Controller tuning is a black art.
In my professional life, have never met anyone
who had a method much better than trial and error,
mixed with some personal rules of thumb.
I know there must be professionals who do.
I just never met them.
There are certain tuning rules ( like Ziegler-Nicholls for PD controllers ) that you will find in every textbook. T
hey require some "a priori" ( known beforehand ) knowledge of the system, and some experimentation while it is running. sThe rationale behind these rules is usually the assumption of a simple system model, like a basic first or second order system. This is not a bad idea in itself.
Such rules are often exercised in the frequency domain. The true professional will do "loop shaping" on the Bode plot or the Nyquist plot of the system response, tweaking the curve to give better response at certain frequencies. It is typically a matter of redistributing the feedback gain from one frequency range to another, a waterbed effect which is a special case of nature's universal law of "conservation of misery".
These methods, however offer no way of making the system perform better across the board. They also do not seem to directly suggest adding extra sensors or relocating existing ones, or changing to a better system architecture.
Since I am by background a time domain person,
I have developed my own personal tactics.
That does not make me a professional by any means,
but in the land of the blind...
PD control has only really been possible since digital computers.
In the analog age, pure differentiators
and pure integrators
were very difficult to implement.
This often led to controllers which were analog filters
( RC circuits consisting of
capacitors and resistors )
like "lead-lag"
The classical tuning methods were, I believe, influenced by these hardware limitations. "Loop shaping" means making soldering RC circuits into the control loop to make bumps in the Bode plot over certain frequency ranges, shifting gain to another frequency range in a zero sum game, sometimes referred to as the "conservation of misery".
When tuning a computer controlled PD loop, it is entirely possible to start with almost pure velocity feedback, up to very high frequencies if needed, and if allowed by the sensors.
The system canthen be driven by hand with a vaiable velocity setpoint...