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Robust energy shaping control of nonlinear systems

Authors
  • Romero Velázquez, José Guadalupe
Publication Date
Feb 08, 2013
Source
HAL-SUPELEC
Keywords
Language
English
License
Unknown
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Abstract

This thesis focuses on the design of robust control for nonlinear systems, mainly on mechanical systems. The results presented are to two situations widely discussed in control theory: 1) The stability of nonlinear systems disturbed; 2) The global tracking trajectory in mechanical systems having only knowledge of the position. We started giving a design method of robust controls to ensure regulation on non-passive output. In addition, if the system is perturbed (constant unmatched), rigorous proof to its rejection is provided. This result is based mainly on change of coordinates and integral dynamic control. When the scenario to deal are mechanical systems with time-varying matched and unmatched, disturbance, the system is endowed with strong properties as IISS (Integral Input-State Stable) and ISS (Input-State Stable). This is achieved based on the design method to rejection of constant disturbances (unmatched). However, due to the nonlinearity of the system, the controllers have a high complexity. For the same problem, a second and elegant result is given making a initial change of coordinate on the momenta variable, such that the controller significantly simplifies, preserving the aforementioned robustness properties. Finally, a convincing answer to the problem of global exponential tracking of mechanical systems is given taking into account only the position information. We solve this problem in two steps. First, some slight variation is presented to the proof of stability of a speed observer based on Immersion and Invariance theory recently published. Note that this is a speed observer satisfying the exponential convergence speed in mechanical systems. Secondly, and based on the change of coordinates (momenta), a globally exponentially stable tracking controller with position and velocity known is proposed. The combination of both results give the first global exponential tracking controller of mechanical systems without velocity measurements.

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