Water level stabilization in open channels using Chebyshev polynomials and teaching–learning-based optimization

Water level fluctuations in open channels can cause serious problems for conveyance systems which lead to economical and performance issues. The problem of water level stabilization in open channels containing two pumping stations at both ends is investigated in this paper. The optimal control that should be imposed at one end of the channel to minimize water surface fluctuations due to sudden increase in water demand at the other end is determined. Chebyshev polynomials are effectively hybridized with a modern teaching–learning-based optimization algorithm for the first time to estimate the optimal control. An efficient shock-capturing model is used to evaluate the value of the objective function. Results are compared with those obtained by the variational approach. The optimal control found by the proposed method shows fewer fluctuations in water level than that found by the variational method. Moreover, the proposed approach is easier to implement and to extend for solving more general problems.