Reconsider the field-controlled motor in Figure 6.47. Equations 6.44 and 6.45 represent the dynamics of the system in terms of the variables \(i_{\mathrm{f}}\) and \(\theta\).

a. Assuming the angle \(\theta\) to be the output, draw a block diagram to represent the dynamics of the field-controlled motor.

b. Derive the transfer functions \(\Theta(s) / V_{\mathrm{f}}(s)\) and \(\Theta(s) / T_{\mathrm{L}}(s)\). All of the initial conditions are assumed to be zero.

c. Determine the state-space form.

Transcribed Image Text:

+ Vr + RE ww elle B Im FIGURE 6.47 An electromechanical system with a field-controlled DC motor.