*3.4. Control*

An elementary open-loop control was developed to show the usefulness of the model using marks in control systems. The process variables to be achieved are target heights of the liquid in the tanks, (or, in this test, arbitrarily chosen from the real simulation with the model, see Figure 2). For example, the ones represented by black dots in Figure 8. These outputs are controlled by the input flows to each tank in form of percentages *k*1(*t*), *k*2(*t*), *k*3(*t*) of the maximal flows *q*1 = *q*2 = *q*3 = 0.01.

**Figure 8.** Three-tank system. Target heights to be achieved in open loop control.

When at instant *t*, the later and nearest target height is above the interval associated to the output mark *h*1(*t*) or *h*2(*t*) or *h*3(*t*), then *k*1(*t*) = 1 or *k*2(*t*) = 1 or *k*3(*t*) = 1. When it is under, then *k*1(*t*) = 0 or *k*2(*t*) = 0 or *k*3(*t*) = 0. Finally, when it is inside the interval, then *k*1(*t*) = *d*1(*t*) or *k*2(*t*) = *d*2(*t*) or *k*3(*t*) = *d*3(*t*), where *d*1(*t*) is the relative distance between the target height and the center of the interval *h*1(*t*) (the same for *d*2(*t*) and *d*3(*t*)).

The result is a set of percentages for every instant, *t*. The output of the model is the band of associated intervals in Figure 9. The target heights are very close to being contained in the corresponding marks. Therefore, they can be considered consistent with the model for the inputs flows defined by *k*1(*t*), *k*2(*t*) and *k*3(*t*).

**Figure 9.** Three-tank system. Simulation results for the open loop control of the liquid heights.
