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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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