# Control effort in mixed sensitivity design

I am dealing with mixed sensitivity controller design in SISO systems and I am comparing this approch with the classic approch. In particular, I have placed a weight for the sensitivity function in order to reach specific desired performances. After doing this, I have plotted the frequency responce of the control effort, and I have found this:

so, what I have found is that the control effort when using the weight is higher the when we don't use any weight.

I haven' t found anything about why the control effort should be higher, but my opinion is that this happens because with a weight the controller has to do more work to force the system to have specific specifications.

Can someone explain why the control effort is higher? Thanks in advance.

[EDIT] To clarify what I am doing is the following:

so I am placing a limitation on the bandwidth, on the resonance peak and on the low frequency, and this limitation is given by the red line, which is my weight, which I tuned with the desired specifications.

And the plant is not non-minimum phase.

[EDIT 2] I can also plot the step response of the control effort:

and also from here is evident that the control effort is higher.

But also I can see that both start from zero, and in particular, the blu line, so the one which identifies the mixed sensitiviy approch remains at a constant value in the step response.

Why this happens? Thanks.

• What is shown in the Bode plot to indicate the control effort? The control sensitivity? What do you mean by "placed a weight"? Is the plant non-minimum phase (delay or right-half-plane zero)? – fibonatic Dec 1 '19 at 20:22
• thaks for answering. You are right I was imprecise. What I have plotted is the control sensitivity function, and what I mean by weight is that I am using the H-infinity to the sensitivity function. In particular by saying that I placed a weight, I mean that I am imposing a lower bound to the resonance peack, the bandwindth and to the low frequency. – J.D. Dec 1 '19 at 21:32