Find Open Loop Response to G(s)=10e^(ts)/s+3

[Kayne]

Hi,I have the equation G(s)=C(s)/M(s)=10e^(ts)/s+3 and I have to find the open loop response c(t) with a unit step which is 1/s
The explanation in the Text book is quite confusing, does anyone know if there are easier explanations like worked exampled on the internet so I can work though then solve this equation

Thanks for your help

 

[Jmf]

Have you studied Laplace Transforms?

if so, then you can get the Laplace transform of the response by multiplying the transfer function of the system - which you have - with the LT of your input - a unit step, which has transform 1/s.

Then you need to take the inverse transform of this, which will yield the response (with respect to time). To do this you'll probably need to make use of a partial fraction expansion.

I don't know any good websites with examples of this though, sorry.

 

[Kayne]

Thanks for your help I have since worked though and found an answer, whether its correct or not that is another story. If anyone understands Laplace transforms my answers are attached, if you can have a look and see if i am wrong or right,

The question I have done is a little different to the above G(s)=C(s)/M(s)=5e^-(ts)/s+5 and I have to find the open loop response c(t) with a unit step which is 1/s.

My answers are attached

Thanks

 

[Jmf]

I got:

$$c(t) = u(t-T) - u(t-T)e^{-5(t-T)}$$

where u(t) is the Heaviside step function, and the T is the constant 't' in your transfer function (I changed it to a big T since it's a bit dodgy to use the same symbol for two different things)

i.e. I took:

$$G(s) = e^{-Ts}\frac{5}{s+5}$$

Though I didn't take much care over it, so I'm not sure I'm correct. The Heaviside function will almost certainly be in your answer though, since there's a time delay in the transfer function.

I'd recommend going and looking up the t-shifting theorem for Laplace Transforms.

 

[DeeNos]

,I would suggest looking for online resources or textbooks that specifically focus on control systems and open loop response. These resources can provide step-by-step examples and explanations that may be easier to understand than the one provided in your current textbook.

One possible approach to solving this equation is to first find the inverse Laplace transform of G(s) by using the properties of the Laplace transform. This will give you the time domain representation of G(s), which is c(t). Then, you can plug in the unit step function 1/s into c(t) and solve for the open loop response.

Alternatively, you can also use the transfer function method to find the open loop response. This involves substituting s with jω in G(s) and then finding the magnitude and phase of the resulting complex number. This will give you the frequency response of G(s), which can then be used to find the open loop response c(t) by taking the inverse Fourier transform.

I would also recommend consulting with a professor or colleague who has expertise in control systems if you are still having difficulty understanding the concept. They may be able to provide additional insights or resources to help you better understand the open loop response.