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 .
(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 ...
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.