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; | gi | = | 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 | b | = | 0.5 V/cm | g | = | 981 cm/s2 |
And the measured outputs are yi = bhi (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 | = | 3.33, 3.35 cm3/Vs | g1,g2 | = | 0.7, 0.6 |
Operating point 2
h1s,h2s | = | 12.6, 13.0 cm | h3s,h4s | = | 4.8, 4.9 cm | v1s,v2s | = | 3.15, 3.15 cm | k1,k2 | = | 3.14, 3.29 cm3/Vs | g1,g2 | = | 0.43, 0.34 |
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