Exercise 4.3

Exercise 4.3#

Control design ∙ Laplace/Frequency domain Analysis ∙ Linear dynamical systems

../_images/ex3-block.svg

Fig. 27 Block diagram of a system affected by a disturbance \(v\)#

A system \(G(s) = \frac{5}{s+2}\) is affected by a disturbance \(v\) via a transfer function \(H(s) = \frac{s+10}{s+2}\).

The system is controlled with a proportional controller \(F(s) = K\), with \(K > 0\), as shown in Fig. 27.

  1. For what values of \(K\) the closed-loop stability is guaranteed?

  2. For what values of \(K\) the steady-state effect of a disturbance \(v = \text{step}(t)\) on the output is less than \(5\%\) in closed-loop?

  3. Show how the control scheme can be changed to explicitly compensate the disturbance.