Chapter 6: FrequencyDomainAnaysis上海交通大学SHANGHAI IIAO TONG UNIVERSITY
Chapter 6: Frequency Domain Anaysis
OutlineConceptIntroduction ofFreguencyResponse店2.Frequency Response of the Typical ElementsGraphical3.Nyquist and Bode Diagram of Open-loopmethodSystemNyquist-criterionAnalysis5.FrequencyResponse Based System Analysis6. FreguencyResponse of Closed-loop Systems上海交通大学SHANGHAIIIAOTONGUNIVERSITY
Outline Concept Graphical method Analysis 1. Introduction of Frequency Response 2. Frequency Response of the Typical Elements 3. Nyquist and Bode Diagram of Open-loop System 4. Nyquist-criterion 5. Frequency Response Based System Analysis 6. Frequency Response of Closed-loop Systems
6-3NyguistandBodeDiagrams for Open-loop SystemGain-phase characteristic diagramNyquist diagram. Log-Magnitude characteristic diagramL-α plotBodeLog-Phase characteristic diagramdiagramβ-o plotPartition of Open-loop System Into Typical ElementsSketching Method of Nyquist DiagramSketching Method of Bode DiagramMinimumPhase System上海交通大学SHANGHAIIIAOTONGUNIVERSITY
6-3 Nyquist and Bode Diagrams for Open-loop System ◼ Partition of Open-loop System Into Typical Elements ◼ Sketching Method of Nyquist Diagram ◼ Sketching Method of Bode Diagram ◼ Minimum Phase System • Gain-phase characteristic diagram • Log-Magnitude characteristic diagram L-ω plot Log-Phase characteristic diagram -ω plot Bode diagram Nyquist diagram
Review of Freguency Characteristics of TypicalElements1.ProportionalelementL()(dB)jY(o)A(の) = K20lgKOdB() = 00K04p(0)()0L(@) = 20lg KX()0.β(@) = 0°02.Integration elementSL(α)(dB)A(0) = 1/ jY(o)-20ndB/decOdBP(@) = -90°.n00=80L(@) = -20lg 0X(0)p(o)()A0Φ() = -90°.n上海文道大学to-90°SHANGHAIJIAOTONGUNIVERSITY
Review of Frequency Characteristics of Typical Elements 1.Proportional element 0 K jY( ) X ( ) 20lgK 0° 0dB ( )( ) L( )(dB) ( ) ( ) 0 A K = = ( ) 20lg ( ) 0 L K = = 2. Integration element 0 jY( ) X ( ) = -20ndB/dec ° 0dB ° ( )( ) L( )(dB) ( ) 1 ( ) 90 A n = = ( ) 20lg ( ) 90 L n = = 1 n s
3.Derivative Element[A(の) = [L() = 20lg 0Φ(@) = 90° . np(の)= 90°. n4.InertialElement1AsymptotesA(@) =0<<1/T, L()~-20lg1=0/1+0?T?p(の) = -arctgoT@>>1/T, L(@)~-20lg@TL(o)(dB）渐近线jY(o)渐近线交接频率D0-10精确曲线1+@1-200=80-3010.50.1/TI/T10/T+ p(0)()40OTp(o) :0=0x(o)1+°T2A(0)00-45F交通大学-901/T0.1/TJOTHAOTONGUNIVERSITY
4.Inertial Element 3.Derivative Element n s ( ) ( ) 90 A n = = ( ) 20lg ( ) 90 L n = = 0 0.5 1 jY( ) X ( ) = ( ) A( ) = 0 2 2 1 T T + 2 2 1 1+ T 0.1/T 1/T 10/T 渐近线 渐近线 精确曲线 交接频率 0.1/T 1/T 10/T ( )( ) L( )(dB) 2 2 1 ( ) 1 ( ) arctg A T T = + = ω<<1/T, L(ω)≈-20lg1=0 ω>>1/T, L(ω)≈-20lgωT Asymptotes