Controller design for water tank

[mariaalmeida2711]

Can you please help me with this problem please??

Translation:

The main objective of this work is to develop a PID control algorithm for the Arduino, and the adjustment
of its parameters. The plant is in this case a water reservoir with a filling pump with
a flow Qi and a leakage flow Q1, adjusted by restriction R1.

The system consists of a water tank 0.5 m high and 0.06 m in diameter, fed by
a pump whose flow rate is controlled from an analogue signal V [0 ; 10] VDC. The pump equation is
given by: 𝑄1=Kb*V com Kb=0.000025

At the bottom of the tank there is a leakage flow, 𝑄1, which can be adjusted through the restrictor 𝑅1.
The constraint will always have a positive value (R1>0).

1. Write the equation that describes the system assuming as input the control voltage of the
pump and output at liquid height;
The. Determine the differential equation that describes the behavior of the system;
B. Assume a step input to the pump from 0 VDC to 4.5 VDC;
ç. Assume that in operation, the tank stabilizes at a level equal to 0.33 m, determine the
value of R1;
d. Write the system transfer function,