Exercise 3.2

Exercise 3.2#

Analysis ∙ Linear dynamical systems Analysis ∙ Feedback control

A vehicle is characterized by the following transfer function, which relates the throttle input \(U(s)\) to the velocity \(Y(s)\),

\[ G(s) = \frac{s+10}{(s+1)^2(s+5)} \]

We need to design a controller that regulates the speed of the vehicle.

  1. Start by designing a proportional controller \(F(s) = K\). For what values of \(K > 0\) is the closed-loop stable? How does the closed-loop performance change when \(K\) is changed?

  2. Consider now \(K=10\). Compute the gain margin \(A_m\) and the phase margin \(\varphi_m\).

Hint

To check the stability of the closed-loop transfer function \(G_c(s)\), you can use the root locus (plotted with MATLAB), or the Routh-Hurwitz criterion.