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

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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