Exercise 5.0

Exercise 5.0#

Analysis ∙ Robustness of feedback controllers

Consider the control system in Fig. 30, where \(n(t)\) is the sinusoidal measurement noise \(n(t) = \sin(50 t)\).

../_images/ex0-block.svg

Fig. 30 Block diagram of the control system#

  1. Assume that \(F(s)=1\). How much is the closed-loop attenuating the measurement noise?

  2. Design a proportional controller \(F(s) = K\), with \(K >0\), that achieves a measurement noise attenuation factor of \(10\).

3. Bonus

Design \(F(s)=\frac{1}{s + \alpha}\), with \(\alpha > 0\), such that

  • The crossover frequency is at least \(10\) rad/s

  • The phase margin is at least \(50^\circ\)

  • The attenuation factor is \(10\)

Tip

Based on the Bode plot of \(G(s)\) reported in Fig. 31, sketch the complementary sensitivity function’s magnitude plot.

../_images/5918d8e6d81883cb380756134f8093ea3ecebe0e3a0a2a4c21bf20f06abc013a.png

Fig. 31 Magnitude Bode plot of \(G(s)\)#