lecture17

# lecture17 - 16.322 Stochastic Estimation and Control Fall...

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16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 1 of 7 Lecture 17 Last time: Ground rules for filtering and control system design General system System parameters are contained in () s wt and n . Desired output is generated by taking the signal through the desired operator. The difference between the actual output and the desired output is the error, whose mean squared value we want to minimize. We require a stable and realizable system. The error et is given by: 11 1 1 1 1 1 1 1 ( ) ()( ) ) ) ) ) sdn en e t w s td ws w n t d wn t d τ ττ ∞∞ ∞ −∞ −∞ −∞ ∞∞ −∞ −∞ =− −− +− ∫∫∫ ∫∫ where esd www . Using the replacement 1 e w reduces the number of terms in ee R from nine to four.

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16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 2 of 7 12 1 2 1 2 1 2 1 2 121 2 1 2 2 1 2 () ()( ) () () ( ) ) ) ) ee ees s ens n nen s nnn n Re t e t dd ww R R R R ττ τ ∞∞ −∞ −∞ −∞ −∞ −∞ −∞ −∞ −∞ =+ ++ ∫∫ )( ) ) ( ) () () j ee ee ee s s en s n ne n s nn n n Ss R e d Fs F s S s F s S s F s S s F s S s ωτ −∞ = =− +− where esd Fs Fs Fs . We know the configuration so we can work out the form of each of the transforms F . Computation of the transfer functions e and n For many system configurations especially with minor feedback loops,
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lecture17 - 16.322 Stochastic Estimation and Control Fall...

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