Human-aided control system for controlling a fluid level in a tank is shown in Figure Q2a. Here H denotes the fluid level inside the tank in meter and Qout be the outflow rate of the fluid from the tank and Qin be the inflow rate of the fluid into the tank. Construct the functional block diagram and identify the controlled variable, controller, actuator, process/plant and measurement element. Qout Valve

4 & 5

Design a PID controller for this system.

Problem #3 - Modeling, Mixing Problem Two tanks are connected by pipes in parallel as shown in Figure 2. Tank 1 starts with 160 lb of salt dissolved in 200 gal of water. Tank 2 starts with 100 gal of pure water. Using the diagram below, solve for the particular solutions of salt concentration in each tank as a function of time. Plot the solutions in Excel on the same plot. Note: some flow rates have been intentionally left out of the diagram below; use the conservation of mass to determine those. As a thought experiment, consider what negative eigenvalues imply. What would it mean if the eigenvalues were positive instead (what would the math say)? i.) ii.) iii.) iv.) v.) vi.) vii.) Use a conservation equation to develop your differential equation model (you should end up with two ODEs to describe the change in salt in both tanks). Write your system of ODEs in matrix form. Set up the eigenvalue problem and then determine the eigenvalues. Use the eigenvalues to determine the…