4.1. THE HIMATEXAMPLE 133
sysn = ["himat";"wdel";"wp"]
in = ["pert(2)";"dist(2)";"control(2)"]
out = ["wdel";"wp";"himat + dist"]
inter = ["control + pert"; "control"; "himat + dist"]
himat ic = sysic(sysn,in,out,inter,himat,wdel,wp)
comment himat ic "Himat design interconnection structure"
4.1.4 H∞Design
The next step is to design an H∞control law for Himat. The function hinfsyn designs
an H∞control law based on the interconnection structure provided. hinfsyn requires
the design interconnection structure, number of measurements,number of controls and
single gamma or bisection bounds on γ.
Optional input arguments are the tolerance for terminatingthe γiteration (tol), a n
epsilon for Hamiltonian jω-axis eigenvalues (epr) and the epsilon for the Riccati
solution positive definite tests (epp). Two Riccati solution metho ds are provided:
eigenvalue or Schur(default) decomposition. hinfsyn returns the control law,kand the
gamma value achieved, gf1.
In this example, the system interconnection structure is himat ic, with 2 measurements,
2 controls, a γlower bisection bound of 0.8, a γupper bisection bound of 6, a tolerance
on the γiteration of 0.05, and we’ll use the eigenvalue decomposition method to solve
the Riccati equations. The default values of epr (0.5*sqrt(eps))andepp (1e-6) will be
used for the epsilon tests.
gamma bounds = [0.8;6.0]
nmeas = 2 # 2 measurements: attack angle & pitch
nctrls = 2 # 2 controls: elevon & canard
comment nmeas "number of controller measurements"
comment nctrls "number of controller outputs"
[k1,gf1] = hinfsyn(himat ic,nmeas,nctrls,gammabounds,{tol=0.05})
Test bounds: 0.8000 < gamma <= 6.0000