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feat: experimental steps use the same model #5407

@martinjrobins

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@martinjrobins

Description

At the moment the equations of the model vary depending on the current experimental step (i.e. current controlled or voltage controlled). It would be advantageous to only have a single model for all steps:

  1. efficiency: you need to build each model, and then the solver needs to convert each model to casadi. During solve you need to map the final state from each model to the initial conditions of the next. this would all be eliminated if we only have a single model for each step.
  2. sensitivities: also need to map the sensitivities from one step to the next. This is complicated by the fact that some variables are created and removed from one step to the other, so sensitivities cannot be tracked for these variables.

Would it be possible to formulate the models so that the model does not change from one step to the next? E.g. have all variables in the state (current, voltage, etc), and the input current or input voltage is done via observer-like equations with a given relaxation parameter r, e.g. d_current / dt = r * (current - observed_current)

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