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4.1. THE HIMAT EXAMPLE 147
d = zeros(2,2)
klp = system(a,b,c,d)
comment klp "loop shape controller"
We will compare the designs, with no error or uncertainty weights, for the nominal case
and with a perturbation block of ∆ = [0.1,0;0,-0.1] for the input multiplicative
perturbation.
The time response will be from 0 to 2 seconds with a sample time of 0.01 seconds. We’ll
look at a unit step input into the first channel.
The unweighted closed loop system is now formed for each controller. The inputs and
outputs to the perturbations are closed around a ∆ = 0 perturbation initially. This is
equivalent to selecting the nominal inputs and outputs.
sysnames = ["himat";"wdel"]
invars = ["pert(2)"; "dist(2)"; "control(2)"]
outvars = ["wdel"; "himat+dist"; "himat+dist"]
connections = ["control + pert";"control"]
gsim = sysic(sysnames,invars,outvars,connections,himat,wdel)
comment gsim "unweighted interconnection"
gsim
mu = starp(gsim,k2)
gsim
hinf = starp(gsim,k1)
gsim
lp = starp(gsim,klp)
comment gsim
mu "closed loop system: mu ctrl"
comment gsim
hinf "closed loop system: hinf ctrl"
comment gsim
lp "closed loop system: klp ctrl"
The nominal systems are studied first.
gsim
mu nom = gsim mu(3:4,3:4)
gsim
hinf nom = gsim hinf(3:4,3:4)
gsim
lp nom = gsim lp(3:4,3:4)