Water Hammer Suppression with Variable Terminal Time via PDE-Constrained Dynamic Optimization

Water hammer suppression is modeled as an optimal boundary control problem with partial differential equations (PDE) constraints. In this study, the time scale variable is introduced to reformulate the problem, making both the length of control horizons and terminal time alterable. Out of further investigating the fast valve closing strategy when maintaining pressure fluctuation in a tolerable range, the valve closure time is penalized in the objective function. Hence, water hammer suppression with variable terminal time is considered under continuous piecewise-linear control. The PDE-constrained dynamic optimization problem is solved by space-time orthogonal collocation on finite elements based simultaneous collocation approach. As expected, the optimal results make the terminal time reduced while the pressure surge is kept under an acceptable level. Numerical simulation demonstrates that water hammer suppression with variable terminal time is effective and has much more flexibility.