Is it possible to use a PID controller to shorten the bandwidth of a wideband band pass filter?
In other words; is it possible to increase the Quality Factor with a PID controller?

 

I doubt it. You would entirely change the effective transfer function. In particular, the PID pole at the origin would cancel the BPF zero at the origin. The response would then become the ratio of two polynomials. It's probably more effective to use multiple higher order filter stages to improve the filter out-of-band cut-off performance and concurrently spread or narrow the corner (-3dB) frequencies as necessary.
An obvious example is to tandem two Sallen-Key stages - one stage being the BPF low frequency cut-off determinant [a high-pass topology type] and the other the high frequency cut-off [a low-pass topology type].

 

I doubt it. You would entirely change the effective transfer function. In particular, the PID pole at the origin would cancel the BPF zero at the origin. The response would then become the ratio of two polynomials. It's probably more effective to use multiple higher order filter stages to improve the filter out-of-band cut-off performance and concurrently spread or narrow the corner (-3dB) frequencies as necessary.
An obvious example is to tandem two Sallen-Key stages - one stage being the BPF low frequency cut-off determinant [a high-pass topology type] and the other the high frequency cut-off [a low-pass topology type].

Personally, I think the Sallen-Key topology looks sufficient as a narrow band filter. I honestly can't see how a PID regulator would change the bandwidth, but it would certainly change the response time. But since response time is more important than stability, even a brutal underdamped system would do. But I wouldn't use the Sallen-Key topology, since I'm a control system engineer, I want to invent new band pass filters.

But I like what you said about using multiple higher order filter stages.
I imagine a plant in the form of G(s)*H(s)*G(s)*H(s)...

 

Personally, I think the Sallen-Key topology looks sufficient as a narrow band filter. I honestly can't see how a PID regulator would change the bandwidth, but it would certainly change the response time. But since response time is more important than stability, even a brutal underdamped system would do. But I wouldn't use the Sallen-Key topology, since I'm a control system engineer, I want to invent new band pass filters.

But I like what you said about using multiple higher order filter stages.
I imagine a plant in the form of G(s)*H(s)*G(s)*H(s)...

As I don't know what design requirements you have in mind I can't comment any further. With respect stability & response time compromises I would suggest most control engineers are trying to optimize both outcomes in a real situation. Process control and instabilities aren't comfortable companions.

Inventing new band pass filters is a bold objective indeed - particularly in the analog realm. You will need to have a clear understanding of what is already established technology and what industry expectations there are in the art of filter design & implementation. Entire books have already been devoted to the subject. I would have thought the primary emphasis in modern industrial control systems would have been in digital filter design & implementation.