In this paper, we use the reduced-order nonlinear model of dynamic systems governed by Burgers' equation with Neumann boundary conditions - recently developed by the authors in [4] - to define low order sliding mode surfaces. While keeping the system states moving on the defined surface, the imposed control law guarantees the stability of the full-order model obtained using a finite element (FE) approximation of the Burgers' equation. The accuracy of the applied reduced-order model obtained from proper orthogonal decomposition (POD) method compared to the FE model is investigated by determining an adequate number of basis functions for the approximating subspace. The reduced-order model is then used to design a sliding mode controller, which is implemented on the FE model demonstrating that the obtained reduced model is suitable for both stabilization of the full-order model and trajectory tracking.