Reconsider the armature-controlled motor in Figure 6.44. Equations 6.31 and 6.32 represent the dynamics of the system in terms of the variables \(i_{\mathrm{a}}\) and \(\theta\).

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

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

c. Determine the state-space form.

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Va Ra La 0000 B eb FIGURE 6.44 An electromechanical system with an armature-controlled DC motor.