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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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Appendix 14.1

The nonlinear modeling equations for the quad tank process are presented by Johansson (2000).

where

Ai=cross-sectional area of tank i;
ai=cross-sectional area of the outlet hole i;
hi=water height of tank i;
ki=pump coefficient i;
γi=flow splits;
g=gravitational constant

The parameter values are

A1,A3=28 cm3
A2,A4=32 cm3
a1,a3=0.071 cm2
a2,a4=0.057 cm2
β=0.5 V/cm
g=981 cm/s2

And the measured outputs are yi = βhi (for i = 1,2). Note that the maximum tank height is 20 cm.

The following states, inputs and coefficients correspond to the two operating points:

Operating point 1

h1s,h2s=12.4, 12.7 cm
h3s,h4s=1.8, 1.4 cm
v1s,v2s=3.00, 3.00 cm
k1,k2

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