Question Solved1 Answer a) Obtain the controllable canonical state space form of the system whose pulse transfer function is given below z-1 + 2z-2 Y(z) U(2) 1 + 4z-1+ 3z-2 b) Obtain the observable canonical state space form of the system with the pulse transfer function given below. z-2 + 4z-3 Y(2) U(2) 1 + 6z-1 + 112-2 + 6z-3
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a) To Obtain canonical state space form. of system form TF:TF=(Y(z))/(u(z))=(z^(-1)+2z^(-2))/(1+4z^(-1)+3z^(-2))convert it into a stanclard TF form{:[(y(z))/(u(z))=((1)/(z)+(2)/(z^(2)))/(1+(4)/(z)+(3)/(z^(2))).],[=((z+2)/(z^(2)))/((z^(2)+4z+3)/(z^(2)))],[TF=(Y(z))/(u(z))=(z+2)/(z^(2)+4z+3)]:}wkt, Standard form of Controlable canonical formisComparing the TF: =(Y(z))/(u(z))=(z+2)/(z^(2)+4z+3.)for 2^("nd ") order system.canonical form is{:[([x_(1)^(')],[z_(2)^(')])=[[0,1],[-a_(7)-a_(2)]][[x_(1)],[z_(2)]]+[[0],[1]]u],[[y]=[[z_(1),b_(y)]]+oo u]:}form TF{:[a_(4)=3quada_(2)=4quadb_(1)=2quadb_(2)=1],[D=0.]:}CSScanned withCamScanner{:[[[z^(˙)],[z^(˙)]]=([0,1],[-3,-1])([z],[z:])+([0],[1])u],[(]=[[2,1]][[2_(1)],[z_(2)]]+0]:}Hence, This is the required controlable cunomical State space form.0) To obtain cbservable Canonical state space fom fom TFTF-(y(z))/(u(z))=(z^(-2)+4z^(-3))/(1+6z^(-1)+11z^(-2)+6z^( ... See the full answer