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4.1. THE HIMAT EXAMPLE 143
comment D1sys "system approx. to D1"
comment D1invsys "system approx. to D1inv"
4.1.7 Design Iteration #2
The new D scales can be pre and post multiplied onto the orginal interconnection
structure.
himat
ic2 = D1sys * himat ic * D1invsys
[,,nx] = size(himat
ic2)
display "himat
ic2 now has " + string(nx) + " states"
himat
ic2 now has 20 states
comment himat
ic2 "interconnection for iteration 2"
Note the increase in states due to the inclusion of the D scales. A new H
∞
controller
can now be designed.
gamma
bounds = [0.9,6.0]
[k2,g2,gf2] = hinfsyn(himat
ic2,nmeas,nctrls,...
gamma
bounds,{tol=0.05})
Test bounds: 0.9000 < gamma <= 1.7000
gamma Hx
eig X eig Hy eig Y eig nrho xy p/f
1.700 2.3e-02 -1.1e-09 2.2e-02 -2.5e-27 0.3120 p
1.300 2.3e-02 -3.1e-12 2.2e-02 -1.4e-29 0.6390 p
1.100 2.3e-02 -1.2e-08 2.2e-02 -3.4e-22 1.1028 f
1.200 2.3e-02 2.2e-14 2.2e-02 -2.1e-15 0.8180 p
1.150 2.3e-02 -7.7e-10 2.2e-02 -1.1e-15 0.9423 p
1.125 2.3e-02 -1.9e-08 2.2e-02 -5.8e-31 1.0171 f
Gamma value achieved: 1.1500
comment k2 "controller: iteration 2"
comment gf2 "gamma value: iteration 2"
Note that we calculate the new closed loop using the original interconnection: himat
ic.