Chapter 6 Pole Place Synthesis
© National Instruments Corporation 6-3 Xmath Interactive Control Design Module
where
dp(s)=sn+a1sn–1 +a2sn–2 +...+an
np(s)=b0sn+b1sn–1 +...+abn
Notice that the order of the plant is n, and allow the possibility that the plant
transfer function is not strictly proper; that is, the plant can have as many
zeros as poles.
Normal Mode
In normal mode, the order (number of poles) of the controller is fixed and
equal to n (the order of the plant), so there are a total of 2n closed-loop
poles. In this case, the 2n degrees of freedom in the closed-loop poles
exactly determine the controller transfer function, which also has 2n
degrees of freedom.
In normal mode, the controller transfer function has order n and is strictly
proper:
C(s)=nc(s)/dc(s)
where
dc(s)=sn+x1sn–1 +x2sn–2 +...+xn
nc(s)=y1sn–1+y2sn–2 +...+2yn
Therefore, the closed-loop characteristic polynomial has degree 2n:
where λ1, …, λ2n are the closed-loop poles chosen by the user.
χs() ncs()nps() dcs()dps()+=
sλ1
()sλ2
()sλ2n
()=
s2nα1s2n1…α
2n+++()=