Question

Using what you learned about frequency response techniques, answer the following A. What are the common indices used to quantify the level of relative stability in a system' B. Mention the typical requirements in frequency response design that must be satisfied for a system for satisfactory performance

Answer 1

ANS

A) In time domain analysis the system response paranmeters delay time ,rise time ,settling time , peak time and most important maximum peak Mp and damping Ratio .

The peak amplitude ratio, Mp and damping ratio is a relative-stability criterion. The higher the peak, the poorer the relative stability

In frequency domain analysis gain margin and phase margin magnitude give the relative stability of system .

B) Typical requirement of frequency response of system are

i) Amplitude ratio (output /input) and phase angle will approximate the ideal values of 1.0 and 0 degrees for some range of low frequencies, but will deviate at higher frequencies as noise is of high frequency so it should attenuate the noise .

ii)The frequency at which a resonant peak occurs, $\omega _{r}$ , is a speed-of-response criterion. The higher $\omega _{r}$ , the faster the system response.

iii) Good gain margin and phase magin are required .

iii)The way uncertainty has been quantified is to assume that either gain changes or phase changes occur. Typically, systems are destabilized when either gain exceeds certain limits or if there is too much phase lag (i.e., negative phase associated with unmodeled poles or time delays).