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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