Given the photovoltaic system described in Problem 65 in Chapter 2 (Agee, 2012) and defining the following state variables, system input and output as y = x₁ = θ_m; x₂ = θ̇_m; x₃ = i_a, and u = e_a, write a state-space representation of the system in the form ẋ = Ax + Bu; y = Cx.

Data From Problem 65 in Chapter 2:

A photovoltaic system is used to capture solar energy to be converted to electrical energy. A control system is used to pivot the solar platform to track the sun’s movements in order to maximize the captured energy. The system consists of a motor and load similar to that discussed in Section 2.8. A model has been proposed (Agee, 2012) that is different from the model developed in the chapter in the following ways: (1) the motor inductance was not neglected and (2) the load, in addition to having inertia and damping, has a spring. Find the transfer function, θ_m(s)/E_a(s), for this augmented system assuming all load impedances have already been reflected to the motor shaft.