Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 929316, 11 pages http://dx.doi.org/10.1155/2013/929316 Research Article Two-Stage Control Design of a Buck Converter/DC Motor System without Velocity Measurements via a Σ−Δ-Modulator R. Silva-Ortigoza, 1 J. R. García-Sánchez, 1 J. M. Alba-Martínez, 1 V. M. Hernández-Guzmán, 2 M. Marcelino-Aranda, 3 H. Taud, 1 and R. Bautista-Quintero 4 1 Instituto Polit´ ecnico Nacional, CIDETEC, ´ Area de Mecatr´ onica, Unidad Profesional Adolfo L´ opez Mateos, 07700 M´ exico, DF, Mexico 2 Universidad Aut´ onoma de Quer´ etaro, Facultad de Ingenier´ ıa, 76150 Quer´ etaro, QRO, Mexico 3 Instituto Polit´ ecnico Nacional, UPIICSA, Secci´ on de Estudios de Posgrado e Investigaci´ on, 08400 M´ exico, DF, Mexico 4 Instituto Tecnol´ ogico de Culiac´ an, Departamento de Metal-Mec´ anica, 80220 Culiac´ an, SIN, Mexico Correspondence should be addressed to R. Silva-Ortigoza; rsilvao@ipn.mx Received 14 February 2013; Accepted 7 April 2013 Academic Editor: Ebrahim Momoniat Copyright © 2013 R. Silva-Ortigoza et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper presents a two-stage control design for the “Buck power converter/DC motor” system, which allows to perform the sensorless angular velocity trajectory tracking task. Te diferential fatness property of the DC-motor model is exploited in order to propose a frst-stage controller, which is designed to achieve the desired angular velocity trajectory. Tis controller provides the voltage profles that must be tracked by the Buck converter. Ten, a second-stage controller is meant to assure the aforementioned. Tis controller is based on fatness property of the Buck power converter model, which provides the input voltage to the DC motor. Due to the fact that the two-stage controller proposed uses the average model of the system, as a practical and efective implementation of this controller, a Σ−Δ-modulator is employed. Finally, in order to verify the control performance of this approach, numerical simulations are included. 1. Introduction In the market of electric servo motor drivers, the most com- mon technology—used in robotics and electric vehicles—is based on solid-state devices. For both velocity and position control purposes, these solid-state servo drives require a power electronic converter which is used as an interface between the input power line and the motor [1]. One of the most common topologies is the Buck-switched DC/DC power converter. Due to the fact that Buck converter contains two energy-storing elements (an inductance and a capacitor), smooth DC output voltages and currents with very small current ripple are generated. In order to obtain—at any time—a high power conversion rate, when angular velocity control is required, the converter design is very important. Previously in the literature, diferent proposals have explored the combination of several topologies of DC/DC power converters with DC motors. Tis work is particularly focused on the velocity control of a DC Motor based on regulating the output voltage of a Buck DC/DC power converter. In 2000, Lyshevski [2] proposed fourth-order mathemat- ical models for coupled systems of both power electronic converters and a permanent magnet DC motor. Furthermore, Lyshevski shows a control design based on PI strategy which is meant to regulate angular velocity for the DC motor. In contrast to previous works, in 2004 Linares-Flores and Sira-Ram´ ırez presented in [3–5] the design of smooth angular velocity control for DC motor powered by a DC/DC Buck converter. Tis approach was validated by numerical simulations. In [3] a diferential fatness control approach was pre- sented, where a second-order model is employed based on neglecting both armature inductance and the current that