Note the relationship between the control canonical form in Fig. 2-9 and the observer canonical form in Fig. 2-10. The diagram of Fig. 2-9 (b) can be converted to that of Fig. 9-10 by changing all signal summing points to signal-distribution points, all signal-distribution points to signal-summing points, and reversing the signal flow direction in each signal path. The coefficient gains remain the same and signals are reversed in the time delay elements. These "transverse" diagrams then have the same transfer function.

(a) Write the state equations for the simulation diagram shown in Fig. 2-6.

(b) Find the "transverse" simulation diagram for this structure.

(c) Write the state equations for this transverse structure.

(d) Show that the transfer function for this transverse structure is given by (2-43).

Fig. 2-9

Fig. 2-10

Fig. 2-6

Transcribed Image Text:

U(z) 1 E(z) 1-"p- u(k) + T (-7)"x 1-"q -a (a) -20 Op- (b) T 1-"q bo b bo x2(k) T y(k) x(k) OY(z)