Automatic Control Theory School of Automation NWPU Teaching Group of Automatic Control Theory

Excecies(20) 5 — 9 买单对数坐标纸 Automatic Control Theory

Review Nyquist Plot of Typical Factors ⑴ ⑵ ⑶ ⑻ ⑸ ⑷ ⑹ ⑺

Automatic Control Theory （ Lecture 20) §5. Analysis and Design of Linear Systems in Frequency-Domain §5.1 Concept of Frequency-Response Characteristics §5.2 Amplitude and phase Frequency Characteristics §5.3 Bode Diagrams §5.4 Nyquist Stability Criterion §5.5 Stability Margins §5.6 System Analysis by Frequency Response Characteristics of Open-Loop Systems §5.7 Nichols Chart §5.8 System Analysis by Frequency Response Characteristics of Closed-Loop Systems §5.9 Control Systems Design by Frequency Response

Automatic Control Theory （ Lecture 20 ） §5.3 Bode Diagrams

§5.3 Bode Diagrams (1) Semilog Coordinate

§5.3 Bode Diagrams (2) ⑴ Magitude multiplication = Logarithm addition Convenient for segment addition ； Longitudinal axis Abscissa Axis Features of the coordinate Features Scaled by lg  ， dec “ Decade ” 按 lgw 刻度， dec “ 十倍频程 ” Marked by  Distance reflecting ratio 按 w 标定，等距等比 “ Decibel ” ⑵ Represents frequency characteristic in large scale; ⑶ L(  ) can be determined by experiment, so can G(s). An introduction for Bode diagrams (Logarithmic Plots)

§5.3 Bode Diagrams (3) §5.3.1 The Bode diagram of typical factors ⑴ The Gain ⑵ Derivertive Factor ⑶ Integral Factor ⑷ First-Order Factor

§5.3 Bode Diagrams (4) The Logarithmic plot of first-order factors is symmetric about the  1/T  point. Prove ： Suppose

§5.3 Bode Diagrams (5) ⑸ Reciprocal First-Oder Factor

§5.3 Bode Diagrams (6) ⑹ Quadratic Factors

§5.3 Bode Diagrams (7) ⑺ Receprocal Quadratic Factors

§5.3 Bode Diagrams (8) ⑻ Delay Link

§5.3 Bode Diagrams (9) Example 1 Obtain the transfer function from the Bode diagram. Solution. From the plot Corresponding relation between the Bode diagram and Nyquist Plot: Turning frequency Cutoff Frequency  c ：

§5.3 Bode Diagrams (10) Example 2 Obtain the transfer function from the Bode diagram. Solution. From the diagram:

§5.3 Bode Diagrams (11) Corresponding relation between the Bode diagram and Nyquist Plot ： Cutoff Frequency  c ：

§5.3 Bode Diagrams (12) Frequency characteristic of typical factors

Excecies(20) 5 — 9 买单对数坐标纸 （ 3dec: 5 张， 4dec: 1 张） Automatic Control Theory

§5.3.2 Bode Diagram For Open-loop Systems （ 1 ） §5.3.2 Bode Diagram For Open-loop Systems

§5.3.2 Bode Diagram For Open-loop Systems （ 2 ） The steps to sketch Bode diagram for open-loop system ⑴ Changing open-loop transfer function G(j  ) into the end of a standard form ⑵ Listing the turning frequency in turn. ⑶ 确定基准线 ⑷ Drawing the diagram Example Inertial link 0.5 First-order composite differential 1 Oscillation Link 基准点 斜率 First- order Inertial link -20dB/dec Composite differential +20dB/dec Second- order Oscillation Link -40dB/dec Composite differential - 40dB/dec  Inertial link -20  First-order composite differential +20  Oscillation Link -40 第一转折频率之左 的特性及其延长线

§5.3.2 Bode Diagram For Open-loop Systems （ 3 ） ⑸ Correction ⑹ Check ① When the turning frequency of two inertial links are close to each other ② When oscillation  (0.38, 0.8) ① The rightmost slope of L(  ) is equal to -20(n-m) dB/dec ② The number of turning point =(Inertial)+(First-order composite differential)+(Oscillation)+(Second-order composite differential) ③  -90°(n-m) 基准点 斜率  Inertial link -20  First-order composite differential +20  Oscillation Link -40

§5.3.2 Bode Diagram For Open-loop Systems （ 4 ） 基点 Example 4. Sketch Bode diagram Solution. ① Standard form ② Turning frequency ③ 基准线 ④ Drawing 斜率 ⑤ Correction The rightmost slope of L(  ) is equal to -20(n-m) =0 The number of turning point = 3  tend to -90 º(n-m)=0º finally

Summary Frequency characteristic of the typical link

Summary The steps to sketch Bode diagram for open-loop system ⑴ Changing open-loop transfer function G(j  ) into the end of a standard form. ⑵ Listing the turning frequency in turn. ⑶ 确定基准线 基准点 斜率 第一转折频率之左 的特性及其延长线 ⑷ Drawing the diagram First- order Inertial link -20dB/dec Composite differential +20dB/dec Second- order Oscillation Link -40dB/dec Composite differential - 40dB/dec ⑸ Correction ① When the turning frequency of two inertial links are close to each other ② When oscillation  (0.38, 0.8) ⑹ Check ① The rightmost slope of L(  ) is equal to -20(n-m) dB/dec ② The number of turning point =(Inertial)+(First-order composite differential)+(Oscillation)+(Second-order composite differential) ③  -90°(n-m)