The CD equation describes the ow of heat, particles, or other physical quantities in situations where there is both diffusion and convection. In this report, we use optimal control input (u) to steer the temperature of a thin rod undergoing convection-diffusion (CD) process along with external forcing (f). Hence the cost function to be minimized consists of con icting objectives that is temperature distribution and amount of control input (u). This formulation is equivalent to linear quadratic regulator (LQR) problem. The objective function is reformulated as quadratic programming problem which has unique analytical solution. Furthermore, we also use gradient descent algo- rithm to arrive at approximated solution which is compared to analytical solution.
Some Resutls
| Optimum temperature distribution | Optimum control input u(x) |
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| Optimum temperature distribution (Box constraint) | Optimum control input u(x) (Box constraint) |
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