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Figure 12.

Shears’ position and torque during cut_
| Parameters | Shears’ angle (°) | Shears’ arm (mm) | Torque on motor side | |
|---|---|---|---|---|
| (Nm) | (% of TR) | |||
| Beginning of cut | 339 | 34.045 | 1,872.2 | 76.14 |
| End of cut | 345 | 24.588 | 1,352.1 | 55 |
Fuzzy control rules_
| e(k)/Δe(k) | NM | NS | Z | PS | PM |
|---|---|---|---|---|---|
| NM | NM | NM | NM | NS | Z |
| NS | NM | NM | NS | Z | PS |
| Z | NM | NS | Z | PS | PM |
| PS | NS | Z | PS | PM | PM |
| PM | Z | PS | PM | PM | PM |
Parameters of NN predictive model_
| Parameters | Value/description |
|---|---|
| Network type | Feedforward NN (MLP) |
| Output | Prediction of motor torque
|
| Input vector | [Tref (k), Tref (k − 1), Tmot (k), Tmot(k − 1), Tload (k), Tload(k − 1)] |
| Hidden layers | 2 |
| Number of neurons | 10–10 |
| Activation functions | Tansig (hidden layers), linear (output layer) |
| Training algorithms | Levenberg–Marquardt |
| Input and output normalisation | Range [−1, 1] |
| Sampling period | Ts = 100 μs |
Performance metrics of the NN torque predictor_
| Abbreviation | Full name | Value | Unit |
|---|---|---|---|
| MAE | Mean absolute error | 1.7645 | Nm |
| RMSE | Root mean square error | 2.3071 | Nm |
| RMSE | Percentage RMSE | 0.0991 | % |
| MaxE | Maximum absolute error | 5.7528 | Nm |
| R2 | Coefficient of determination | 0.9999 | - |
Summary of dynamic performance metrics for all tested control structures and compensation strategies at different strip speeds_
| Strip speed [m/min] | Control structure | Compensation | Speed drop [%] | Absolutely speed drop [m/min] | Speed overshoot [%] | Settling time [ms] |
|---|---|---|---|---|---|---|
| 20 | P | No | 10.71 | 2.144 | 0.115 | 54.2 |
| PI | No | 9.12 | 1.824 | 1.534 | 82.3 | |
| P | Yes | 4.74 | 0.948 | 4.38 | 50.1 | |
| P | Anticipative | 5.71 | 1.143 | 4.21 | 50.7 | |
| P + fuzzy | No | 1.66 | 0.332 | 0 | 34.7 | |
| P | NN compensation | 1.07 | 0.214 | 0.06 | 35.7 | |
| 40 | P | No | 5.03 | 2.014 | 0.32 | 34.5 |
| PI | No | 4.35 | 1.740 | 4.48 | 53.1 | |
| P | Yes | 1.16 | 0.464 | 1.62 | 25.5 | |
| P | Anticipative | 0.78 | 0.311 | 1.58 | 16.6 | |
| P + fuzzy | No | 0.86 | 0.344 | 0 | 16.2 | |
| P | NN compensation | 0.55 | 0.222 | 0.02 | 19.4 | |
| 80 | P | No | 2.28 | 1.825 | 0.13 | 23.5 |
| PI | No | 2.03 | 1.621 | 1.47 | 44.2 | |
| P | Yes | 0.56 | 0.448 | 0.52 | 19.8 | |
| P | Anticipative | 0.47 | 0.377 | 0.45 | 19.5 | |
| P + fuzzy | No | 0.43 | 0.344 | 0 | 8.3 | |
| P | NN compensation | 0.28 | 0.226 | 0.01 | 10 | |
The shears’ angular velocity drop during the cut considering freewheeling shears (i_e_ without controllers)_
| Strip speed (m/min) | Shears’ angular velocity | |||
|---|---|---|---|---|
| Steady state (rad/s) | After cut (rad/s) | Difference (rad/s) | Difference (%) | |
| 20 | 14.74 | 7.63 | 7.11 | 48.34 |
| 50 | 36.847 | 34.021 | 2.862 | 7.77 |
| 80 | 58.938 | 57.180 | 1.758 | 2.98 |
Rotary shears motor parameters_
| Parameters | Symbol | Unit | Value |
|---|---|---|---|
| Rated power | PR | kW | 190 |
| Rated voltage | VR | V | 400 |
| Rated speed | nR | rpm | 800 |
| Motor inertia | Jmot | kg/m2 | 4.2 |
| Rated current | IR | A | 335 |
| Rated frequency | fR | Hz | 27.2 |
| Rated torque | TR | Nm | 2,328 |
| Maximum torque | Tmax | Nm | 4,250 |
| Rated power factor | cos(ϕ) | - | 0.942 |
| Rated efficiency | η | % | 89 |
| Torque control loop time constant | τT | ms | 2 |