2
c
 , g0c2, g1c2, g2c2
for self tuning pole placement regulator(c2) the various operating regions are shown in Fig.5.
C. Estimation of model parameters:
The model parameters are a1c1, a2c1, b0c1, b1c1 for self tuning tuning regulators and a1c2, a2c2, b0c2, b1c2 for self
tuning pole placement controller for various operating regions are listed in table II. The process parameters are
updated using least square algorithm. In adaptive control for every second the process parameters are to be

estimated in order to adapt the controller parameters. Initially at 0 sec the process parameters are at zero and for
every second the process parameters are estimated and for every iteration process parameters are updated. For
0-150 sec(R1), 150-300 sec(R2), 300-400 sec(R3) and 400-500 sec (R4) are tabulated in Table II.
Fig. 5: Adaptation of the controller parameters.
Table II: Estimation Of Process Parameters For Self Tuning Pole Placement Controller.
Regio
n
Self tuning Regulator Self tuning pole placement controller
a1c1 a2c1 b0c1 b1c1 a1c2 a2c2 b0c2 b1c2
R1 -0.084 -1.305 0.159 0.3093 -1.226 0.0081 0.2398 0.7054
R2 -0.082 -1.293 0.164 0.295 -1.251 0.2292 0.2557 0.6052
R3 -0.080 -1.123 0.169 0.1246 -1.266 0.1291 0.269 0.7303
R4 -0.079 -1.237 0.172 0.2378 -1.279 0.1238 0.2821 0.7056
The adaptation of estimated model parameters a1c1, a2c1, b0c1, b1c1 for c1 and a1c2, a2c2, b0c2, b1c2 for the
various operating regions are shown in Fig. 6.
Fig. 6: Estimated Process Parameters.
V.Time Integral Criteria and simple Criteria Values:
The time integral criteria values are obtained for various operating regions. The ISE and IAE values are
obtained and the values are tabulated in Table III.
Table III: Time Integral Criteria Values For Self Tuning Regulator And Self TuningPole Placement Controller.
Region Self tuning regulator(c1) Self tuning pole placement controller(c2)
ISE IAE ITAE ISE IAE ITAE
R1 364 103.9 2240 105.8 33.04 234.5
R2 386.5 136.9 9159 168.5 57.96 4510
R3 417.2 171.4 2.08*104
247.8 105.2 2.035*104
R4 440 203.8 3.5*104
300.9 122.2 2.721*104
The simple criteria values are obtained for various operating regions and tabulated in Table IV.
Table IV: Simple Criteria Values For For Self Tuning Regulator And Self Tuning Pole Placement Controller.
Region
Self tuning regulator(c1) Self tuning pole placement controller(c2)
ts tp %Mp ts tp %Mp
R1 73 10 100 50 8 6
R2 32 7 15.73 28 12 2
R3 30 7 11.7 21 12 1.153
R4 35 7 9.5 16 12 0.294

Conclusion:
This paper has dealt with the design and implementation of Self tuning regulator and self tuning pole
placement controller. The comparison of the present two controllers reveals that when comparing the time
integral criteria values for two controllers self tuning pole placement controller(c2) gives lesser ISE, IAE and
ITAE values than Self tuning regulator(c1). From the servo response it can be found that the process with
controller c2 settles faster and have no offset when comparing with c1and also it has less settling time.From the
regulatory response it can be found that c1 rejects disturbance faster than c2.
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