Laplace transform - Continuous and Discrete Time Signals and Systems - page 318

Fig. P6.25. Interconnected
systems specified in Problem
6.25.

1

( s + 6)

1

( s + 5)

− −

∑

+ +

1 1 1 1

y ( t )

x ( t )

∑

( s + 1) ( s + 2) ( s + 3) ( s + 4)

(i)

1

( s + 5)

+ −
∑

+

1 1 1

x ( t ) y ( t )

∑

( s + 1) ( s + 2) ( s + 3)

−

1

( s + 4)

(ii)

1 1 1

x ( t ) y ( t )

∑

( s + 1) ( s + 2) ( s + 3)

+

1

( s + 7)

1

( s + 6)

−

+

1 1

∑

( s + 4) ( s + 5)

(iii)

configuration to the specified transfer function to make its causal imple-
mentation stable.

6.25 Determine the overall transfer function for the three interconnected sys-
tems shown in Fig. P6.25.

6.26 Using the function residue available in M ATLAB toolboxes, calculate
the partial fraction coefficients for the transfer functions considered in
Problem 6.3.

6.27 Using the functions tf and bode available in the M ATLAB control
toolbox, plot the frequency characteristics of the systems with transfer
functions considered in Problem 6.15.

6.28 Repeat Problem 6.27 using the function freqs available in the M ATLAB
signal toolbox.

6.29 Using the functions tf and impulse available in the M ATLAB con-
trol toolbox, calculate the impulse response of the systems with transfer
functions considered in Problem 6.15.