The atomic force microscope (AFM) introduced the surface investigation with true atomic resolution. In the frequency modulation technique (FM-AFM) both the amplitude and the frequency of oscillation of the micro-cantilever must be kept constant even in the presence of tip-surface interaction forces. For that reason, the proper design of the Phase-Locked Loop (PLL) used in FM-AFM is vital to system performance. Here, the mathematical model of the FM-AFM control system is derived considering high order PLL In addition a method to design stable third-order Phase-Locked Loops is presented. (C) 2010 Elsevier B.V. All rights reserved.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)