- #1
Master1022
- 611
- 117
- Homework Statement
- Given transfer functions [itex] G(s) [/itex] and [itex] C(s) [/itex], find the state space models for those systems. Then find the state space model when they are connected in series
- Relevant Equations
- Transfer function
Hi,
I have a question about a homework problem: I am not sure why I do not seem to get the same answers when using different methods.
Question: Given transfer functions [itex] G(s) = \frac{s - 1}{s + 4} [/itex] and [itex] C(s) = \frac{1}{s - 1} [/itex], find the state space models for those systems. Then find the state space model when they are connected in series.
Attempt:
Intuitively I think that the following methods should both yield the same answer:
1) Find the state space models separately and then combine them in series
2) Combine the transfer functions in series and then convert to state space
however, these methods do not seem to give the same answer and I am unsure why.
Here is my attempt to convert [itex] G(s) [/itex] to a state space model.
and here is my working to convert [itex] C(s) [/itex]. The bottom of the page uses a general formulation of two state-space models to derive a formula for a state-space model of the series system. The first state space model (representing [itex] C(s) [/itex]) has no [itex] d_1 [/itex] just like [itex] C(s) [/itex]. I could have included it, but it would be 0 anyways.
The general formula derivation is continued and substituting values into the formula:
I am not sure why the two methods wouldn't give the same answer and any help would be greatly appreciated.
Thanks
I have a question about a homework problem: I am not sure why I do not seem to get the same answers when using different methods.
Question: Given transfer functions [itex] G(s) = \frac{s - 1}{s + 4} [/itex] and [itex] C(s) = \frac{1}{s - 1} [/itex], find the state space models for those systems. Then find the state space model when they are connected in series.
Attempt:
Intuitively I think that the following methods should both yield the same answer:
1) Find the state space models separately and then combine them in series
2) Combine the transfer functions in series and then convert to state space
however, these methods do not seem to give the same answer and I am unsure why.
Here is my attempt to convert [itex] G(s) [/itex] to a state space model.
and here is my working to convert [itex] C(s) [/itex]. The bottom of the page uses a general formulation of two state-space models to derive a formula for a state-space model of the series system. The first state space model (representing [itex] C(s) [/itex]) has no [itex] d_1 [/itex] just like [itex] C(s) [/itex]. I could have included it, but it would be 0 anyways.
The general formula derivation is continued and substituting values into the formula:
I am not sure why the two methods wouldn't give the same answer and any help would be greatly appreciated.
Thanks