In control systems, it is possible to make good guesses about system transient response in the time domain using steady-state frequency response. For example, large peak magnitude for closed-loop system means oscillatory transients, and a low sensitivity function over wide range of frequencies indicates fast disturbance rejection. Is there any intuitive explanation for this?
Frequency response techniques enable you to estimate transfer function for a given system. The transients are hidden in the the details.
For example, let's assume that you have identified a system for a range of frequencies and a second order transfer function fit to the frequency response data looks like w^2/(s^2+2*zeta*w*s + w^2) with zeta
Dear Al-Motasem
Remember any time series can be expressed as a combination of cosine (or sine) waves with differing periods and amplitudes
https://onlinecourses.science.psu.edu/stat510/node/71
this is the basis of an FFT where time and frequency are different representations of the same signal or control time series.
More higher frequency components may mean faster transients but sometimes also more noise junk in the control, all depending on phase of the various components.
regards
Gerhard
Dear Colleagues,
Good Day,
I absolutely agree with Dr. Baranwal , you can obtain (Identify) the your transfer function , from your plot ( bode plot- ie Mag./dB Vs. frequency( log scale ) in rad/sec or Hz. From that Transfer Function you can obtain Step/ Ramp / Acceleration plot (Transient Response) easily after that.
Please , see any Control Engineering book regarding Bode plot!!
Higher the open loop gain (magnitude in the Bode plot), better the disturbance rejection. This is the basic feedback idea. Additionally, you can relate the crossing frequency with the closed loop system peak response time (approx. t_p = 3/w_c) and the phase margin with the overshoot (approx. M_p = 60(70) - Pm).
If you want to see the transient time, you should approximate the frequency response with a transfer function and then analyse it.
The frequency response of a continuous-time system is comprised of a continuum complex sinusoids of infinite extent (-inf
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