Hi there,
Examine the state-space model sys_ss:
>> sys_ss
Note that it has a non-unity E matrix. This happens because your H, a pure derivative, is improper. The connect command represents that block as a two-state ss with a non-unity E matrix - a descriptor ss. When connect builds the interconnected system, it preserves those states, so it yields a descriptor system.
And that means that your call to ss2tf, which only uses A,B,C, and D, is missing part of the dynamics of the system. sys_tf doesn't represent the same dynamics as sys_ss.
This is one of the reasons that ss2tf is not a great command to use when converting from ss to tf form. Try this instead:
>> sys_tf = tf(sys_ss)
This time when you plot the step responses, they match up. Also, tf removes those two extra states.
You can also reduce and simplify sys_ss into explicit form (E = 1) using the 'explicit' option of the ss command:
>> sys_ss_ex = ss(sys_ss,'explicit')
Now all of the system dynamics are described by A,B,C, and D.
For more information about explicit and descriptor state-space models, see the reference page for ss.
>> doc ss
Hope this helps!
