Design and implementation of a backstepping controller for regulating temperature in 3D printers based on selective laser sintering

In this paper we investigate the preheating temperature control problem in 3D printers based on the selective laser sintering (SLS) technology. We formulate the process as a temporal sequence of diffusion partial differential equations (PDEs), where each of these PDEs represent the temperature distribution of the layers and the control variable appears at one of the boundary conditions. We propose a full-state feedback control law, an state observer and the associated output feedback control law for the boundary input. The associated output feedback controller ensures the exponential stability of the estimation error in the ${{\mathcal{L}}_2}$ norm. The theoretical results were tested through numerical simulations and experiments. These results are promising as a method for industrial implementation of the backstepping controller.