Control Systems Help: Open & Closed Loop Gains

[impedance]

Hello there,

I just got a question in control systems that i need help on... Hopefully, somebody genius on this forum can help me out..

If F(s) = 1 / (5s + 1)

1) Determine the DC gains of the open loop system and the closed loop system

2) Determine the time constant of the open loop system and the close loop system

3) Which one has a faster dynamics the open loop or the close loop system?

Given a system, how is it possible to find the closed loop and open loop gains from the system??

Isn't the system just one? open-loop or closed loop etc..

Thanks again for ur help
dino.

 

[chroot]

We generally do not provide help unless you first show your work and where you got stuck.

- Warren

 

[impedance]

oh ok.

well, for the closed loop system.

The DC gain is F(0) right.. so, its 1/(5*0 + 1) = 1

But, for the open loop system, how do i find the dc gain?

 

[ninaricci]

F(s) = 1 / (5s + 1)

generally , the equation can be wriiten as k0/1+s/wo
Dc gain =1
time constant = 1/wo=5

 

[ninaricci]

i think in order to find the dc gain for open loop or closed loop , the equation of each must be writtten based on the system provided(original system ) and later on dc gain can be determined as k when the equation is simpified to the form k0/1+s/wo after that the time constant is 1/wo
best wishes

 

[SGT]

oh ok.

well, for the closed loop system.

The DC gain is F(0) right.. so, its 1/(5*0 + 1) = 1

But, for the open loop system, how do i find the dc gain?

F(s) is the open loop system. The closed loop is:
$$M(s)=\frac{F(s)}{1+F(s)}$$

 

[impedance]

ya i got it. the closed loop transfer function would be: 1/(5s +2)

Neway, how do i find the time constant of open and closed loop??

thanks
dino.

 

[SGT]

ya i got it. the closed loop transfer function would be: 1/(5s +2)

Neway, how do i find the time constant of open and closed loop??

thanks
dino.

The time constant of
$$F(s)=\frac{K}{as+b}$$ is $$T=-\frac{b}{a}$$