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

Excecies(24) 5 — 28 (2), 29, 31 Automatic Control Theory

Middle band Tri-Band in Frequency Higher band Lower band Corresponding performance Expectation L()L() The ability of anti-high-frequency noise Open-loop gain K System type v e ss Cutoff frequency  c Phase margin  Dynamic Performance Steep ， High Moderate, Wide Low ， Steep Frequency Band Tri-Band does not give the steps to design systems, but it show the way to adjust the system structure for better performance. §5.6 Analysis by Frequency Response of O.L. Systems （ 12 ）

Automatic Control Theory （ Lecture 25) §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

Automatic Control Theory §5.7 Nichols Chart §5.8 System Analysis by Frequency Response Characteristics of Closed- Loop Systems （ Lecture25 ）

§5.7 Nichols Chart （ 1 ） Why Closed-Loop frequency responses (1) Indices of closed-loop frequency characteristics are used widely in practice; (2) The closed-loop frequency characteristics system are easily obtained by experimental method; (3) The system performance specifications can be estimated by the closed-loop frequency indices.

§5.7 Nichols Chart （ 2 ） §5.7.1 Vector Correlation between OL and CL Frequency Responses

§5.7 Nichols Chart （ 3 ） Constant M / N circles Constant M circle — A locus corresponding to a constant Let Rewrite: — Constant M circles equation

§5.7 Nichols Chart （ 4 ） Let Rewrite: — Constant N circles equation Constant N circle — A locus corresponding to a constant

§5.7 Nichols Chart （ 5 ） Constant M / N circles → Nichols chart

§5.7 闭环频率特性曲线的绘制 （ 6 ） Example 1 Determine

§5.8 System Analysis by Frequency Response of C-L Systems （ 1 ） §5.8.1 Indices of Closed-Loop Frequency Response Example 2 First-order system CL (1) Zero-Frequency Value Second-Order underdamped system (3) Bandwidth Frequency The frequency where M(  ) drops to M 0 (2) Resonant frequency  r Resonant peak M r

§5.8.2 Correlation between T.-Domain and F.-Domain Criteria of CL Systems (1) 2 nd -Order system §5.8 System Analysis by Frequency Response of C-L Systems （ 2 ）

Solution. According to the figure, it’s a 2nd-order underdamped system. From Example 3 The CL frequency response is measured in the figure. Obtain the dynamic performance (σ%, t s ) of the system. Fig 5-52 Fig 5-61 We have Then §5.8 System Analysis by Frequency Response of C-L Systems （ 3 ）

(2) Higher-order system §5.8 System Analysis by Frequency Response of C-L Systems （ 4 ）

That is Example 4 Consider a recorder. Within 5Hz the magnitude error should not be larger than 10% of the measured signal. Determine the band width  b of the recorder. §5.8 System Analysis by Frequency Response of C-L Systems （ 5 ） Solution. Thus,

Summary Estimate dynamic performance by frequency response Experiments Stability Stability Margins Indices of closed-loop frequency response Nyquist criterion Log criterion P.208

Excecies(24) 5 — 28 （ 2 ）， 29 ， 31 Automatic Control Theory