1.2.2 Obtaining State Space Model fromTransfer FunctionMethodl:DirectDecompositionFirstly, the strictly proper system will be discussed.- +b,s"-? +...+bn--$+b,Y(s)b.sG(s) :U(s)s" +as"-1 +...+an-is +anBy introducingan intermediatevariable1U(s)Z(s) =-/s"+as"-1+...+an-is+anU(s)Z(s)Y(s)1b.sn-l+b,s2+..s+b.+bs"+asn--+.+an-s+an
1.2.2 Obtaining State Space Model from Transfer Function
1.2.2 Obtaining State Space Model fromTransfer FunctionMethod1:DirectDecompositionU(s)Y(s)Z(s)-2.5-1s+b..+an-s+athesystemcanbedecomposedasY(s) = (b,s"-1 + b, s"-2 + .. + b,-$ + b,)Z(s)s"z(s) =-a,sn-iz(s) -...- an-isZ(s) - a,Z(s) +U(s)By taking the inverse Laplace transform and assuming thezero initial conditions hold true, the following equation maybe obtained(n-1)(n)=-0az+u
1.2.2 Obtaining State Space Model from Transfer Function
1.2.2 Obtaining State Space Model fromTransfer FunctionMethodl:DirectDecomposition= -α, =(r-1)an-μ=-an=+u1Thestatevariablesmaybe selectedas2=X2XZ=X3X一Differentiating x,(n-1)=xnx(n-2)x77-(n)_(n-1)a,z+uan-12(n-1)x,二n=-anxi-an-1x2-..-ax,+u
1.2.2 Obtaining State Space Model from Transfer Function
1.2.2 Obtaining State Space Model fromTransfer FunctionMethodl:DirectDecompositionX=2=X2X, =2=X3.(n-1)=Xn-(n)(n-1)中a=+udan-1=72二ax,+uanrian-112stateequation[0]专0001xi0本20001X2十u00010n-X-11xnanar-1ar-2aX
1.2.2 Obtaining State Space Model from Transfer Function
1.2.2 Obtaining State Space Model fromTransfer FunctionMethodl:DirectDecompositionU(s)Z(s)Y(S)1+..+b.s+b+hs"+as"-+.+an-s+anY(s) = (b,sn-1 + b, s"-2 + ... + bn-1s + b,)Z(s)By taking the inverse Laplace transform of and assumingzero initial conditions hold true, the output equation can beobtained as +y=b,x, +bn-x, +...+b,xn-1 +b,x
1.2.2 Obtaining State Space Model from Transfer Function