Consider the electromechanical system in Figure 2.71.

(a) Draw the electrical circuit and the free-body diagram that can be used to represent this system.

(b) Justify the choice of the vector of state variables as

\[x=\left[\begin{array}{llll}q & \dot{q} & x & \dot{x}\end{array}ight]^{T} .\]

(c) Derive the State-Variable model for this electromechanical system, where the output is the force \(f_{e}\) on the movable plate and the inputs are the voltage \(v(t)\) and sound force \(f_{s}(t)\).

Transcribed Image Text:

k ww 2 L i(t) R w 1 A b m f,(t) + Figure 2.71 A simple electromechanical system. x(t)