Variable Structure Control and Sliding Mode (VSC-SM) is based on changing the structure of the controller, in response to changing system state in order to obtain the desired response. This is accomplished through the use of a control law with high switching frequency, which forces the trajectory of the system to remain in a given surface. The system is insensitive to variations and disturbances of certain parameters while the state trajectory is on the switching surface. This type of control is characterized by the existence of the sliding mode, which occur when the state of the system repeatedly crosses the switching surface due to the fact that any movement in the vicinity of the surface is directed to it. The sliding mode has two very important features in robust performance and design of the VSC-SM. The first characteristic is that the component that implements the discontinuous function switches in high frequency and therefore implements a high gain, which is theoretically infinite, reducing the influence of disturbances and uncertainties of the system. The second feature is that the order of the equation of motion is reduced because the trajectory of the sliding mode belongs to a surface smaller than the system. Thus, the sliding mode system behaves as an autonomous system of lower order, called the equivalent system, whose movement is different from the subsystem constituents. The design of the switching surface for Full-Order Variable Structure Control with Sliding Mode (FOVSC-SM) can be done directly through classical linear control techniques. The basic idea is to address the problem of switching surface design for the FOVSC-SM for linear and time invariant systems through LMI, eigenvalues placement and linear quadratic regulator (LQR). This approach combines classical controller design techniques with a robust control technique for systems subject to disturbances. The aim is also to implement these controllers in the equipment available in the Laboratory of Control and Servo-mechanisms in order to analyze the performance achieved compared with computer simulations and theoretical results.
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