HW11

HW11

by Chaloupecký Tomáš -
Hello,

I am afraid I don't know how to apply the knowledge from lecture into this problem. We are supposed to use some error signal but there are none. Are we supposed to make those up? Are y1 and y2 supposed to act like error even though we would like to control from those?

In case we are supposed to make our own Z outputs, I don't know where to place those. I can't see any way how to create the arbitrary system from this generalized plant so it would correspond to any template in the lecture (mixed sensitivity problems).

Would you please mind giving us a hint?

Re: HW11

by Hurák Zdeněk -
While the two groups of inputs – exogenous inputs w and control inputs u – are certainly disjoint (either you can influence the value of that signal or not), the two groups of outputs – regulated outputs z and measured outputs y – can easily overlap, no problem. You can thus require that some output signal be small (close to zero) and at the same time you can measure it. In fact, that would be the familiar situation from classical control – what is new in this framework is that you may also regulated (bring towards zero) signals that you do not measure.

Is this sufficient as a hint? You may also consult Skogestad's book (the two-and-a-half-page section 9.3.6. on signal-based H-inf control).  

Re: HW11

by Chaloupecký Tomáš -
I am not quite sure... does that mean I can just tak outputs y1 and y2, feed those through some lowpass filters and label it as Z1 and Z2 signals? Then in matrix P write transfer functions from each input to each Z1, Z2, Y1 and Y2 and call hinfsyn to get the controller? I am trying to do so but with quite poor result. Do I get it right that the step response from disturbance should go to zero on Y2 and U2, right?

Re: HW11

by Hurák Zdeněk -
The idea with weighting filters, yes.
But then, well, the assignment specifies which variables should be kept small. And these are not exactly the couple y1 and y2, right? Also note that even with the best effort you will hardly make the step response from the disturbance to the regulated variables zero. At best you could make it close to zero but not exactly equal to zero.

Re: HW11

by Chaloupecký Tomáš -
Oh... Ok...but are these signals supposed to go infinitely to zero or is some small constant error also sufficient? If is it so then I missunderstood the ≈ symbol 😅

Re: HW11

by Hurák Zdeněk -
Sure. I only wanted to clarify that it is perfectly possible that in response to a step input, these regulated outputs can be pretty much nonzero in the transient phase. And we are only trying our best to make them small.

For example, this is what I get from Simulink simulation with my controller (beware that unlike in the problem assignment here I distinguish between the outputs and their delayed measurements, but I mention it just to avoid confusion, it was not necessary).




I hope I am not much worse than what you guys can design úsměvScreenshot of a Simulink session.