Drawing the open loop block diagram between valve and pump is straightforward (please see illustration). But why should $v$ be an additional disturbance in this system (please see solution)? $v$ is going out of the tank?



  • $\begingroup$ Did you notice the minus sign on top of the adder? $\endgroup$
    – Matt L.
    Commented Feb 15, 2021 at 13:10
  • $\begingroup$ Why is it not after G_t(s)? $\endgroup$
    – Dovendyr
    Commented Feb 15, 2021 at 13:47
  • 1
    $\begingroup$ @Dovendyr Because the tank's transfer function input signal is the net flow, the tank will start to drain if the outflow is larger than the inflow, i.e. $v- x\gt 0$, whereas it will start filling up if $v-x \lt 0$. $\endgroup$
    – kalgoritmi
    Commented Feb 16, 2021 at 9:22

1 Answer 1


The pump keeps the tubing pressurized, the desired input flow is tuned via the valve. However the net flow rate that feeds the tank is not this inflow, it is the difference between the inflow and outflow.

The outflow caused by the pump is modeled as a disturbance because, in the current example, the goal is to model the liquid's level inside the tank. The outflow maybe considered a byproduct of the pump's operation.

Although the above diagram describes the plant (the physical process of the hydraulic system), if the control of the plant was studied later a possible design goal could be to maintain a constant and controllable level of the liquid in the tank (this requires feedback control aka a closed loop) and/or reaching the steady state value(desirable level in the tank) fast.

In addition a pump's flow rate tends to decrease as the pressure inside the tubing increases.

Think about a garden's hose, which sinks water into a flower pot at some flow rate and the water drains out of the flower pot through the bottom. Then if the inflow is much larger than the outflow the soil's surface will be flooded not being able to properly absorb the incoming flow of water. On the other hand, if the outflow is close enough to the inflow then the soil will be able to absorb the incoming water flow, not resulting in the flower pot's water overflow.

The block $G_t(s)$ describes the tank's response therefore the inflow-outflow difference is its input. The system $G_v(s)$ is the valve's response to the user input.


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