Modeling a multipurpose water tank plant

This work develops nonlinear and linear dynamic models of a multipurpose plant: a water tank fed by two flow rates (cold and hot water), which are mixed to produce an outflow rate. Such a plant is a MIMO (Multiple Input, Multiple Output) process with two inputs: cold and hot water flow rates, and two outputs: level and temperature of the water in the tank. This plant exhibits interaction between its inputs and outputs because the variation of one input affects the behavior of another output. Some experiments were performed to determine maximum values of the cold and hot flow rates, and to compute the discharge coefficient of the outflow rate. Applying the laws of physics and using the parameters obtanined experimentally, a MIMO nonlinear dynamic model of the plant was obtained. The corresponding state–space representation of the nonlinear model was linearized in order to generate its LTI (Linear Time–Invariant) state–space form. Nonlinear and linear models of the plant are necessary to implement, e.g., model–based control algorithms. For instance, a future work will use the developed LTI state–space model to design a FO (Fractional Order) MIMO controller.