Suppose that, for the system of Fig. 5-20, equation (5-34) is [ y(k)=mathbf{C v}(k)+d_{2} m(k) ] (a)

Question:

Suppose that, for the system of Fig. 5-20, equation (5-34) is

\[
y(k)=\mathbf{C v}(k)+d_{2} m(k)
\]

(a) Derive the state model of (5-37) for this case.

(b) This system has an algebraic loop. Identify this loop.

(c) The gain of the algebraic loop is \(-d_{1} d_{2}\). What is the effect on the system equations if \(d_{1} d_{2}=-1\) ?

(d) We can argue that algebraic loops as in this case cannot occur in physical systems, since time delay is always present in signal transmission. Quite often we can ignore this delay. Under what conditions can we obviously not ignore delay in this system?

Fig. 5-20