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In the last years hybrid automata have been applied in the design and verification of embedded systems. Once a hybrid model of the system has been proved to be correct with respect to the desired properties, it would be valuable to extract a correct-by-construction HW/SW implementation of it. This work discusses a methodology and a corresponding tool chain that allow to extract a HW/SW implementation of a controller modeled by a subclass of timed automata, named elastic controllers, operating in an environment represented by a hybrid automaton. The required tools have been either developed from scratch or extended from the current state-of-the-art in order to support an automated flow from hybrid automata specifications to correct-by-construction discrete implementations described in the SystemC language.