Note that the gains K P and K D produce numerator dynamics in the command transfer function of Example 10.7.4 and that the K D term produces an unrealistic impulse in the torque T (t) when the command...

Note that the gains K_P
and K_D
produce numerator dynamics in the command transfer function of Example 10.7.4 and that the K_D
term produces an unrealistic impulse in the torque T (t) when the command is a step function. We can eliminate the numerator dynamics by measuring the angular velocity ω and using this measurement to modify the output of the controller. This replaces the derivative action. The proportional action is preserved by using an additional internal-feedback loop with the measurement of θ. The diagram is shown in Figure 10.7.6. Compare its performance with the PID system of Example 10.7.4 using the same performance specifications.