J044046467

Binu P. Mathew et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 4( Version 4), April 2014, pp.64-67
www.ijera.com 64 | P a g e
Modified Smith Predictor Based Control Of Cascaded Chemical
Reactor
Binu P. Mathew*, L. D. Vijay Anand**
*(Department of Electronics and Instrumentation Engineering, Karunya University, Coimbatore-46)
** (Department of Electronics and Instrumentation Engineering, Karunya University)
ABSTRACT
A cascade control with modified smith predictor is used for controlling an open loop unstable time delay
process. It has three controllers, one is for servo response other two are for regulatory response. For two
disturbance rejection controllers an analytical design method is used by proposing closed loop complementary
sensitivity function. These two controllers are PID controller cascaded with second order lead/lag filter. Setpoint
tracking controller is designed by using direct synthesis method. The main advantage of this control scheme is
that the servo response can be decoupled from the regulatory response.
Keywords – Cascade control, Disturbance rejection, Servo response, Smith predictor, Regulatory response
I. INTRODUCTION
Cascade control usually used in process
control industries-one of the most commonly used
multi loop control method, for the control of
parameters like temperature, pressure, flow etc. It
utilizes two loops- slave loop and master loop. Slave
loop is embedded within the master loop. Cascade
controllers are used when single loop controllers are
difficult to regulate the output in load disturbance.
The inner loop takes speeder response as
compared to the outer loop because inner loop
provides faster disturbance attenuation and minimizes
the disturbance before they affect the primary loop. A
better regulatory response is obtained by cascade
control than that existing in the slave loop. But if a
long time delay occurs in the outer loop it may not
give the satisfactory response to setpoint changes. In
order to avoid that problem a smith predictor scheme
is used in the outer loop of the cascade control
structure.
II. SYSTEM DESCRIPTION
2.1 Temperature process system
The temperature process is a nonlinear
process whose parameters vary with respect to the
process variable .In this air is drawn from atmosphere
by centrifugal blower is driven past a heater grid.
And the air is flowing through length of tube to
atmosphere again. Process is temperature level.
Control equipment measure the air temperature,
compare it with the value set by the operator and
generate a control signal which determine the amount
of electric power delivered to correcting element.
Figure1: Block Diagram of a Temperature Process
Figure 2: Hardware setup for Temperature Process
RESEARCH ARTICLE OPEN ACCESS

2.2 Block diagram:
Figure 3: Block diagram of proposed method
Cascade control structure with modified
smith predictor for open loop unstable process is
shown Fig.3 Gp1 and Gp2 are primary and secondary
process and Gm1 and Gm2 are the primary and
secondary model. Gcs is the setpoint tracking
controller for servo response, Gc1 and Gc2 are the
disturbance rejection controller for regulatory
response.
2.3 Process model
The Fig.4 shows the stirred chemical reactor
where cooling water flows through reactor jacket to
regulate the reactor temperature. The disturbance
variables such as reactant feed temperature and feed
composition is caused to change the reactor
temperature. The disturbance is handled by adjusting
cooling water on the inlet stream. However an
increase in cooling water temperature cause a
increase in reactor temperature cause the reduction in
the heat removal rate.
Figure 4: Process model of proposed system
If dynamic lag occur in the jacket as well as in the
reactor a feedback controller for the jacket
temperature whose setpoint is determined by reactor
temperature controller is added for cascade control
where reactor temperature controller is the primary
controller and jacket temperature controller is the
secondary controller.
LT : Level transmitter.
TT : Temperature transmitter
LC : Level controller
TC : temperature controller
III. MATHEMATICAL MODELLING:
The chemical reactor [2] is the process
considered which is given in Figure 5.
Figure 5: chemical reactor
HA : Partial molar enthalpies
ρi, ρ : Density of inlet and outlet
nA : Number of moles of A in the mixture
Fi, F : Volumetric flow rates of inlet and outlet
R : Rate of reaction per unit volume
Cp : Specific heat energy
P : Potential energy
K : Kinetic energy
U : Internal energy
E : Total energy
Using the law of conservation of mass,
accumulation of input of output of
total mass total mass total mass
time time time
     
     
      
     
     
     
  .............(1)i
d
V
dt
   
Using law of conservation of energy
accumulation of input of output of energy removed
total energy total energy total energy by coolant
time time time time
       
       
         
       
       
       
   i i i i
dH
Fh T Fh T Q
dt
    ……………..(2
)
Summarizing the above steps in the
modeling of a chemical reactor, we have
State Variables are V, T, CA
State Equations are

  /
0
...............................................(3)
.(4)
i
E RTiA
Ai A e A
p
dV
F F
dt
FdC Q
C C k C
dt V C V

 
   
IV. CONTROLLER DESIGN:
4.1 Design of slave loop controller:
For disturbance rejection the nominal
complementary sensitivity function for slave loop is
^
2 22
2 2 2
.............................(5)
1
c
dslave
G Gpd
T
d Gc Gp
 

The asymptotic constraint for rejecting step load
disturbance is
21/
lim (1 ) 0......................................(6)dslave
s
T

 
should be satisfied. Based on IMC theory
complimentary sensitivity function is
22
2
2
1
...............................(7)
( 1)
s
dslave
s
T e
s





The inner loop controller
Gc2=
2
1
1
dslave
dslave p
T
T G
…………………….(8)
22
2
2 1
s
p
k
G e
s





…………………………….(9)
And finally the inner loop controller
2
2 2
2
2 2 2
( 1)( 1)
[( 1) ( 1) ]
c s
s s
G
k s s e 
 
  
 

  
………(10)
4.2. Design of master loop controller:
For disturbance rejection nominal regulatory
response transfer function for master loop is
1 1 2
1 1 2
............................(11)
1
c p p
dslave
c p p
G G G
T
G G G


The asymptotic constraint for rejecting load
disturbance is
11/
lim (1 ) 0.................................(12)dslave
s
T

  B
ased on the IMC the desired closed loop
complementary sensitivity [3] function is
1
3
1
1
............................(13)
( 1)
ms
dslave
s
T e
s





and 1 2m   . The primary process
Gp1=
11
1 1
sk
e
s




………………………………....(14)
Finally the primary controller from the above result
1 1 2
1
1 2 1 1
( 1)( 1)( 1)
.........(15)
[( 1)( 1) ]
c ms
s s s
G
k k s s e 
  
  
  

 
4.3 Design of setpoint tracking controller:
The setpoint response transfer function is
taken in the form of low pass filter with time delay
for a unit step setpoint. The sepoint tracking
controller Gcs is obtained as
1 2 1 2 1 2
1 2
( ) 1
...........(16)
( 1)
cs
cs
s s k k
G
k k
   

   


V. RESULTS AND DISCUSSIONS:
MATLAB is a high performance
programming language for technical computation. It
integrates computation, visualization and
programming in an easy to use environment.
Fig6: Block diagram of cascade with smith predictor
Fig7: Nominal response of cascade with smith
predictor

Fig8: Cascaded smith with disturbance
Fig9: Response of cascaded smith with disturbance
5.1 Explanation:
The two controllers here are in the form of
PIDF ie.PID controller in series with lead/lag filter.
These two controllers rejects disturbances entering in
the two loops.ie the proposed control scheme gives
smoother control signals. It is clear that this scheme
provides robust performance in load disturbance
rejection.
VI. CONCLUSION AND FUTURE
WORK:
The controlling problem of an open loop
unstable process with time delay has been avoided by
proposing this control scheme. The cascade control
structure has ability to improve regulatory response
and the modified smith predictor compensate the
dead time.
This project can be extended using PSO algorithm
in order to obtain optimized results.
REFERENCES
[1] Jeo Gao, Multiple degrees of freedom
control for cascade process with time delay,
ISA Transactions 15 (2012) 3-7.
[2] Mohammad Ahamadi, Temperature control
of a continuous stirred tank reactor by two
different intelligent strategies, Internat J on
smart sensing and intelligent system 4 2011
2
3] Yin Cheng-qiang, Cascade control based on
minimum sensitivity in outer loop for
process with time delay, J Central South
University 19 2011 2689-2696.
[4] Tao Liu. “Enhanced IMC based load
disturbance rejection for integrating process
with slow dynamics”. ISA Transactions
(2010) 345-357.
[5] A. Seshagiri Rao, Enhancing the
performance of parallel cascade control
using smith predictor, ISA Transactions 40
2009 220-227.
[6] Ibrahim Kaya,A new smith predictor and
control of process with long dead time, ISA
Transactions 42 2009 101-110.

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