Question

I'm having some troubles understanding what needs to be done in Simulink in MatLab.

System 1:    y[k]−1.3y[k−1] + 0.4y[k−2] = x[k]. Transfer Function: (z^2) / (z^2)-1.3(z)+0.4

System 2:    y[k]−1.8y[k−1] = c[k] + x[k]    (2a)

c[k] = αy[k−1] (2b) Transfer Function: (z) / [(z)- (1.8+ a)]

1. Realize system (1) through transfer function block.

2. Realize system (1) through cascade connection of two first order systems.

3. Realize system (1) through parallel connection of two first order systems.

4. Compare the responses of 1 to 3 with input x[k] = 1, x[k] = 1.5k and x[k] = 3k.

5. Realize system (2) through feedback connection.

6. Simulate the impulse response and the step response for three sets of parameters:

i) α = 0

ii) α = 1

iii) α = −1

with zero initial conditions. Discuss your observation.

Answer 1

1,2,3)

4)all responce for given input are same

for X[K]=1

for X[K]=1.5K

for X[K]=3K

5)

6)for a=0

for a=1

for a=-1