Acc shams

Abstract— The proposed PID tuning method has similar
approach to the recently published paper of Shamsuzzoha and
Skogestad (2010). It is one step procedure to obtain the PI/PID
setting which gives the better performance and robustness. The
method requires one closed-loop step setpoint response
experiment using a proportional only controller with gain Kc0.
On the bases of simulations for a range of first-order with delay
processes, simple correlations have been derived to give PI/PID
controller settings. The controller gain (Kc/Kc0) is only a
function of the overshoot observed in the setpoint experiment.
The controller integral and derivative time (τI and τD) is mainly
a function of the time to reach the first peak (tp). The proposed
tuning method shows better performance than Shamsuzzoha
and Skogestad [1] for broad range of processes.
I. INTRODUCTION
He proportional, integral, and derivative (PID) controller
is widely used in the process industries due to its
simplicity, robustness and wide ranges of applicability in the
regulatory control layer. One survey of Desborough and
Miller [2] indicates that more than 97% of regulatory
controllers utilize the PID algorithm. A recent survey of
Kano and Ogawa [3] shows that the ratio of applications of
different type of controller e.g., PID control, conventional
advanced control and model predictive control is about
100:10:1. Although the PID controller has only three
adjustable parameters, they are difficult to be tuned properly.
One reason is that tedious plant tests are required to obtain
improved controller setting.
There are two approaches for the controller tuning and one
may use open-loop or closed-loop plant tests. Most tuning
approaches are based on open-loop plant information;
typically the plant’s gain (k), time constant (τ) and time delay
(θ). One popular approach is direct synthesis (Seborg et
Manuscript received September 25, 2011.
Acknowledgement: The authors would like to acknowledge the support
(Project Number: SB101016) provided by the Deanship of Scientific
Research at King Fahd University of Petroleum and Minerals (KFUPM).
M. Shamsuzzoha is with the Department of Chemical Engineering, King
Fahd University of Petroleum and Minerals, Daharan, 31261, Kingdom of
Saudi Arabia, Phone: +966-3-860-7360, (email: mshams@kfupm.edu.sa)
Moonyong Lee is with the School of Chemical Engineering and
Technology, Yeungnam University, Kyongsan 712-749, Korea, Phone:
+82-53-810-2512, (email: mynlee@ynu.ac.kr)
Hiroya Seki is with the Chemical Resources Laboratory, Tokyo Institute
of Technology, 4259-R1-19 Nagatsuta, Midori-ku, Yokohama, 226-8503
Japan (e-mail: hseki@pse.res.titech.ac.jp)
al.,[4]) and other is the IMC-PID tuning method of Rivera et
al.[5]. Both the methods give very good performance for
setpoint changes but sluggish responses to input (load)
disturbances for lag-dominant (including integrating)
processes with τ/θ>10. To improve load disturbance
rejection, Skogestad [6] proposed the modified SIMC
method where the integral time is reduced for processes with
a large value of the time constant τ. The SIMC rule has one
tuning parameter, the closed-loop time constant τc, and for
“fast and robust” control is recommended to choose τc= θ,
where θ is the (effective) time delay. However, these
approaches require that one first obtains an open-loop model
of the process and then tuning of the control loop. There are
two problems here. First, an open-loop experiment, for
example a step test, is normally needed to get the required
process data. This may be time consuming and may upset the
process and even lead to process runaway. Second,
approximations are involved in obtaining the process
parameters (e.g., k, τ and θ) from the data.
The main alternative is to use closed-loop experiments. One
approach is the classical method of Ziegler-Nichols [7]
which requires very little information about the process.
However, there are several disadvantages. First, the system
needs to be brought its limit of instability and a number of
trials may be needed to bring the system to this point.
Another disadvantage is that the Ziegler-Nichols [7] tunings
do not work well on all processes. It is well known that the
recommended settings are quite aggressive for lag-dominant
(integrating) processes (Tyreus and Luyben,[8]) and quite
slow for delay-dominant process (Skogestad, [6]). A third
disadvantage of the Ziegler-Nichols [7]) method is that it can
only be used on processes for which the phase lag exceeds -
180 degrees at high frequencies. For example, it does not
work on a simple second-order process. Recently,
Shamsuzzoha and Skogestad [1] have developed new
procedure for PI/PID tuning method in closed-loop mode.
Their method is based on the SIMC tuning rule and provides
satisfactory result for both the performance and robustness.
For the PID tuning parameter they need to repeat the
experiment with PD controller on the basis of the prior
information obtain from P controller test. They
recommended adding the derivative action only for dominant
second-order process.
Closed-loop PI/PID Controller Tuning for Stable and Unstable
Processes
M.Shamsuzzoha*, Moonyong Lee, Hiroya Seki
T
2012 American Control Conference
Fairmont Queen Elizabeth, Montréal, Canada
June 27-June 29, 2012
978-1-4577-1096-4/12/$26.00 ©2012 AACC 2368

Therefore, it is important to have other tuning method based
on the closed-loop experiment which gives better
performance and robustness. In this method it is simple to
obtain the PID tuning parameters in one step for improved
performance while satisfying the other concern during the
closed-loop experiment like reduces the number of trails, and
works for a wide range of processes. IMC-PID Controller
Tuning Rule
The motivation of this section is to develop IMC-PID
controller tuning for first order process with delay. In
process control, a first-order process with time delay is a
common representation of the process dynamics:
-
( )
1
s
ke
g s
s
θ
τ
=
+
(1)
Here k is the process gain, τ lag time constant and θ the time
delay. Most processes in the chemical industries can be
satisfactorily controlled using a PID controller:
( )
1
1c D
I
c s K s
s
τ
τ
 
= + + 
 
(2)
The other structure of the PID controller like series form of
PID can easily be transform from Eq. (2). The conventional
feedback controller which is equivalent to the IMC controller
can be expressed by following relation.
( )
1
q
c s
gq
=
− %
(3)
where g% denotes the process transfer function, c and q are the
conventional and IMC controller, respectively. The IMC
controller is designed in two steps:
Step 1: The process model g% is decomposed into two parts:
M Ag p p=% (4)
where pm and pA are the portions of the model inverted and
not inverted, respectively, by the controller (pA is usually a
non-minimum phase and contains dead times and/or right
half plane zeros); pA(0)=1.
Step 2: The IMC controller is designed by
-1
Mq p f= (5)
The IMC filter f is usually given as 1( 1)r
cf sτ= + and cτ is an
adjustable parameter which controls the tradeoff between the
performance and robustness; r is selected to be large enough
to make the IMC controller semi-proper. Consider
approximation of the dead time term in Eq. (1) by first order
Pade approximation:
( )
1-
2
( )
1 1
2
k s
g s
s s
θ
θ
τ
 
 
 =
 
+ + 
 
(6)
The resulting IMC-PID tuning formula after simplification is
obtain in Eq.(7) for the given process in Eq. (1).
( )
2
2
c
c
K
k
τ θ
τ θ
+
=
+
(7a)
2
I c
θ
τ τ= + (7b)
2
D
τθ
τ
τ θ
=
+
(7c)
The PID controller designed on the basis of the IMC
principle provides excellent set-point tracking, but has a
sluggish disturbance response, especially for processes with
a small θ/τ ratio [4,6,9]. To improve the load disturbance
response Skogestad [6] recommended modifying the integral
time as
I cτ =4(τ +θ) (8)
Therefore, the integral time in Eq.(7b) is modified for the
improved disturbance
I cτ =min , 4(τ +θ)
2
c
θ
τ
  
+  
  
(9)
τc= θ has been recommend which gives maximum sensitivity
(Ms)=1.70 approximately. The revised tuning method for the
PID controller tuning is given as:
2
3
cK
k
τ θ
θ
+
= (10a)
min , 8
2
I
θ
τ τ θ
  
= +  
  
(10b)
2
D
τθ
τ
τ θ
=
+
(10c)
I. CLOSED-LOOP EXPERIMENT
This section is devoted for the development of the PI/PID
controller based on the closed-loop data which resembles the
proposed tuning method in Eq.(10). The simplest closed-
loop experiment is probably a setpoint step response (Fig. 1)
where one maintains full control of the process, including the
change in the output variable. The simplest to observe is the
time tp to reach the (first) overshoot and its magnitude, and
this information is therefore the basis for the proposed
method.
The proposed procedure is as follows (Shamsuzzoha and
Skogestad, [1]):
1. Switch the controller to P-only mode (for example,
increase the integral time τI to its maximum value or set the
integral gain KI to zero). In an industrial system, with
bumpless transfer, the switch should not upset the process.
2. Make a setpoint change that gives an overshoot between
0.10 (10%) and 0.60 (60%); about 0.30 (30%) is a good
value. Record the controller gain Kc0 used in the experiment.
Most likely, unless the original controller was quite tightly
tuned, one will need to increase the controller gain to get a
sufficiently large overshoot.
Note that small overshoots (less than 0.10) are not
considered because it is difficult in practice to obtain from
experimental data accurate values of the overshoot and peak
time if the overshoot is too small. Also, large overshoots
(larger than about 0.6) give a long settling time and require
2369

more excessive input changes. For these reasons we
recommend using an “intermediate” overshoot of about 0.3
(30%) for the closed-loop setpoint experiment.
3. From the closed-loop setpoint response experiment, obtain
the following values (see Fig. 1):
• Fractional overshoot, (∆yp - ∆y∞) /∆y∞
• Time from setpoint change to reach peak output
(overshoot), tp
• Relative steady state output change, b = ∆y∞/∆ys.
Here the output variable changes are:
∆ys: Setpoint change
∆yp: Peak output change (at time tp)
∆y∞: Steady-state output change after setpoint step test
To find ∆y∞ one needs to wait for the response to settle,
which may take some time if the overshoot is relatively large
(typically, 0.3 or larger). In such cases, one may stop the
experiment when the setpoint response reaches its first
minimum and record the corresponding output, ∆yu.
∆y∞ = 0.45(∆yp + ∆yu) (11)
The details about how to obtaining Eq.(11) is given in
Shamsuzzoha and Skogestad (2010).
II. CORRELATION BETWEEN SETPOINT RESPONSE AND THE
IMC-PID-SETTINGS
The objective of this paper is to provide a one step
procedure in closed-loop for controller tuning similar to the
Shamsuzzoha and Skogestad (2010) and Ziegler-Nichols
(1942) method. Thus, the goal is to derive a correlation,
preferably as simple as possible, between the setpoint
response data (Fig. 1) and the Proposed PID settings in Eq.
(10), initially with the choice τc=θ. For this purpose, we
considered 15 first-order with delay models g(s)=ke-θs
/(τs+1)
that cover a wide range of processes; from delay-dominant to
lag-dominant (integrating):
τ/θ=0.1,0.2,0.4,0.8,1.0,1.5,2.0,2.5,3.0,7.5,10.0,20.0,50.0,100
Since we can always scale time with respect to the time delay
(θ) and since the closed-loop response depends on the
product of the process and controller gains (kKc) we have
without loss of generality used in all simulations k=1 and
θ=1.
For each of the 15 process models (values of τ/θ), we
obtained the PID-settings using Eq. (10) with the choice
τc=θ. Furthermore, for each of the 15 processes we generated
6 closed-loop step setpoint responses using P-controllers that
give different fractional overshoots.
Overshoot= 0.10, 0.20, 0.30, 0.40, 0.50 and 0.60
In total, we then have 90 setpoint responses, and for each of
these we record four data: the P-controller gain Kc0 used in
the experiment, the fractional overshoot, the time to reach
the overshoot (tp), and the relative steady-state change, b =
∆y∞/∆ys.
Controller gain (Kc). We first seek a relationship between
the above four data and the corresponding proposed
controller gain Kc. Indeed, as illustrated in Fig. 2, where we
plot kKc as a function of kKc0 for the 90 setpoint
experiments, the ratio Kc/Kc0 is approximately constant for a
fixed value of the overshoot, independent of the value of τ/θ.
Thus, we can write
c
c0
K
=A
K
(12)
py∆
pt
y∞∆ sy∆
t
0t =
θ
uy∆
sy∆
Fig. 1. Closed-loop step setpoint response with P-only control.
0 20 40 60 80 100 120
0
10
20
30
40
50
60
70
kKc0
kKc
0.10 overshoot
kK
c
=1.1621kK
c0
0.20 overshoot
kK
c
=0.9701kK
c0
0.30 overshoot
kK
c
=0.841kK
c0
0.40 overshoot
kK
c
=0.7453kK
c0
0.50 overshoot
kK
c
=0.6701kK
c0
0.60 overshoot
kK
c
=0.6083kK
c0
Fig. 2. Relationship between P-controller gain kKc0 used in setpoint
experiment and corresponding proposed controller gain (Eq. 10a) kKc.
where the ratio A is a function of the overshoot only. In Fig.
3 we plot the value of A, which is obtained as the best fit of
the slopes of the lines in Fig. 2, as a function of the
overshoot. The following equation (solid line in Fig. 3) fits
the data in Fig. 2 well and given as:
A=[1.55(overshoot)2
-2.159 (overshoot)+1.35] (13)
2370

0.1 0.2 0.3 0.4 0.5 0.6
0.7
0.8
0.9
1
1.1
overshoot (fractional)
A
y = 1.55*(overshoot)2
- 2.159*(overshoot) + 1.35
Fig. 3. Variation of A with overshoot using data (slopes) from Fig. 2.
0.1 0.3 0.5 0.6
0
0.1
0.2
0.3
0.4
0.5
Overshoot
θ/tp
0.43 (τI1
)
0.305 (τI2
)
τ/θ=0.1
τ/θ=8
τ/θ=100
τ/θ=1
Fig. 4. Ratio between delay and setpoint overshoot peak time (θ/tp) for P-
only control of first-order with delay processes (solid lines); Dotted lines:
values used in final correlations, Shamsuzzoha and Skogestad (2010).
Integral time (τI). It is interesting to find a simple
correlation for the integral time. The proposed method in Eq.
(10b) uses the minimum of two values, it seems reasonable
to look for a similar relationship, that is, to find one value
(τI1 =τ) for processes with a relatively large delay, and
another value (τI2 =8θ) for processes with a relatively small
delay including integrating processes.
(1) Process with relatively large delay: This case arise
when processes have a relatively large delay i.e., τ/θ<8, the
integral action in the proposed tuning rule is to use τI = (τ+
θ/2). Rearrangement of Eq.(10a) is given as
3
2
ckK θ θ
τ
−
= (14)
Adding both the side θ/2 in Eq.(14) and substitute (τ+
θ/2)=τI, we get
I 1.5 ckKτ θ= (15)
In Eq. (15), we also need the value of the process gain k, and
to this effect write
kKc= kKc0.Kc/ Kc0 (16)
Here, the value of the loop gain kKc0 for the P-control
setpoint experiment is given from the value of b:
c0
b
kK =
(1-b)
(17)
Substituting kKc from Eq. (17) and Kc/ Kc0=A into Eq. (15)
and given as
I
b
1.5A
(1-b)
τ θ= (18)
To prove this, the closed-loop setpoint response is ∆y/∆ys =
gc/(1+gc) and with a P-controller with gain Kc0, the steady-
state value is ∆y∞/∆ys = kKc0/(1+kKc0)=b and we derive
Eq.(17). The absolute value is included to avoid problems if
b>1, as may occur for an unstable process or because of
inaccurate data.
It is possible to obtain the value of time delay θ directly from
the closed-loop setpoint response, but usually this is not
always easy task. The reasonable correlation has been
developed by Shamsuzzoha and Skogestad [1] for the θ and
the setpoint peak time tp which is easier to observe.
For processes with a relatively large time delay (τ/θ<8), the
ratio θ/tp varies between 0.27 (for τ/θ= 8 with overshoot=0.1)
and 0.5 (for τ/θ=0.1 with all overshoots). For the
intermediate overshoot of 0.3, the ratio θ/tp varies between
0.32 and 0.50. A conservative choice would be to use
θ=0.5tp because a large value increases the integral time.
However, to improve performance for processes with smaller
time delays, we propose to use θ=0.43tp which is only 14%
lower than 0.50 (the worst case).
In summary, we have for process with a relatively large time
delay:
0.645
(1- )
I p
b
A t
b
τ = (19)
(2) Process with relatively small delay. Shamsuzzoha and
Skogestad [1] method and in this proposed tuning rule have
same integral action for the lag-dominant process. The
integral time for a lag-dominant (including integrating)
process with τ/θ>8 the proposed tuning rule for integral time
gives
τI2=8θ (20)
For τ/θ>8 we see from Fig. (4) that the ratio θ/tp varies
between 0.25 (for τ/θ=100 with overshoot=0.1) and 0.36 (for
τ/θ=8 with overshoot 0.6). We select to use the average value
θ= 0.305tp which is only 15% lower than 0.36 (the worst
case). Also note that for the intermediate overshoot of 0.3,
the ratio θ/tp varies between 0.30 and 0.32. In summary, we
have for a lag-dominant process
I2 pτ =2.44t (21)
Conclusion. Therefore, the integral time τI is obtained as the
minimum of the above two values:
I pτ =min 0.645 , 2.44t
(1- )
p
b
A t
b
 
  
 
(22)
2371

Derivative action (τD): Although a significant number of the
PID controllers switched off their derivative part but proper
use of derivative action can increase stability and improve
the closed-loop performance. The derivative action is very
important for slow moving loops where overshoot is
undesirable e.g., temperature loop. The motivation of this
section is to develop the approach for inclusion of the
derivative action from closed-loop data. In the proposed
study the derivative action is recommended for the process
having 1τ θ ≥ which can give performance improvement.
Substitute the value of 0.5Iτ τ θ= − into 1τ θ ≥ and after
rearrangement the resulting equation is
( )0.5
1Iτ θ
θ
−
≥ (23)
After simplification it is 1.5Iτ θ ≥ and resulting constrain is
1.0ckK ≥ . The corresponding closed-loop condition for the
derivative action is given as:
( )
b
A 1
1-b
≥ (24)
Case I: For approximately integrating process (τ>> θ),
where integral time is τI =8θ and in the closed-loop the time
delay θ= 0.305tp. The derivative time τD1 in Eq. (10c) can be
approximated as
1
0.305
0.15
2 2 2
p
D p
t
t
τθ θ
τ
τ
≈ = = = (25)
Case II: The processes with a relatively large delay, for this
case integral time τI=(τ+0.5θ) and time delay in closed-loop
is θ=0.43tp. For such cases the derivative action is
recommended only if τ/θ ≥ θ. Assuming the case when τ=θ
the τD2 is given from Eq. (10c) as
2 2
2
0.43
0.1433
2 3 3 3
p
D p
t
t
θ θ θ
τ
θ θ θ
≈ = = = =
+
(26)
The derivative action is only recommended for the process
having 1τ θ ≥ and in the closed-loop this criteria is
( )
b
A 1
1-b
≥
.
Summary: The derivative action for both the cases i.e., τD1
and τD2 are approximately same and the conservative choice
for the selection of τD is given as
( )
0.14 1
1-
D p
b
t if A
b
τ = ≥
(27)
Selection of Proportional Controller Gain (Kc0): An
overshoot of around 0.3 is recommended for the proposed
study. Sometimes achieving the P-controller gain (Kc0) via
trial and error which gives the overshoot around 0.3 can be
time consuming.
Therefore, an effective approach to get the value of Kc0
which gives the overshoot around 0.3 is very significant for
the proposed method. It is important to note that this
procedure requires initial information of the first closed-loop
experiment. Let’s assume for the first closed-loop test P-
controller gain of Kc01 is applied and resulting overshoot OS1
is achieved that is between 0.1 to 0.60 but not around 0.30.
Let the target overshoot be OS and the target P-controller
gain be Kc0. In the proposed closed-loop tuning method the
goal is to match the performance with IMC-PID tuning rule
and for this only maintains a constant P gain Kc, regardless
of the overshoot that resulted from the closed-loop setpoint
test. Ideally, Kc should be the same as that determined with
different overshoots from various closed-loop setpoint test
and the resulting correlation is given as:
( ) ( ) ( ) ( )2 2
1 1 01 01.55 OS 2.159 OS 1.35 1.55 OS 2.159 OS 1.35c cK K   − + = − +      
(28)
The above Eq.(28) gives a general guideline for choosing the
P-controller gain for the next closed-loop setpoint test. As it
is mentioned earlier the proposed method is good agreement
with the IMC-PID for the overshoot around 0.3. Therefore
the overshoot in Eq.(28) is set as 0.3 and after simplification
the gain for the next closed-loop test is recommended as:
( ) ( )( )2
0 1 1 011.19 1.45 OS 2.02 OS 1.27c cK K= − + (29)
It is important to note that we are not keen to achieve the
precise fractional overshoot of 0.3, so few trial is sufficient
to achieve the desire overshoot around 0.3 from above
equation.
III. SIMULATION
The proposed closed-loop tuning method has been tested on
broad class of the process model. It provides the acceptable
controller setting for all cases with respect to both the
performance and robustness. To show the effectiveness of
the proposed method two cases have been shown as a
representative example i.e., integrating with time delay and
higher order process with time delay. The simulation has
been conducted for three different overshoot (around 0.1, 0.3
and 0.6) and are compared with the recently reported method
of Shamsuzzoha and Skogestad[1].
Example 1: ( )
( )( )
2
1
6 1 2 1
s
s e
s s
−
− +
+ +
Example 2:
s
e
s
−
Figure 5 and 6 presents a comparison of the proposed
method with Shamsuzzoha and Skogestad [1] by introducing
a unit step change in the set-point at t = 0 and an unit step
change of load disturbance (at t = 100 for Example 1 and t =
50 for Example 2) at plant input. It is clear from Figure 5
and 6 that the proposed method gives better closed-loop
response for both the high order and integrating processes.
There are significant performance improvements in both the
case for the disturbance rejection while maintaining setpoint
performance.
The overshoot around 0.1 typically gives slower and more
robust PID-settings, whereas a large overshoot around 0.6
2372

gives more aggressive PID-settings. It is good because a
more careful step response results in more careful tunings
settings.
0 50 100 150 200
0.2
0.6
1
1.4
time
OUTPUTy
Shamsuzzoha and Skogestad method with F=1(overshoot=0.119)
Shamsuzzoha and Skogestad method with F=1 (overshoot=0.344)
Shamsuzzoha and Skogestad method with F=1(overshoot=0.608)
Proposed method with F=1 (overshoot=0.119)
Fig. 5. Responses for PID-control of high order process ( )
( )( )2
1
6 1 2 1
s
s e
s s
−
− +
+ +
,
Setpoint change at t=0; load disturbance of magnitude 1 at t=100.
IV. CONCLUSION
A simple approach has been developed for PI/PID controller
tuning by the closed-loop setpoint step using a P-controller
with gain Kc0. The PID-controller settings are then obtained
directly from following three data from the setpoint
experiment:
• Overshoot, (∆yp - ∆y∞) /∆y∞
• Time to reach overshoot (first peak), tp
• Relative steady state output change, b = ∆y∞/∆ys.
If one does not want to wait for the system to reach steady
state, one can use the estimate ∆y∞ = 0.45(∆yp + ∆yu).
The proposed tuning PID tuning method is:
c c0K =K A
I pτ =min 0.645 , 2.44t
(1- )
p
b
A t
b
 
  
 
( )
0.14 1
1-
D p
b
t if A
b
τ = ≥
where, A=[1.55(overshoot)2
-2.159 (overshoot)+1.35]
The proposed method works well for a wide variety of the
processes typical for process control, including the standard
first-order plus delay processes as well as integrating, high-
order, inverse response, unstable and oscillating process.
0 10 20 30 40 50 60 70 80 90 100
0
0.5
1
1.5
2
2.5
3
time
OUTPUTy
Fig. 6. Responses for PID-control of integrating processes
s
e s−
, Setpoint
change at t=0; load disturbance of magnitude 1 at t=50.
V. REFERENCES
[1] M. Shamsuzzoha, S. Skogestad, “The setpoint overshoot method: A
simple and fast closed-loop approach for PID tuning”, Journal of
Process Control, vol.20, pp.1220–1234,(2010).
[2] L. D. Desborough, R. M. Miller, “Increasing customer value of
industrial control performance monitoring—Honeywell’s
experience”. Chemical Process Control–VI (Tuscon, Arizona, Jan.
2001), AIChE Symposium Series No. 326. Volume 98, USA
(2002).
[3] M. Kano, M. Ogawa, “The state of art in chemical process control in
Japan: Good practice and questionnaire survey, Journal of
Process Control, (20), pp.969-982, (2010).
[4] D. E. Seborg, T. F. Edgar, D. A. Mellichamp, “Process Dynamics
and Control”, 2nd
ed., John Wiley & Sons, New York, U.S.A,
(2004).
[5] D. E. Rivera, M. Morari, S. Skogestad, “Internal model control. 4.
PID controller design”, Ind. Eng. Chem. Res., vol.25 (1) pp. 252–
265, (1986).
[6] S. Skogestad, “Simple analytic rules for model reduction and PID
controller tuning”, Journal of Process Control, vol.13, pp.291–
309, (2003).
[7] J. G. Ziegler, N. B. Nichols, “Optimum settings for automatic
controllers”, Trans. ASME, vol. 64, pp.759-768, (1942).
[8] B. D. Tyreus, W. L. Luyben, “Tuning PI controllers for
integrator/dead time processes”, Ind. Eng. Chem. Res. pp.2628–
2631, (1992).
[9]M. Shamsuzzoha, M. Lee, “IMC-PID controller design for improved
disturbance rejection” Ind. Eng. Chem. Res, vol. 46, No. 7, 2007,
pp. 2077-2091.
2373

Acc shams

More Related Content

What's hot

Viewers also liked

Similar to Acc shams

Recently uploaded

Acc shams