# Sensitivity function - control theory

Started by July 25, 2017
```I watched this video about the sensitivity function, highly instructive, but at
around 9 minutes, the author says that the maximum of the sensitivity function
should be between 1.3 and 2.

What's wrong with having a sensitivity less than 1.3 ?

Regards
```
```On Wednesday, July 26, 2017 at 3:12:32 AM UTC+12, benjamin....@gmail.com wrote:
> I watched this video about the sensitivity function, highly instructive, but at
around 9 minutes, the author says that the maximum of the sensitivity function
should be between 1.3 and 2.
>
>
> What's wrong with having a sensitivity less than 1.3 ?
>
> Regards

I know part of that video is wrong. He says that the reason for a slower response is
that the gain is lower at low frequencies. In fact speed of response is determined
by unity gain crossover freq or bandwidth. Be careful of academics, they don't
always understand real problems and are Matlab engineers
```
```On Friday, July 28, 2017 at 6:19:19 PM UTC-7, gyans...@gmail.com wrote:

(snip)

> I know part of that video is wrong. He says that the
> reason for a slower response is that the gain is lower
> at low frequencies. In fact speed of response is
> determined by unity gain crossover freq or bandwidth.
> Be careful of academics, they don't always understand
> real problems and are Matlab engineers

Okay, but for simpler filters, the response will be monotonically
increasing with frequency, so lower gain at low frequencies implies
lower crossover.

With a higher order filter, I suppose they are not so
coupled.
```
```On Saturday, July 29, 2017 at 2:24:11 PM UTC+12, herrman...@gmail.com wrote:
> On Friday, July 28, 2017 at 6:19:19 PM UTC-7, gyans...@gmail.com wrote:
>
> (snip)
>
> > I know part of that video is wrong. He says that the
> > reason for a slower response is that the gain is lower
> > at low frequencies. In fact speed of response is
> > determined by unity gain crossover freq or bandwidth.
> > Be careful of academics, they don't always understand
> > real problems and are Matlab engineers
>
> Okay, but for simpler filters, the response will be monotonically
> increasing with frequency, so lower gain at low frequencies implies
> lower crossover.
>
> With a higher order filter, I suppose they are not so
> coupled.

Correct but don't make excuses for him. The gain at low frequencies is for
disturbance rejection and good tracking. Distinct from the unity gain frequency
which determines speed of response. I see all the time in textbooks going back to
the 70s of authors saying a phase lag compensator slows a system down because it
reduces teh gain at low frequencies. In fact you keep the bandwidth as high as is
practical based on the physical limitations of the loop which again is never
discussed (structural resonance or high frequency roll-off poles)
```
```On Tue, 25 Jul 2017 08:12:26 -0700, benjamin.couillard wrote:

> I watched this video about the sensitivity function, highly instructive,
> but at around 9 minutes, the author says that the maximum of the
> sensitivity function should be between 1.3 and 2.
>