Register to reply 
Steady State Error Calculation to Input Step and Ramp Input 
Share this thread: 
#1
Mar813, 02:49 PM

P: 33

Hi all,
I am getting confused about how to calculate steady state error in a system. My particular transfer function is: G(s)= 4.992/(s^2+3s1) Firstly, with an input step am I right in saying that the Steady State error will always be zero? If so can someone explain the reason behind this, is it because it has negative real parts? Also, what happens when I apply a ramp input? An example would be great if possible. Thanks in advance Steve 


#2
Mar913, 04:04 PM

P: 428

Since G(s) is unstable in open loop (it has poles in the right halfplane), I'm going to assume we're talking about using it in a feedback configuration.
Let the system error, e(t), be given as: e(t) = r(t)  c(t) where r(t) and c(t) are the system input and output, respectively. For a unity feedback system, the Laplace transform of e(t), E(s), is then given as: [tex] E(s) = \frac{1}{1 + G(s)} R(s) [/tex] The system steadystate error, e_ss, is then given by the final value theorem as: [tex] e_{ss} = \lim_{s \rightarrow 0} s \frac{1}{1 + G(s)} R(s) [/tex] For a step input, R(s) = 1/s, we have: [tex] e_{ss} = \lim_{s \rightarrow 0} s \frac{1}{1 + \frac{4.992}{s^2 + 3s  1}} \frac{1}{s} = \frac{1}{1  4.992} \approx 0.2505 [/tex] For a ramp input, R(s) = 1/s^2, we have: [tex] e_{ss} = \lim_{s \rightarrow 0} s \frac{1}{1 + \frac{4.992}{s^2 + 3s  1}} \frac{1}{s^2} = \lim_{s \rightarrow 0} \frac{1}{s + \frac{4.992s}{s^2 + 3s  1}} = \infty [/tex] The steadystate error for a step input will thus be a constant and for a ramp input it will be unbounded. This is what you would expect for a type 0 system (no free integrators), if that makes sense to you. 


Register to reply 
Related Discussions  
Does input resistance in negative feedback increase input offset current of op amp?  Engineering, Comp Sci, & Technology Homework  4  
Steady State Error of a PI Controlled System (parabolic input)  Engineering, Comp Sci, & Technology Homework  1  
MATLAB, how to input step functions.  Engineering, Comp Sci, & Technology Homework  2  
Zero state / zero input repsonse and transient and steady state responce..  Engineering, Comp Sci, & Technology Homework  0  
Electrical and Computer Engineering, 2input LookUp tables designed with 2input XOR  Engineering, Comp Sci, & Technology Homework  0 