Hybrid reset control systems. Analysis, design and applications

Resumo

The introduction of hybrid systems constitutes a recent fork in automatic control in the last years with a growing number of published results. In this literature the hybrid dynamical systems are defined with mathematical frameworks that characterize the continuous flow and discrete jump modes and its interaction, which can be modelled with different tools at each research area. In this work we are interested in the point of view of control design and more specifically in the transformation of continuous linear controllers into hybrid reset controllers, that is, when the discrete jump mode is introduced by means of the application of discrete jumps to the controller states. The adoption of the hybrid transformation introduces new capabilities that allow, for example, to overcome the fundamental linear limitations, but it also adds additional issues related to the stability of the response. In particular properties like frequency lag cancellation with sinusoidal input reference or elimination of overshoots and undershoots in step input reference (fast over-damped error response) can be achieved with the proposed transformation, but the discrete jump mode must be executed with a guaranty of preservation for the stability properties of the system response. The aim of this thesis is thus to contribute with new solutions in the field of hybrid reset controllers with base linear systems. The contributions include novel reset concepts (multiple anticipations and conic confinement) analysis and design tools (in the frequency domain, by Lyapunov or Lyapunov-Krasovskii and by hybrid phase-plane techniques) and applications (in particular to resonant controllers).