This talk consists of the finite element analysis of a distributed optimal control problem governed by the von Kármán equation that describe the deflection of very thin plates defined on a polygonal domain of R2 with box constraints on the control variable. In this talk we discuss a numerical approximation of the problem that employs the Morley nonconforming finite element method (FEM) to discretize the state and adjoint variables. The control is discretized using piecewise constants. A priori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions on the exact solution. Error estimates in lower order norms for the state and adjoint variables are derived. The lower order estimates for the adjoint variable and a post-processing of control leads to an improved error estimate for the control variable. Finally we discuss several numerical results to illustrate our theoretical results.