Consider the dynamic system represented by the following Block Diagram model in Figure 2.76.

(a) Find the Transfer Function model of the system.

(b) Express this Transfer Function model in controllable canonical form and deduce the StateVariable Matrix model.

(c) By directly analysing the block diagram in Figure 2.76, develop the state equations in terms of the given state variables. Deduce the State-Variable Matrix model.

(d) Explain why the two models obtained from (b) and (c) are different.

(e) From the State-Variable Matrix model in (c), use matrix algebra to find the Transfer Function model of the system.

(f) Is the Transfer Function model obtained in (e) the same as that from (a)? Explain why this is the case.

Transcribed Image Text:

1 X4 1 X1 U(s) G G = 2s S+4 X3 H 1 5S == Figure 2.76 Block diagram model. + x2 H = LTC S + Y(s)