The optimal periodic control problem with the main and the additional optimality criterion for a system described by differential equations is investigated. The energy and raw material consumption are considered as the additional criteria. The problem characterized is approximated by a sequence of discretized optimization problems using trigonometric polynomials and penalty functions. Sufficient conditions are given for the convergence of solutions of discretized problems to the regular optimal solution, which minimizes the additional criterion over the set of solutions minimizing the main criterion. Strong convergence in the case where the energy consumption is the additional criterion is proven.