Table 2 Numerical report on simulations with the conventional and the linear rampdown pulse shapes, and locally optimal pulse shapes * starting from corresponding initial guesses
From: An optimal control problem for single-spot pulsed laser welding
Pulse shape | Welding depth | \(J_{\text{penetration}}\) | \(J_{\text{velocity}}\) | \(J_{\text{completeness}}\) | \(J_{\text{control}}\) | \(J_{\text{total}}\) |
|---|---|---|---|---|---|---|
conventional | 0.11875 | 0.9758 | 278.9010 | 0.0000 | 0.1406 | 280.0173 |
rampdown | 0.11875 | 2.4323 | 0.0055 | 0.0000 | 0.1889 | 2.6267 |
conventional * | 0.11875 | 0.8611 | 27.2947 | 0.0000 | 0.1413 | 28.2972 |
rampdown * | 0.11250 | 0.0001 | 0.0000 | 0.0000 | 0.1674 | 0.1675 |