how to build an h-infinity controller with integral action?

Hello to all,

I have to design an H-infinity controller (K) for a given plant G(s), using Matlab's robust control toolbox. Only problem is, G(0)=0. This means that, as the sensitivity S=1/(1+GK), unless K tends to infinity for the low frequencies, S(0)=1. But the matlab tools only provide controllers who tend to a constant (K(0)=cst). Thus the matlab functions are incapable of dealing with this kind of situation, and S=1 for the low frequencies, which is of course unacceptable. I therefore thought of trying to include integral action in my controller: that way, the pole s=0 of the controller would cancel the zero s=0 of the plant. However I have not managed to find a way to do this; I think that, since the poles of Ws (the weight function associated to the sensitivity S) are poles of K, I need to put integral action in Ws; but Matlab wont allow unstable weight functions, because then certain properties allowing to build the controller are violated. So I'm stuck, I can't find a way to build an H infinity controller with integral action.

has anyone encountered this problem before? thanks in advance for your help!!

Answer 1

[Amir]

Have you tried W=1/(s+epsilon), where epsilon is a small, but stable number?

[jamy barmes]

yes I have, but without success... the mixsyn function just comes back with a very high gamma, to compensate for the low value of Ws^-1 for low frequencies and keep S equal to one!