Mathematical Description of the Process

Both a nonlinear model and a linearized model are given in [2] for the Four Tank System. The models used for this work include the disturbance effects of flows in or out of tanks three and four. The nonlinear differential equations governing the heights in this four tank system are given in Table 2, and the linearized version is seen in Table 3. The liquid levels in tanks one and two, h ₁ and h ₂, are considered measured variables. The speed of the pumps,  and , are considered as manipulated inputs. The pump speeds are manipulated as a percentage of the maximum pump speed. The disturbances d₁ and d₂ model the unmeasured disturbance effects of flows in or out of tanks three and four. This model is a simple mass balance, assuming Bernoulli's law for flow out of the orifice. The gamma values, , correspond to the the portion of the flow going into a upper tank from pump i. In [2], it is shown that inverse response in the modeled outputs will occur when . A modification introduced by the students in the class was the presence of a disturbance introduced by a submersible pump in the upper tanks. These disturbances effects are modeled as a constant leak into or out of the upper tanks. 
1999-07-20