A feedback control system is used to control the tank temper

A feedback control system is used to control the tank temperature (T). Steam flow rate in the heating coil is selected as the manipulated variable.

Dynamic system behavior

Describe the system (give background)

Derive the model equations. (Chapter 2)

Using the information shown below, derive transfer function for the process. (Chapter 3)

Determine the response of the outlet temperature to the tank to a step change in the inlet temperature of from 60°C to 70°C. (Chapter 4)

Discuss the stability of the process. (Chapter 5)

Control Scheme

Draw a block diagram of a classical feedback control system. (Chapter 7)

Using the information shown below, derive a transfer function for each block. (Chapter 4-8)

Simulate the closed-loop response for the PI controller with Kc= 5, 10, 20,100 and a +20 % step change in disturbance variable. (Chapter 10)

Simulate the closed-loop response for the PI controller setting given below and a -30 % step change in disturbance variable. (Chapter 10)

Simulate the closed-loop response for the PI controller setting given below and a -10 % step change in the set point. (Chapter 10)

Carryout controller tuning by Ziegler-Nicholas method to get the best controller parameters for PI controller. (Chapter 11)

Compare the responses for Tyreus-Luyben PI parameters with Zeigler-Nicholas PI. (Chapter 11)

Carryout out stability analysis using Bode criterion. (Chapter 13)

Use appropriate values of gain margin and phase margin to design the controller. (Chapter 13)

Design a closed loop IMC controller that gives a first order plus time delay response for a step change. Assuming that the model perfectly captures the process behavior. (Chapter 11)

Volume of the tank= 1000 L

Volumetric flow rate= 200 L/min

Gv 2/(0.5s 1)

Solution

solution:

1)we have to design control system to control temperature of tank within given limit ,where its block diagram is as follows

where Kc=gain of PI controller

Gv= control valve gain

Gm=feedback gain

2)operation:

in this control system,tank tmperature is sense by thermocouple via measurement system and converted into feedback signal by feedback element with gain Gm and then it is sum up and compare by differential amplifier and corresponding error signal is then process by PI controller with gain Kc and it will devloped corresponding manipulated signal to control valve with gain Gv ad control valve accordingly set flow rate and it will set the temperature of tank ,this is algorithm with which control system will works and gives us controlled output.

3)here transfer function of system is given by

To(s)/Ti(s)=Kc*Gv/[1+(Kc*Gv*Gm)]

on putting value given in system data and with Kc=5 we get transfer function as

T.F.=To(s)/Ti(s)=20s+60/s^2+5s+66

where on taking inverse laplace transform it will gives us for step input of =70-60=10 C as

To(t)=200*exp^(-2.5t){cos(7.7298t)+(12.9369)sin(7.7298t)}

5)in this way above points gives us control system,transfer function,its model equation in time domain and output response as mention above.

6)in this way by bode plot we get stability of system by bode plot as follows

transfer function as follows=T.F.=To(s)/Ti(s)=20s+60/s^2+5s+66

N(s)=20s+60

we get zeroes as S=-3

and for D(s)=s^2+5s+66

S=-2.5 or S=-2.5

as all roots are negative in real part and hence all roots are lies in LH plane and hence system output response is stable for input response.

7)in this way first five subpoints are covered in above answer