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lqg2stan
LQG to standard problem
Calling Sequence
[P,r]=lqg2stan(P22,bigQ,bigR)
Arguments
- P22
syslin
list (nominal plant) in state-space form- bigQ
[Q,S;S',N]
(symmetric) weighting matrix- bigR
[R,T;T',V]
(symmetric) covariance matrix- r
1
x2
row vector = (number of measurements, number of inputs) (dimension of the 2,2 part ofP
)- P
syslin
list (augmented plant)
Description
lqg2stan
returns the augmented plant for linear LQG (H2) controller
design.
P22=syslin(dom,A,B2,C2)
is the nominal plant; it can be in continuous
time (dom='c'
) or discrete time (dom='d'
).
. x = Ax + w1 + B2u y = C2x + w2
for continuous time plant.
x[n+1]= Ax[n] + w1 + B2u y = C2x + w2
for discrete time plant.
The (instantaneous) cost function is [x' u'] bigQ [x;u]
.
The covariance of [w1;w2]
is E[w1;w2] [w1',w2'] = bigR
If [B1;D21]
is a factor of bigQ
, [C1,D12]
is a factor of bigR
and [A,B2,C2,D22]
is
a realization of P22, then P
is a realization of
[A,[B1,B2],[C1,-C2],[0,D12;D21,D22]
.
The (negative) feedback computed by lqg
stabilizes P22
,
i.e. the poles of cl=P22/.K
are stable.
Examples
ny=2;nu=3;nx=4; P22=ssrand(ny,nu,nx); bigQ=rand(nx+nu,nx+nu);bigQ=bigQ*bigQ'; bigR=rand(nx+ny,nx+ny);bigR=bigR*bigR'; [P,r]=lqg2stan(P22,bigQ,bigR);K=lqg(P,r); //K=LQG-controller spec(h_cl(P,r,K)) //Closed loop should be stable //Same as Cl=P22/.K; spec(Cl('A')) s=poly(0,'s') lqg2stan(1/(s+2),eye(2,2),eye(2,2))
See Also
- lqg — LQG compensator
- lqr — LQ compensator (full state)
- lqe — linear quadratic estimator (Kalman Filter)
- obscont — observer based controller
- h_inf — Continuous time H-infinity (central) controller
- augment — augmented plant
- fstabst — Youla's parametrization of continuous time linear dynmaical systems
- feedback — feedback operation
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