09-10Chapter 7-6 Phase Margin and Gain Margin

09-10Chapter 7-6 Phase Margin and Gain Margin - Phase...

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Phase Margin and Gain Margin Principle of Automatic Control CHAPTER 7 requency Response (P244 Ch 8) By Hui Hui Wang Wang Frequency Response (P.244, Ch.8) 浙江大学控制科学与工程学系
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Phase Margin and Gain Margin Review of Nyquist’s Stability Criterion 9 Nyquist 稳定判据可知:若已知系统的开环函数 G(s)H(s), 即可 知开环的不稳定极点数(位于 S 的右半平面) P R ,在画出该开环传 递函数的极坐标图( Nyquist 图)之后,闭环系统的稳定性则由 Nyquist 图包围点( -1, j0 )的圈数 N 决定。闭环系统稳定的充要条 件是:位于 S 右半平面的极点数 Z R 0 Z R P R N 多情况下 环传递函数的某些系数发生变化时 yquist 9 许多情况下,开环传递函数的某些系数发生变化时, Nyquist 也随之发生改变,闭环稳定性也会发生变化。 9 Nyquist 穿过 1 环系统临界稳定 yqu st 图穿过(- , j0 )点时,闭环系统临界稳定。 9 稳定性研究中,将(- 1 j0 )点称为临界点。 Nyquist 图相对于 该点的位置即偏离临界点的程度,反映了系统的相对稳定性。 9 如果稳定性不够?? -- 校正 2
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Phase Margin and Gain Margin Outline of Chapter 7 9 Introduction 9 Bode Plots (Logarithmic plots) 9 Direct Polar Plots 9 Nyquist’s Stability Criterion-Part 1 9 Nyquist’s Stability Criterion-Part 2 hase Margin and Gain Margin and Their Relation to 9 Phase Margin and Gain Margin and Their Relation to Stability 9 tability From the Nichols Plot Stability From the Nichols Plot 9 Compensation 9 ……… 3 Maple
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Phase Margin and Gain Margin requency Response Frequency Response 5. Phase Margin and Gain Margin and Their Relation to Stability The stability and approximate degree of stability can be determined from the Lm and phase diagram. The stability characteristic is specified in terms of the following quantities. g q Gain crossover (幅值穿越频率--增益临界点) This is the point on the plot of the transfer function at which the magnitude of G(j ω ) is unity [LmG(j ω )=0dB]. The frequency at gain crossover is called the phase-margin frequency ω Φ . ( 有中文教材称此为截止频率 ω C ) hase argin ngle 角裕度 Phase margin angle (相角裕度) This is 180 ° plus the negative trigonometrically consider angle of the transfer function at the gain-crossover point. It is designated as the angle γ , which can be expressed as γ =180 ° + Φ , where G(j ω Φ )= Φ is negative . 4
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Phase Margin and Gain Margin requency Response Frequency Response 5. Phase Margin and Gain Margin and Their Relation to Stability LmG(j ω ) For stable system γ =180 ° + Φ >0 0dB ω Φ -1 Φ -90 ° ω Φ γ (+) -135 ° -180 ° ω→ hase margin The polar plot of G(j ω ) ω G(j ω ) -225 ° -270 ° Phase margin angle, γ (+) 5 pp ( j Log magnitude and phase diagram of G(j ω )
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Phase Margin and Gain Margin requency Response Frequency Response 5. Phase Margin and Gain Margin and Their Relation to Stability LmG(j
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This note was uploaded on 12/01/2011 for the course EE 400 taught by Professor Hui during the Spring '11 term at Zhejiang University.

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09-10Chapter 7-6 Phase Margin and Gain Margin - Phase...

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