美国麻省理工大学：《航空系统的估计与控制》教学资源（讲义）Handout 8：Lead compensation

Handout 8: Lead compensation Er March 1. 2004 Lead Compensation goals: Raise phase(and gain) at high frequen- cies while not touching low-frequency systems characteristics: Can extend anonical lead element: s/a+1 ad(8)= 0<a<b. Typical lead Bode Plot

March 1, 2004

Table of maximum phase lead for lead compensator 3 30 10 20 Plant under stud 1/10 +1)(/10 0+ Requirements: Want to increase BW beyond 4rad/sec, must beat p(w) Compensation Scheme: We first adjust the gain K in the feedback Phase Margin is Gain Margin is BW is

10(5+0512 Bode Diagram L 135 equency(rad/sec)

Bode Diagram 135

dartielel bt Lead compenent on1411利aaPh彩( and gain} at high【r=qe e not touching low-trequency ayotem'a characterlatlea can extend (\w bandwidth of systen ement I wpace( l Dmm) Typical lead Bode plot bte ot chase lead fo lead compensator: i‘41m1 tibf plant \apace( 10mmsh uirementer want to inerease ak heyend s4 rad/secs, met beat sp41\omegaS \! Compensation Dehe) we tirat aduse the gain sks in the p当e \apace agrm reheat ient Final desian: Bode plot Reet1o心ua u for Proport ional conpanaat Bode and swat piot. for Pirportionel ceecensater margin becoma iere when pain⊥ Aa seen from reference .nput te output: apace(10Dm) Ao seen feam unmodel ed dynamica output te uncertain dynamics input

Ma:‰ (5+)(5+/)2 S 2s t/ Bode Diagram Nf(以 C 225 Frequency(rad/sec)

Lead com K(s=5/a+1 /b+1 3

Final design: Bode plot 4