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Posted: 2023-01-1411:40 AM
Controller design for water tank
Can you please help me with this problem please??
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,