MAE 340 EXPERIMENT 7 - ANALOG SIMULATION
 
 
 
 

INTRODUCTION
 
 

This experiment involves the simulation of a simple two-tank problem using the analog computer experience that you developed in the last laboratory experiment. The problem is defined below in physical form and a set of parameters is presented to specifically define the state equations of the system. You will use the laboratory analog computers to simulate the specified transient response. Matlab will then be used to compare the analog and digital solutions.
 
 
 
 

THE SYSTEM
 
 

The two tank system is shown on the right. An input flow may drive the system or it may simply respond to initial conditions on the heights of water in the tanks h1 and h2. The state equations for the system may be shown to be:
 
 
 


 


 
 

where A1 and A2 are the tank areas. For this problem, consider
 
 


 
 


 
 
 
 

RESULTS SECTION
 
 

  1. Use the laboratory analog computers to solve the two tank state equations for the system above with initial conditions of h1 = 1 and h2 = 0 for the case of no input flow to tank #1 (Qo = 0).
     

  2. Determine the maximum height of the water in tank two during the transient and establish the time at which the maximum height occurs.
     

  3. Capture the transient response of h1 and h2 vs. time with the VirtualBench Scope. Pass the resulting data file into excel and make an Excel plot of the transient until at least the time of the h2 peak. (This is required plot #1.)
     

  4. Output a convenient text file from Excel prepared to be used as Matlab input.
     

  5. Prepare a Matlab program that solves the two tank state equations and reads the analog data for comparison plotting.
     

  6. Your Matlab program should output two figures. The first figure should have plots of h1 vs. time showing a curve for the Matlab results and data points for the Excel analog results. The second figure should show plots of h2 vs. time with a curve for the Matlab result and data points for the Excel analog results. (These are required plots #2 and #3.)

 
 

SPECIFIC QUESTIONS
 
 

  1. Derive the state equations for the two tank problem shown on page 1. Of course, the pressure at the bottom of the tanks is given by the product of mass density, gravity and height.
     

  2. How do your analog and digital computer results compare? Can you explain any differences?

 
 

REPORT
 
 

Reports for this experiment should be submitted in short form. Individual reports are required.