PLEASE ANSWER QUESTION 8

A liquid vessel has an inlet and an outlet streams. The outlet stream flows through a valve having a resistance R. To control the level at a specified value a PI (Proportional-Integral) controller placed on the inlet stream is used. You have been tasked with the design of the control system.

1. Develop a dynamic model of the liquid level behaviour.

2. Find the transfer function of the process system.

3. Determine the gain and the time constant of the process.

4. Specify the instrumentation required by the level control loop.

5. Draw a block diagram of the control system. Include any disturbance variables in the block diagram.

6. Determine the characteristic equation of the block diagram transfer function Assume that the transfer function of the PI controller is given by

7. Assuming a desired closed-loop time constant min determine the tuning parameters and of the PI controller using the Direct Synthesis Method.

8. Determine the time response of the level as a result of a unit step change in inlet flow.

9. Plot the level response as function of time.

10. If instead of feedback control feedforward control is desired how would implement such feedforward control in this process? Draw a diagram to illustrate your solution.

Data

Assume that the outflow can be expressed as where is the level in the surge vessel and is the valve resistance to flow.

Control valve transfer function

Transmitter transfer function

Surge vessel area 5 m2

Liquid level 2 m

Liquid flowrate 5 m3 /minute

A liquid vessel has an inlet and an outlet streams. The outlet stream flows through a valve having a resistance R. To control the level at a specified value a PI (Proportional-Integral) controller placed on the inlet stream is used. You have been tasked with the design of the control system.

1. Develop a dynamic model of the liquid level behaviour.

2. Find the transfer function of the process system.

3. Determine the gain and the time constant of the process.

4. Specify the instrumentation required by the level control loop.

5. Draw a block diagram of the control system. Include any disturbance variables in the block diagram.

6. Determine the characteristic equation of the block diagram transfer function Assume that the transfer function of the PI controller is given by

7. Assuming a desired closed-loop time constant min determine the tuning parameters and of the PI controller using the Direct Synthesis Method.

8. Determine the time response of the level as a result of a unit step change in inlet flow.

9. Plot the level response as function of time.

10. If instead of feedback control feedforward control is desired how would implement such feedforward control in this process? Draw a diagram to illustrate your solution.

Data

Assume that the outflow can be expressed as where is the level in the surge vessel and is the valve resistance to flow.

Control valve transfer function

Transmitter transfer function

Surge vessel area 5 m2

Liquid level 2 m

Liquid flowrate 5 m3 /minute