Description
lqg2stan returns the augmented plant for linear LQG (H2) controller
design problem defined by:
The nominal plant
P: described by
The (instantaneous) cost function
.The noises covariance matrix
LQG to standard problem
[P_aug, r] = lqg2stan(P, Qxu, Qwv)
State space representation of the nominal plant (nu
inputs, ny outputs, nx states).
[Q, S ; S', N] symmetric nx+nu by
nx+nu weighting matrix.
[R,T;T',V] symmetric nx+ny by
nx+ny covariance matrix.
Row vector [ny nu].
Augmented plant state space representation (see: syslin)
lqg2stan returns the augmented plant for linear LQG (H2) controller
design problem defined by:
The nominal plant P: described by
The (instantaneous) cost function
.
The noises covariance matrix
If [B1; D21] is a factor of
Qxu, [C1, D12] is a
factor of Qwv (see: fullrf) then
P_aug = syslin(P.dt, P.A, [B1,P.B], [C1;-P.C], [0,D12;D21,P.D])
ny = 2; nu = 3; nx = 4; P = ssrand(ny,nu,nx); Qxu = rand(nx+nu,nx+nu); Qxu = Qxu * Qxu'; Qwv = rand(nx+ny,nx+ny); Qwv = Qwv * Qwv'; [P_aug, r] = lqg2stan(P, Qxu, Qwv); K = lqg(P_aug,r); // K=LQG-controller spec(h_cl(P_aug, r, K)) // Closed loop should be stable //Same as Cl = P/.K; spec(Cl('A')) lqg2stan(1/(%s+2), eye(2,2), eye(2,2)) |  |  |
| Version | Description |
| 6.0 | It is no longer necessary to enter -P to get P_aug
instead of -P_aug
(bug 13751 fixed). |