Centro de Investigación y Estudios Avanzados del I . P . N . Unidad Guadalajara México Super - Twisting Sliding Mode

Nowadays, the major advancements in the control of motion systems are due to the automatic control theory. Motion control systems are characterized by complex nonlinear dynamics and can be found in the robotic, automotive and electromechanical area, among others. In such systems it is always wanted to impose a desired behavior in order to cope with the control objectives that can go from velocity and position tracking to torque and current tracking among other variables. Motion control systems become vulnerable when the output tracking signals present small oscillations of finite frequency known as chattering. The chattering problem is harmful because it leads to low control accuracy; high wear of moving mechanical parts and high heat losses in power circuits. The chattering phenomenon can be caused by the deliberate use of classical sliding mode control technique. This control technique is characterized by a discontinuous control action with an ideal infinite frequency. When fast dynamics are neglected in the mathematical model such phenomenon can appear. Another situation responsible for chattering is due to implementation issues of the slidingmode control signal in digital devices operating with a finite sampling frequency, where the switching frequency of the control signal cannot be fully implemented. Despite of the disadvantage presented by the sliding mode control, this is a popular technique among control engineer practitioners due to the fact that introduces robustness to unknown bounded perturbations that belong to the control sub-space; moreover, the residual dynamic under the sliding regime, i.e., the sliding mode dynamic, can easily be stabilized with a proper choice of the sliding surface. A proof of their good performance in motion control systems can be found in the book by Utkin et al. (1999). A solution to this problem is the high order sliding mode (HOSM) technique, Levant (2005). This control technique maintains the same sliding mode properties (in this sense, first-order sliding mode) with the advantage of eliminating the chattering problem due to the continuous-time nature of the control action. The actual disadvantage of this control technique is that the stability proofs are based on geometrical methods since the Lyapunov function proposing results in a difficult task, Levant (1993). The work presented in Moreno & Osorio (2008) proposes quadratic like Lyapunov functions for a special case of second-order sliding mode controller, the super-twisting sliding mode controller (STSMC), making possible to obtain an explicit relation for the controller design parameters. Jorge Rivera1, Luis Garcia2, Christian Mora3, Juan J. Raygoza4 and Susana Ortega5 1,2,3,4Centro Universitrio de Ciencias Exactas e Ingenierías, Universidad de Guadalajara 5Centro de Investigación y Estudios Avanzados del I.P.N. Unidad Guadalajara México Super-Twisting Sliding Mode in Motion Control Systems 13