Tham khảo tài liệu 'ogata - modern control engineering part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | curves for any function of the form 1 jdi T 1. If such a template is not available we have to locate several points on the curve. The phase angles of 1 jtoT 1 are 45 at CD T at 1 CD 2T at 1 a . 10T at 2 CD at CD - T For the case where a given transfer function involves terms like 1 j i T n a similar asymptotic construction may be made. The corner frequency is still at cư ỈỈT and the asymptotes are straight lines. The low-frequency asymptote is a horizontal straight line at 0 dB while the high-frequency asymptote has the slope of -20m dB decade or 20n dB decade. The error involved in the asymptotic expressions is n times that for 1 cd T 1. The phase angle is n times that of 1 4- jcoT at each frequency point. Quadratic factors 1 2t jc j 0Jn Jo on 2 1. Control systems often possess quadratic factors of the form 1 8-1 . d . cd 2 1 7 f- If c 1 this quadratic factor can be expressed as a product of two first-order factors with real poles. If 0 1 this quadratic factor is the product of two complexconjugate factors. Asymptotic approximations to the frequency-response curves are not accurate for a factor with low values of . This is because the magnitude and phase of the quadratic factor depend on both the corner frequency and the damping ratio The asymptotic frequency-response curve may be obtained as follows Since 1 20 log -20 log 2 for low frequencies such that CD CD the log magnitude becomes -20 log 1 OdB The low-frequency asymptote is thus a horizontal line at 0 dB. For high frequencies such that CD cDn the log magnitude becomes -20 log -40 log dB 480 Chapter 8 Frequency-Response Analysis The equation for the high-frequency asymptote is a straight line having the slope 40 dB decade since -40 log -40 - 40 log The high-frequency asymptote intersects the low-frequency one at O - On since at this frequency co _ -40 log -40 log 1 0 dB This frequency On is the corner frequency for the quadratic factor considered. The two asymptotes just derived are .