Two canals are evaluated by the ASCE Task Committee (Clemmens et al. 1998) in several scenarios. Each canal has eight pools separated by undershot sluice gates. All the canal pools have been discretized and numbered in the direction of flow from upstream to downstream. Geometric characteristics of canal 1 (Maricopa Stanfield canal) are shown in Tables 7 and 8 and Figure 10, and for canal 2 (Corning canal) in Tables 9 and 10 and Figure 11. In both canals, there are gravity outlet orifices at the downstream end of each canal pool but only in canal 2 is there direct pumping at the end of the last pool. The ASCE Committee proposes four cases to test feedback controllers in real time, two in the Corning canal and two in the Maricopa Stanfield. We only test one case in each canal with our overall control diagram taking into account the case with more unscheduled flow changes. The initial conditions for all tests are shown in Table 11 (Maricopa Standfield) and Table 12 (Corning canal). All scenarios are evaluated in Bonet (2015).
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Table 7
Features of Maricopa Stanfield canal pools
| Pool number | Pool length (km) | Bottom slope | Side slopes (H:V) | Manning's coefficient (n) | Bottom width (m) | Canal depth (m) |
|---|---|---|---|---|---|---|
| I | 0.1 | 2 × 10−3 | 1.5:1 | 0.014 | 1 | 1.1 |
| II | 1.2 | 2 × 10−3 | 1.5:1 | 0.014 | 1 | 1.1 |
| III | 0.4 | 2 × 10−3 | 1.5:1 | 0.014 | 1 | 1.0 |
| IV | 0.8 | 2 × 10−3 | 1.5:1 | 0.014 | 0.8 | 1.1 |
| V | 2 | 2 × 10−3 | 1.5:1 | 0.014 | 0.8 | 1.1 |
| VI | 1.7 | 2 × 10−3 | 1.5:1 | 0.014 | 0.8 | 1.0 |
| VII | 1.6 | 2 × 10−3 | 1.5:1 | 0.014 | 0.6 | 1.0 |
| VIII | 1.7 | 2 × 10−3 | 1.5:1 | 0.014 | 0.6 | 1.0 |
| Pool number | Pool length (km) | Bottom slope | Side slopes (H:V) | Manning's coefficient (n) | Bottom width (m) | Canal depth (m) |
|---|---|---|---|---|---|---|
| I | 0.1 | 2 × 10−3 | 1.5:1 | 0.014 | 1 | 1.1 |
| II | 1.2 | 2 × 10−3 | 1.5:1 | 0.014 | 1 | 1.1 |
| III | 0.4 | 2 × 10−3 | 1.5:1 | 0.014 | 1 | 1.0 |
| IV | 0.8 | 2 × 10−3 | 1.5:1 | 0.014 | 0.8 | 1.1 |
| V | 2 | 2 × 10−3 | 1.5:1 | 0.014 | 0.8 | 1.1 |
| VI | 1.7 | 2 × 10−3 | 1.5:1 | 0.014 | 0.8 | 1.0 |
| VII | 1.6 | 2 × 10−3 | 1.5:1 | 0.014 | 0.6 | 1.0 |
| VIII | 1.7 | 2 × 10−3 | 1.5:1 | 0.014 | 0.6 | 1.0 |
Table 8
Maricopa Stanfield control structures
| Target points | Gate discharge coefficient | Gate width (m) | Gate height (m) | Step (m) | Length from gate 1 (km) | Orifice offtake height (m) |
|---|---|---|---|---|---|---|
| 0 | 0.61 | 1.5 | 1.0 | 1.0 | 0 | – |
| 1 | 0.61 | 1.5 | 1.1 | 1.0 | 0.1 | 0.45 |
| 2 | 0.61 | 1.5 | 1.1 | 1.0 | 1.3 | 0.45 |
| 3 | 0.61 | 1.5 | 1.0 | 1.0 | 1.7 | 0.40 |
| 4 | 0.61 | 1.2 | 1.1 | 1.0 | 2.5 | 0.45 |
| 5 | 0.61 | 1.2 | 1.1 | 1.0 | 4.5 | 0.45 |
| 6 | 0.61 | 1.2 | 1.0 | 1.0 | 6.2 | 0.40 |
| 7 | 0.61 | 1.0 | 1.0 | 1.0 | 7.8 | 0.40 |
| 8 | – | – | – | – | 9.5 | 0.40 |
| Target points | Gate discharge coefficient | Gate width (m) | Gate height (m) | Step (m) | Length from gate 1 (km) | Orifice offtake height (m) |
|---|---|---|---|---|---|---|
| 0 | 0.61 | 1.5 | 1.0 | 1.0 | 0 | – |
| 1 | 0.61 | 1.5 | 1.1 | 1.0 | 0.1 | 0.45 |
| 2 | 0.61 | 1.5 | 1.1 | 1.0 | 1.3 | 0.45 |
| 3 | 0.61 | 1.5 | 1.0 | 1.0 | 1.7 | 0.40 |
| 4 | 0.61 | 1.2 | 1.1 | 1.0 | 2.5 | 0.45 |
| 5 | 0.61 | 1.2 | 1.1 | 1.0 | 4.5 | 0.45 |
| 6 | 0.61 | 1.2 | 1.0 | 1.0 | 6.2 | 0.40 |
| 7 | 0.61 | 1.0 | 1.0 | 1.0 | 7.8 | 0.40 |
| 8 | – | – | – | – | 9.5 | 0.40 |
Table 9
Features of Corning canal pools
| Pool number | Pool length (km) | Bottom slope | Side slopes (H:V) | Manning's coefficient (n) | Bottom width (m) | Canal depth (m) |
|---|---|---|---|---|---|---|
| I | 7 | 1 × 10−4 | 1.5:1 | 0.02 | 7 | 2.5 |
| II | 3 | 1 × 10−4 | 1.5:1 | 0.02 | 7 | 2.5 |
| III | 3 | 1 × 10−4 | 1.5:1 | 0.02 | 7 | 2.5 |
| IV | 4 | 1 × 10−4 | 1.5:1 | 0.02 | 6 | 2.3 |
| V | 4 | 1 × 10−4 | 1.5:1 | 0.02 | 6 | 2.3 |
| VI | 3 | 1 × 10−4 | 1.5:1 | 0.02 | 5 | 2.3 |
| VII | 2 | 1 × 10−4 | 1.5:1 | 0.02 | 5 | 1.9 |
| VIII | 2 | 1 × 10−4 | 1.5:1 | 0.02 | 5 | 1.9 |
| Pool number | Pool length (km) | Bottom slope | Side slopes (H:V) | Manning's coefficient (n) | Bottom width (m) | Canal depth (m) |
|---|---|---|---|---|---|---|
| I | 7 | 1 × 10−4 | 1.5:1 | 0.02 | 7 | 2.5 |
| II | 3 | 1 × 10−4 | 1.5:1 | 0.02 | 7 | 2.5 |
| III | 3 | 1 × 10−4 | 1.5:1 | 0.02 | 7 | 2.5 |
| IV | 4 | 1 × 10−4 | 1.5:1 | 0.02 | 6 | 2.3 |
| V | 4 | 1 × 10−4 | 1.5:1 | 0.02 | 6 | 2.3 |
| VI | 3 | 1 × 10−4 | 1.5:1 | 0.02 | 5 | 2.3 |
| VII | 2 | 1 × 10−4 | 1.5:1 | 0.02 | 5 | 1.9 |
| VIII | 2 | 1 × 10−4 | 1.5:1 | 0.02 | 5 | 1.9 |
Table 10
Corning canal control structures
| Target points | Gate width (m) | Gate height (m) | Step (m) | Length from gate 1 (Km) | Orifice offtake height (m) | Lateral spillway height (m) |
|---|---|---|---|---|---|---|
| 0 | 7 | 2.3 | 0.2 | 0 | – | 3 |
| 1 | 7 | 2.3 | 0.2 | 7 | 1.05 | 2.5 |
| 2 | 7 | 2.3 | 0.2 | 10 | 1.05 | 2.5 |
| 3 | 7 | 2.3 | 0.2 | 13 | 1.05 | 2.5 |
| 4 | 6 | 2.1 | 0.2 | 17 | 0.95 | 2.3 |
| 5 | 6 | 2.1 | 0.2 | 21 | 0.95 | 2.3 |
| 6 | 5 | 1.8 | 0.2 | 24 | 0.85 | 1.9 |
| 7 | 5 | 1.8 | 0.2 | 26 | 0.85 | 1.9 |
| 8 | – | – | – | 28 | 0.85 | 1.9 |
| Target points | Gate width (m) | Gate height (m) | Step (m) | Length from gate 1 (Km) | Orifice offtake height (m) | Lateral spillway height (m) |
|---|---|---|---|---|---|---|
| 0 | 7 | 2.3 | 0.2 | 0 | – | 3 |
| 1 | 7 | 2.3 | 0.2 | 7 | 1.05 | 2.5 |
| 2 | 7 | 2.3 | 0.2 | 10 | 1.05 | 2.5 |
| 3 | 7 | 2.3 | 0.2 | 13 | 1.05 | 2.5 |
| 4 | 6 | 2.1 | 0.2 | 17 | 0.95 | 2.3 |
| 5 | 6 | 2.1 | 0.2 | 21 | 0.95 | 2.3 |
| 6 | 5 | 1.8 | 0.2 | 24 | 0.85 | 1.9 |
| 7 | 5 | 1.8 | 0.2 | 26 | 0.85 | 1.9 |
| 8 | – | – | – | 28 | 0.85 | 1.9 |
Table 11
Initial and unscheduled offtake changes in test case 1-2
| Pool number | Offtake initial flow (m3/s) | Check initial flow (m3/s) | Unscheduled offtake changes at 2 hours (m3/s) | Check final flow (m3/s) |
|---|---|---|---|---|
| Heading | – | 2.0 | – | 2.0 |
| 1 | 0.2 | 1.8 | – | 1.8 |
| 2 | 0.0 | 1.8 | 0.2 | 1.6 |
| 3 | 0.4 | 1.4 | −0.2 | 1.4 |
| 4 | 0.0 | 1.4 | 0.2 | 1.2 |
| 5 | 0.0 | 1.4 | 0.2 | 1.0 |
| 6 | 0.3 | 1.1 | −0.1 | 0.8 |
| 7 | 0.2 | 0.9 | – | 0.6 |
| 8 | 0.9 | 0.0 | −0.3 | 0.0 |
| Pool number | Offtake initial flow (m3/s) | Check initial flow (m3/s) | Unscheduled offtake changes at 2 hours (m3/s) | Check final flow (m3/s) |
|---|---|---|---|---|
| Heading | – | 2.0 | – | 2.0 |
| 1 | 0.2 | 1.8 | – | 1.8 |
| 2 | 0.0 | 1.8 | 0.2 | 1.6 |
| 3 | 0.4 | 1.4 | −0.2 | 1.4 |
| 4 | 0.0 | 1.4 | 0.2 | 1.2 |
| 5 | 0.0 | 1.4 | 0.2 | 1.0 |
| 6 | 0.3 | 1.1 | −0.1 | 0.8 |
| 7 | 0.2 | 0.9 | – | 0.6 |
| 8 | 0.9 | 0.0 | −0.3 | 0.0 |
Table 12
Initial and unscheduled offtake changes in test case 2-2
| Pool number | Offtake initial flow (m3/s) | Check initial flow (m3/s) | Unscheduled offtake changes at 2 hours (m3/s) | Resulting check flow (m3/s) |
|---|---|---|---|---|
| Heading | – | 13.7 | – | 2.7 |
| 1 | 1.7 | 12.0 | −1.5 | 2.5 |
| 2 | 1.8 | 10.2 | −1.5 | 2.2 |
| 3 | 2.7 | 7.5 | −2.5 | 2.0 |
| 4 | 0.3 | 7.2 | – | 1.7 |
| 5 | 0.2 | 7.0 | – | 1.5 |
| 6 | 0.8 | 6.2 | −0.5 | 1.2 |
| 7 | 1.2 | 5.0 | −1.0 | 1.0 |
| 8 | 0.3 + 2.0* | 2.7 | −2.0* | 0.7 |
| Pool number | Offtake initial flow (m3/s) | Check initial flow (m3/s) | Unscheduled offtake changes at 2 hours (m3/s) | Resulting check flow (m3/s) |
|---|---|---|---|---|
| Heading | – | 13.7 | – | 2.7 |
| 1 | 1.7 | 12.0 | −1.5 | 2.5 |
| 2 | 1.8 | 10.2 | −1.5 | 2.2 |
| 3 | 2.7 | 7.5 | −2.5 | 2.0 |
| 4 | 0.3 | 7.2 | – | 1.7 |
| 5 | 0.2 | 7.0 | – | 1.5 |
| 6 | 0.8 | 6.2 | −0.5 | 1.2 |
| 7 | 1.2 | 5.0 | −1.0 | 1.0 |
| 8 | 0.3 + 2.0* | 2.7 | −2.0* | 0.7 |
*Changes in downstream pump discharge with no change in offtake flow.
Figure 10
Maricopa Stanfield canal profile. The arrows mark the position of checkpoints. The first pool is number I and the first checkpoint is number 1.
Figure 10
Maricopa Stanfield canal profile. The arrows mark the position of checkpoints. The first pool is number I and the first checkpoint is number 1.
Figure 11
Corning canal profile. The arrows mark the position of checkpoints. The first pool is number I and the first checkpoint is number 1.
Figure 11
Corning canal profile. The arrows mark the position of checkpoints. The first pool is number I and the first checkpoint is number 1.