1)the parameterization of the0controller0isC=X+MQ/Y-NQ。where N,M are right coprime factors of P,X,Y satisfy NX+MY=1,Q∈RH∞
2)According to the right coprime factorization of P, N=,M=,X=,Y=By the performance of the closed-loop system
N(0)[X(0)+M(0)Q(0)]=1 N(10j)[Y(10j)-N(10j)Q(10j)]=0，So take Q in the form Q(s)=x1+x2·1/s+1+x3·1/(x+
1)²
we can get the solution of Q。x1=,x2=,x3=,Q=Finally,the controller is C=
步骤:S=1-λ/λ代人 P(λ)=λ²/6λ²-5λ+1
X=-q2/r2 ,y=1+q1q2/r2 λ=1/s﹢1
N(S)=1/(s+1)²
M(s)=(s-1)(s-2)/(s+1)² X(s)=19s-11/s+1Y(s)=s+6/s+1
C=X+MQ/Y-NQ
N(0)[X(0)+M(0)Q(0)]=1 N(10j)[Y(10j)-N(10j)Q(10j)]=0
Q(0)=6，Q(10j)=-94+70j Q (s)=x1+x2·1/s+1+x3·1/(x+
1)²
x1=-79 x2=-723 x3=808 Q(s)=(-79s²-881s+6)/(s+1)²C(s)=[-60s4-598s32
2+2515s-1794s+1]/[s(s+100)(s+9)]
A control system is stable if the number of encirclements of the(-1,0) point by the GH plot is equal to the number of poles of GH with positive real parts.The direction of encirclement must be in a direction opposite to τs.GH is on open loop transfer function.τs is open right half of s-plane.一个控制系统是稳定的数量是否包围的(1,0)点的GH图的数量相等的两极与积极的真实部分GH。被包围的方向都必须在一个τs的相反方向。
“GH”是在开环传递函数上。τs在s-plane的右半平面开放。
二．The proce of designing a control system generally involves many steps.A typical scenario is as follows:
1.Study the system to be controlled and decide what types of sensors and actuators will be used and where they will be placed.
2.Model the resulting system to be controlled.
3.Simplify the model if neceary so that it is tractable.
4.Analyze the resulting model; determine its properties.5.Decide on performance specifications.6.Decide on the type of controller to be used.7.Design a controller to meet the specs, if poible; if not, modify the specs or generalize the type of controller sought.8.Simulate the resulting controlled system, either on a computer or in a pilot plant.9.Repeat from step 1 if neceary.10.Choose hardware and software and implement the controller.11.Tune the controller on-line if neceary.r．reference or command inputvsensor outputuactuating signal, plant inputdexternal disturbanceyplant output and measured signaln．sensor noise
