Simulink: The two-tank problem
Q. In the two tank problem, we have a square pulse input flow, qi= (u(t-1)-u(t4))*Q where Q=0.012 m^3/s is the magnitude of the input flow in m3/sec and
u(t-a) is a step function at t=a. In this problem, we have A1(area of cross section
of tank 1) = 10 m^2 and A2 (area of cross section of tank 2) = 10 m^2. The two
tanks are initially filled with water up to 10 m and 5 m heights respectively.
(Take R1=10^5 and R2=10^5) where R1 and R2 are the resistances associated
with the pipes connecting tank 1 and 2 and the other serving as a opening for
tank2.
Solution: First of all, we will produce the input pulse with the help of two step
inputs s1 and s2. S1 having step at 1 and having magnitude 0.012, and s2 having
a step at 4 and magnitude as -0.012. These two signals are then combined with
the Sum Block available in the Math operations tab of Simulink library to
produce the resultant input.
 Now let’s write the governing equations of the combined system.
 Now as we can see, both the systems are interdependent on each other
and both have one state variable, which means there would in total 2
integrator blocks in our simulation diagram. Building the simulation
diagram with the help of previous notes of Simulink, we have the block
diagram as follows:
Fig. Final Simulation Diagram
 Now, we save our Simulink file and open a MATLAB file in the same
folder from which we can give values to our variables inside the Simulink
file and call the Simulink file with the uploaded values.
 Simulation results:
Configuration
parameters settings:
Start Time: 0
Stop Time: 10
Max Step Size: 0.05
Fig. H1 versus time graph
Fig. H2 versus time graph