150 CHAPTER 4. DEMONSTRATION EXAMPLES
The loopshaping design gives a decoupled response. Both the H∞and µdesigns trade
decoupling for speed of response and, as we shall see, robustness with respect to
perturbations.
The simulation is repeated with a perturbation of size 0.1. Notethat this is only 10% of
the size perturbation that we were analyzing and designing for in the above.
delta = [.1,0;0,-0.1]
comment delta "example perturbation"
gsim mu pert = starp(delta,gsim mu)
gsim hinf pert = starp(delta,gsim hinf)
gsim lp pert = starp(delta,gsim lp)
comment gsim mu pert "perturbed closed loop sys: mu ctrl"
comment gsim hinf pert "perturbed closed loop sys: hinf ctrl"
comment gsim lp pert "perturbed closed loop sys: klp ctrl"
ymu pert = gsimmu pert*u
yhinf pert = gsimhinf pert*u
ylp pert = gsimlp pert*u
comment y mu pert "perturbed response: mu ctrl"
comment y hinf pert "perturbed response: hinf ctrl"
comment y lp pert "perturbed response: klp ctrl"
The loop shaping controller performs poorly on the perturbed system.Ag ain the time
response of each system is plotted.
gph8 = plot(ymu pert,{rows=3,row=1,grid,...
title="Kmu step dist. response (perturbed)",...
xlab="time",y max=1.5,y min=-1});
gph8 = plot(yhinf pert,gph8,{row=2,grid,...
title="Kinf step dist. response (perturbed)",...
xlab="time",y max=1.5,y min=-1});
gph8 = plot(ylp pert,gph8,{row=3,grid,...
title="Klp step dist. response: (perturbed)",...
xlab="time",y max=1.5,y min=-1})?