USE SIMULINK Matlab

PROBLEM: The system shown in figure below is controlled by a proportional controller. The concentration of salt in the solution leaving the tank is controlled by adding a concentrated solution through a control valve.

The following data apply:

• Concentration of concentrated salt solution C₁ = 25 lb salt/ft³ solution.
• Stream outlet is numbered with 3. Controlled concentration at output C₃ = 0.1 lb salt/ft³ solution.
• Control valve: The flow through the control valve varies from 0.002 to 0.0006 ft³/min with a change of valve-top pressure from 3 to 15 psi. This relationship is linear.
• Distance velocity lag: It takes 10 min for the solution leaving the tank to reach the concentration-measuring element at the end of the pipe. Assume gain of 1 for the measurement element.
• Neglect lags in the valve.
• Assume constant hold up.
• Stream 2 is pure water that fed is without any salt.
• The disturbance variable is flowrate of stream 2: q₂

1. Determine the transfer functions for C₃/Q₁ and C₃/Q₂.
2. Assume the process is controlled with a proportional controller. Create a block diagram for the process. Identify all the transfer functions.
3. If the gain of proportional controller is 100, plot the output of the controller for a unit-step change in load and set point, using simulink. Report the offset in each case.
4. Make a first order Pade approximation (1/1) for the time delay, use Routh stability criteria to determine the stability limits for K_c.
5. Use Simulink to identify K_cu and P_u by hit-and-trial.
6. Use ZN settings for the proportional-integral controller and plot using Simulink the output for a unit step set point change.
7. Use ZN settings for the proportional-integral-derivative controller and plot using Simulink the output for a unit step set point change.

Controller C = 25 lb/ft 1 ft3/min of water Holdup volume 3 f3 C