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

Excecies(29) 5 — 37,40 联系实验四 Automatic Control Theory

Tasks and the Structure of the Course General Concepts Mathematical Model Time-Domain Method Performance Specifications Complex-Domain Method Frequency-Domain Method Analysis Design The structure of the course

Automatic Control Theory （ Lecture 29) §5. Analysis and Adjustments 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

Summary (1) Review of Chapter 4 and Chapter 5 I. Single Choice 1 ． Suppose the open-loop transfer function of a system is ○ the substitutional open-loop transfer function for sketching the root-loci is.

Summary (2) ○ 2 ． Consider the following open-loop transfer functions. When K=0→∞,which of them has 0º root-loci. ○ 3 ． The closed loop frequency response of a system is shown in the figure. The bandwidth frequency is

Summary (3) ○ 4 ． The middle band of the open-loop frequency response determines A ． System type ； B ． Anti-disturbance ability ； C ． Steady state error ； D ． Dynamic performance; ○ 5 ． The necessary and sufficient condition for the closed-loop stability of minimum phase systems is A ． The Nyquist curve does not encircle point (-1,j0); B ． The Nyquist curve encircles point (-1,j0); C ． The Nyquist curve encircles point (-1,j0) clockwise; D ． The Nyquist curve encircles point (-1,j0) anticlockwise;

Summary (4) ○ 6 ． When the bode diagram is shifted to the left along the  axis A.  c reduced,  unchanged ； B.  c reduced,  unchanged ； C.  c increased,  unchanged;D.  c unchanged,  unchanged ○ 7 ． If two prototype second-systems have the same overshoot  ﹪, they have the same A. nature frequency  n ； B. phase margin  ; C. damped oscillation frequency  d ；D. open-loop gain K;

Summary (5) 8 ． Consider the open-loop transfer function of a feedback system ○ The magnitude margin is ○ 9 ． The transfer function of cascade compensation device is A. lag compensation; B. lag–lead compensation; C. lead compensation ； D. none of above It is

Summary (6) ○ 10 ． The Bode diagram of an open-loop system is shown in the figure. The corresponding open-loop transfer function is

Summary (7) ○ 11. Consider the Bode diagram of a unity feedback minimum phase system shown in the figure. If, which of the following is to be used. A. Lead Compensation ； B. Lag Compensation; C. Lag-lead compensation D. All cascade compensations do not work

Summary (8) ○ 12 ． The greater the overshoot of a prototype second-order system is, Ａ． the smaller the resonance peak is Ｂ． the greater the damping ratio is; Ｃ． the greater the closed-loop gain is; Ｄ． the smaller the phase margin is smaller.

Summary (9) II. Choose the correct answers 1. The frequency response of a system A. is a function of the frequency; B. depends on the magnitude of the input; C. depends on the output; D. depends on the time t; E. is determined by the structure and parameters of the system ○○○○○

Summary (10) ○○○○○ 2 ． Which of the following open-loop transfer function has the 180°root-loci?

Summary (11) 3 ． The stability of unity feedback systems can be determined by A ． the location of open-loop zeros and poles; B ． the closed-loop characteristic equation; C ． the root-loci and the open-loop gain; D ． the open-loop Nyquist plot; E ． the open-loop Bode diagram. ○○○○○

Summary (12) ○○○○○ 4 ． Which of the following are indices of the closed- loop frequency response? A ． Band width frequency  b; B ． Phase angle margin  ; C ． Zero frequency value M(0); D ． The resonance peak value M r ; E ． Cut-off frequency w c.

Summary (13) 5. For minimum phase systems, A. the L(  ) can determine a unique  ); B. the open-loop transfer function can be uniquely obtained from the L(  ); C. the closed-loop Bode diagram can be obtained from the open-loop L(  ) by using the Nichols chart; D. the stability of the closed-loop system can be determined by the open-loop frequency response; E. the closed-loop transfer function can be uniquely obtained by the open-loop L(  ). ○○○○○

Summary (14) 6. For prototype under-damped second-order systems,when the open-loop gain K is increased, A. the damping ratio x , the overshoot s ％  ; B. the damping ratio x , the overshoot s ％  ; C. the damping ratio x , the overshoot s ％  ; D. the undamped nature frequency  ; E. the undamped nature frequency . ○○○○○

Summary (15) ○○○○○ 7 ． Which of the following are indices of the open-loop frequency response? A ． The gain margin h; B ． The resonance frequency  r ; C ． The Cut-off frequency  c ; D ． The Band width frequency  b ; E． The phase margin 

Summary (16) ○○○○○ 8. For non-minimum phase systems A. 0°root-loci are sketched; B. There exists a range of the open-loop gain where the closed-loop system is unstable. C. The closed-loop system is unstable; D. The absolute value of the variation of the phase is not less than the minimum phase system’s. E. The transfer function can be obtained by L(w).

Summary (17) ○○○○○ 9. 9.For prototype second-order systems, when  =0.707, the relations between the undamped nature frequency  n, damped oscillation frequency  d and resonance frequency  r are

Summary (18) ○○○○○ 10 ． For the thri-band theory, which of the following are not correct? A ． If the lower band is high enough, the steady state error can be sufficiently small; B ． The closed-loop stability can be guaranteed if the slope of the middle is -20dB/dec; C ． Low higher band reflects high ability of the open-loop system to resist high frequency noise; For closed-loop system, the higher band of the closed-loop Bode diagram needs to be studied; D. The tri-band theory provides the method for cascade compensation; E ． The longer the middle band with the slope of -20dB/dec, the better the dynamic performance (  ％， ts).

Summary (19) III Consider an unity feedback system with the open-loop transfer function. Obtain the following indices: ① Overshoot  ％ = ⑥ Phase margin  = ② Setting time t s = ⑦ Amplitude margin ｈ = ③ When r(t)=1(t),e ss = ⑧ Resonance frequency w r = ④ When r(t)= t,e ss = ⑨ Resonance peak M r = ⑤ Cut-off frequency  c = ⑩ Band frequency  b =

Summary (20) Solution. 2. Determine the stability of the following systems. Obtain the number of closed-loop poles on the left half plane.

Summary (21) Solution. ( Critical) Stable 3. Consider the polar plot shown the figure. Suppose K=100 and P=0. Determine the stable range of open-loop gain K

Summary (22) 4. The polar plot of a closed-loop unity feedback underdamped system is shown in the figure. (1) Determine the cut-off frequency  c0, phase margin  0 and dynamic performance ％ and t s. (2) Determine the  c, , ％ and ts if the following casvade compensation device is adopted.

Excecies(29) 5 — 37,40 联系实验四 Automatic Control Theory