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.
But this is just my opinion, because I haven't found any reference about this.
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:
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.