Old spec 4.6 exercise (ENGR5001) - Revisica

Old spec 4.6 exerciseExercise sheetCurrent spec2:28 min

ENGR202 (old spec) Control 4.6 Derivative and Velocity, exercise

Draw the block diagram for velocity feedback (instead of derivative action) applied to the second order plant, and use the block diagram to derive the Closed Loop Transfer Function.

$X(s) = \frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}U(s) \qquad u(t) = d(t) - k_v\frac{dx(t)}{dt}$

Formulas you may need

Negative feedback rule: $\dfrac{G_1}{1 + G_1 G_2}$ (learn this)
Velocity feedback: $u(t) = d(t) - k_v\dfrac{dx}{dt}$ , i.e. $U = D - k_v sX$ (given in the question)
Generalised second order form $s^2 + 2\zeta\omega_n s + \omega_n^2$ (learn this)

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