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

Excecies (28) 5 — 36 ( 用坐标纸 ) Automatic Control Theory

（ Lecture 28) §5. Analysis and Adjustments of Linear Systems in Frequency-Domain §5.1 Concept of Frequency-Response Characteristics §5.2 Amplitude-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

Review §5.9.1 Lead compensation For ： Essential — Use the phase lead of the network to increase the phase margin. Steps ： ① ③ ④ Design ⑤ Check ② Effects ： Lower band unchanged To Satisfy Middle band altered Higher band raised Incapable of anti-high-frequency noise to improve dynamic performance

Review §5.9.2 Lag Compensation For ： Essential: Reduce the magnitude to use the “phase savings” of the original system. Steps ： ① ④ Design ⑤ Chec ② ③ Sketch the curve Effects ： Lower band unchanged k To Satisfy Middle band reduced Higher band depressed Capable of anti-high-frequency noise Swiftness loss for stability

Automatic Control Theory §5.9 Control Systems Design by Frequency Response Lead Compensation Lag Compensation Lag-Lead Compensation PID Design （ Lecture 28 ）

§5.9.3 Lag-Lead Compensation （ 1 ） §5.9.3 Lag-Lead Compensation (1) Lag-Lead network

§5.9.3 Lag-Lead Compensation （ 2 ） (1) Lag-Lead network Lead part Lag part Features of Lag-Lead network ： Magnitude Decreased ， Phase Lead

§5.9.3 Lag-Lead Compensation （ 3 ） (2) Lag-Lead Compensation Essential—Utilize the merits of both Lag Compensation ( Magnitude Attenuation) and Lead Compensation (Phase Lead) to Improve the performance. ① From ③ Determine ④ Design ② From do not work. Both Lag Lead Algorithm (Given index ) ⑤ Check whether satisfy the requirements.

§5.9.3 Lag-Lead Compensation （ 4 ） Example1

§5.9.3 Lag-Lead Compensation （ 5 ） 希望特性校正法

§5.9.3 Lag-Lead Compensation （ 6 ）

§5.9.3 Lag-Lead Compensation （ 7 ）

§5.9.4 PID Design （ 1 ） (1) PID circuit

§5.9.4 PID Design （ 2 ） Example3

Summary Cascade compensation in F.-Domain fits for — The minimum phase angle system with unity feedback unity fdck sys.min. phase sys. For non-unity feedback system For non-minimum phase system: Sketch both L(w) and  (w); Take care of stability.

Summary （ 2 ） Comparison of cascade compensations ① Lead compensation Features ② Lag compensation ③ Lag-Lead Compensation Methods Application situation Effect Magnitude raised Phase lead Magnitude suppressed Phase lag Magnitude suppressed Phase lead When the above two do not work  c   Higher Band   c  Higher Band   c  ～  Higher Band ～

Excecies(28) 5 — 36 ( 用坐标纸 ) Automatic Control Theory