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State Space Model of a Heater Element

Please see the attached file for full problem description.

Please answer with full explanations.
After solving the part a to part f , please discuss the energy dynamics of the question .

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(a) x(t) is actually i(t) i.e. the current of the inductor. v(t) is the input voltage and the output is Ri^2(t) i.e. which is twice the power consumed by the resistor (the delivered heat).

(b) The system is nonlinear due to x^2(t) in the output. The system is time invariant provided R and L are ...

Solution Summary

This solution provides an explanation of a state space model of a heater element, by discussing physical variables corresponding to the model state, calculations of linearity/nonlinearity and time dependence of the model, and a Euler solution for the state equation of the model.
Also included is a structural SIMULINK implementation of the model.