The copper removal process (CRP) aims to reduce the copper ion concentration in zinc sulphate solution to a specific range by zinc addition. The satisfaction of production constraints and minimization of zinc consumption are vital but difficult to achieve. In this article, the dynamic optimization for CRP is conducted for optimal zinc control trajectory design considering constraints at least cost. First, a dynamic optimization problem with both state and control constraints is constructed for CRP. Then, a constrained dynamic optimization method is proposed, where a wavelet-based control parameterization method and a smooth penalty method are adopted. Specially, a hybrid optimization strategy is proposed to achieve a robust and efficient optimization performance. Numerical experiments are provided to illustrate the effectiveness of the proposed method. Results show that the proposed method can produce not only the optimal control trajectory with a qualified outlet ion concentration but also the less zinc consumption.