Fuzzy operating condition of temperatures. The servo response of

Fuzzy
based PID controller is implemented to control the reactant temperature of a
continuous stirred tank reactor (CSTR). The plant is modelled mathematically
for the normal operating condition of CSTR. Then the transfer function model is
obtained from the process. The analysis is made for the given process for the
design of controller with conventional PID (trial and error method), Ziegler
Nichols method and Fuzzy logic method. The servo response is obtained for all
the above three methods and traced different operating condition of
temperatures. The servo response of Fuzzy based PID controller has given better
setpoint tracking capability than the Ziegler-Nichols method and conventional
PID method.

SYSTEM IDENTIFICATION

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A.   
EXPERIMENTAL
SETUP

A
real time experimental setup is constructed for CSTR. The process control
system is interfacing DAQ module to the user controlling system i.e. personal
computer. The laboratory set up for this system is shown in figure I. it
consists of a feed tank a cold water reservoir, pumps, rotameter, temperature sensors
(RTD), a pneumatic pressure control valve, electro-pneumatic converter (I/P
converter) an interfacing DAQ module and a personal computer (PC). Temperature
sensors are interfaced with computer using DAQ module in the USB port of the PC.
The experimental control algorithm developed on .MATLAB SIMULINK on the
personal computer and implemented on the system through the DAQ module.

After
computing the control algorithm in the PC, control signal is transmitted to I/P
converter in the form of current signal (4-20mA), which passes the air signal
to the pneumatic control valve. The pneumatic control valve is actuated by this
signal to produce the required flow of water through the cooling jacket.

B.    
System
Identification

In
order to implement the Model predictive Controller, the model of the system is
required and it needs to be derived. The model is found out by empirically
determining the system. By keeping the average inlet flow rate constant of the
feeding hot water to the reactor, the output temperature of the reactor is
continuously monitored. A step change was given in the feeding temperature and
again the reactor temperature is measured. This open loop input and output data
is recorded, and is used in System Identification Toolbox to find out the model
of the system. From this transfer function is obtained, which again exhibits
the nonlinear response. The following transfer function is obtained. This
transfer function will be further used for the controlling temperature of the
reactor using model predictive controller scheme. The transfer function model
of the CSTR real process is realized using MATLAB and simulations are performed.

Transfer
function of the CSTR:

Thus
the mathematical model of CSTR real process was obtained in the discrete state
space form as follows.

COMPUTING CONTROL
STRATEGIES

 

A.   
PID
CONTROLLER

 

Traditional
PID controllers are easy to understand and implement, and is very popular in
linear control systems. However, PID always has this requirement of re-tuning
when desirable working condition changed or emergency happens. As implied by
the name, a PID (proportional-integral-derivative) controller consists of three
parts: proportional part, integral part and derivative part.

The weighted sum of these three parts is used to adjust
the process via a control valve. Usually a PID is formulated as follows:

Here Kp, Ki and Kd are called proportional gain and derivative
gain. They are key parameters of the PID controller. The tuning of the PID
controller is performed in MATLAB Simulink.

 

B. MPC Controller

The model predictive control is a strategy that is based
on the explicit use of some kind of model of the system which is able to
predict the future values of the output over a certain time horizon, the prediction
horizon. The control algorithm can be described as follows as follows 3.

1.
At each sampling time, the value of the controlled variable y (t + k) is
predicted over the prediction horizon k=1,……P. This prediction depends on the
future instant values of the control variable u (t + k) within control horizon
of k=1,……M, where M?P.

2.
A reference trajectory r (t + k), k=1,……N is defined which describes the
desired trajectory to be followed as reference over the prediction horizon by
the system response.

3.
The future control action u (t + k) is computed such that a cost function is
minimised.

4.
The optimised control is then applied to the plant and the plant outputs are
measured.by using these measurements of the plant states as the initial states
of the model to perform the next iteration.

 

Step
1 to 4 are to be repeated at each sampling instant; this is called receding
horizon strategy. The above steps can be expressed by the following equations:

where
k is the time step, u(k) is the control vector at time k, () and x(k) are the desired
output (reference) and predicted output vector of the model at time k respectively,
p is the prediction horizon time. The block diagram of a model predictive
controller is shown in Figure 3.

As
the control variables in a MPC controller are calculated based on the predicted
output, the model reflects the dynamic behaviour of the system accordingly.

 

 

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