I know we can calculte steady state error by using final value theorem. I don't know about the input. Its the complete statement.Joshy said:Is the equation ##s^2+2 \zeta \omega_n s + w_n^2##?
##\zeta## is your damping ratio; so you'll want to fix that to 0.5. I've never heard of "the fraction of derivative of error." I'm going to guess that's your steady-state error. What's your input? Is it a step? May you provide the equation for the steady-state error or for this "fraction of derivative of error"? I get the feeling once you get that and plug in ##\zeta = 0.5## you're going to be very close to what you want if not already done with the problem.
Joshy said:Does it have any graphs or other specifications?
No graphs are thereJoshy said:Does it have any graphs or other specifications?
the question is from ELECRTRONICS AND COMMUNICATION (ch name is control system) objective book written by HANDA. In this book only multiple choice questions are present with no/little literature. I am following this book to prepare for junior engineer test conducted in my country. They mostly take question from this book if you want i can post complete ch in pdfJoshy said:Does your textbook have a definition of "the fraction of derivative of error" or is it the steady-state error? Which book are you using? I'm looking through Modern Control Systems by Dorf.
Interestingly he refers to ##\zeta## as the damping ratio, but also ##\zeta \omega_n## as the closed-loop damping constant. I never noticed that before (maybe I just liked its reciprocal ##\tau## too much); I bring this up because I'm wondering if 0.5 is the damping ratio or the damping constant. We might have an extra variable hidden in subtle vocabulary I was unaware of.
I'm struggling to really understand the question not knowing what this "fraction of derivative of error" is. I would have done the same approach final value theorem for the steady-state error, but once you set ##s## to zero it makes that damping irrelevant; it's more relevant for the overshoot and the time it takes to settle. Overshoot doesn't seem to match the context, but I went for it anyways and got about 16%. Looks nothing like the options above.
The only other thing I stumbled upon is after you do the Laplace transform of the second order system with response to a step it's 1 minus some damped sinusoidal. The amplitude of that sinusoidal is ##1/\sqrt{1-\zeta^2}##. Still not exactly what I was hoping for, but the ##\sqrt{1-\zeta^2}## is about 0.86; this is just out of desperation for an answer and exploring- I don't think it's right.
The damping ratio in a control system is a measure of the rate at which the system's oscillations decrease over time. It is represented by the Greek letter ζ (zeta) and is calculated by dividing the system's damping coefficient by the critical damping coefficient.
The damping ratio affects the response of a control system by determining the type of response it will have. A higher damping ratio leads to a more stable response with less overshoot and settling time, while a lower damping ratio can result in a more oscillatory and slower response.
The ideal damping ratio for a control system depends on the specific application and desired response. In general, a damping ratio of 1 (or 100%) is considered critically damped and results in the fastest and most stable response. However, some applications may require a lower or higher damping ratio for optimal performance.
The damping ratio and natural frequency of a control system are inversely related. As the damping ratio increases, the natural frequency decreases, and vice versa. This means that a system with a higher damping ratio will have a slower response, while a system with a lower damping ratio will have a faster response.
Yes, the damping ratio can be adjusted in a control system by changing the system's parameters, such as the damping coefficient or the critical damping coefficient. It can also be adjusted by using different control strategies or feedback methods to achieve the desired response.