The steady$-$state gain $K=1$

The time constant for the pump is $=1$

$\frac{\text{F}\text{l}\text{o}\text{w}(s)}{\text{F}\text{l}\text{o}\text{w}\text{c}\text{o}\text{n}\text{t}\text{r}\text{o}\text{l}(s)}=\frac{F(s)}{FC(s)}=\frac{K}{s+1}$

The flow control settings input is provided in the diagram.

$($s$)$Three pumps are used in a pumping station. The change in the pumping rate of the pumps is done in stages in order not to put unnecessary stress on the electrical circuit. Pump number $1$ starts at time $0,$ pump number two at time $1$ and pump number three at time $2.$ The flow increase profile for each pump is the same and independent of the others. This profile is shown in the figure. How much volume has been pumped after $20$ seconds?