1a) Find the transfer function for the state variable model below. Check your answer using the Matlab command, ss2tf(), which converts a state space model to a transfer function.

b) Use the Matlab ss2tf() command to find the transfer function for the following 4th-order!! state variable model:

2a) Find a block diagram for the transfer functionusing:

i) Phase variables

ii) Parallel Decomposition

iii) Cascade Decompostion

b) From your three different block diagrams, find three state variable models. Check your answer using the Matlab command ss2tf(). Do you obtain the correct H(s) for each state variable model?

c) Use the Matlab command, tf2ss(), to directly transfer H(s) to a state variable model. Do you obtain one of your answers to part b) (remember, the choice of state variables is not unique!)?

d) Using your block diagram for Parallel Decomposition (i.e., your answer to 2a) part ii)), find an op-amp circuit which has H(s) as a transfer function.

e) Can you reduce your op-amp circuit down to just 5 op-amps?