lecture21

lecture21 - 16.322 Stochastic Estimation and Control, Fall...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 1 of 8 Lecture 21 Last time: () cs Fs K sd s = + L Ac s s ascsbs Ac a caba B s as + = ⎡⎤ ⎣⎦ +−− ++ =≡ Plugging in for the optimum compensator: 0 () ( ) L LL i i L n n s Hs Fs F s S s Bs d s a s asKcsSbs Bs d s SK c s b s = = + + = This means that in the cascade of 0 with Fs , the effect of the RHP zero on the amplitude of the product is cancelled out, but the effect on the phase is not. In fact, the phase lag due to the RHP zero is doubled in the product. Note: Cancellation of K and two LHP poles in Zero at sc = (RHP) is not cancelled, but a pole is placed at the symmetric point =− Another pole is added at sb = − which is beyond the signal cut-off by an amount which depends on n A S Also the gain n B S depends on n A S directly Also: R s has the form ( ) ef s CD csbs csbs + += −−
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 2 of 8 Then () ( ) ( ) RR i i R R Ls F s Fs S s s Kc s b s e f s sdsascsbs Ke f s sdsas ε =− ⎣⎦ −−+ −−−−− + −−− which is analytic in the LHP and varies as 2 1 s for large . s Necessary condition: must be analytic in LHP and go to zero for large s at least as fast as 1 s . Now find the loop compensator if the feedback transfer is unity. 0 2 0 1 n nn B sd s H KS C HFD B Bc sb c s c b SS + == + ⎛⎞ ++ + + ⎜⎟ ⎝⎠ Cancellation of the pole at the origin leaves the system with an uncontrollable mode corresponding to that pole. This is not good since that normal mode does not attenuate. As a practical matter, it might be better to move that zero away from the origin a bit. That also means the system will not have unit input-output sensitivity . Also note that the in-the-loop compensator need not be stable . It depends on the parameter values. End of Quiz 2 material.
Background image of page 2
16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 3 of 8 Estimation We wish to estimate the values of a set of parameters which may be - static - dynamic
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

lecture21 - 16.322 Stochastic Estimation and Control, Fall...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online