Closed-loop dead-time control of contact force of an end-effector

I am robotically controlling the contact force at the end of a surgical tool with an embedded force sensor sampled at 20Hz. The surface motion is inherent tissue motion (with a fair amount of compliance). I do not have the ability to track the motion of the tissue, unfortunately - I presume you were hinting to feedfoward control.

I was given the surgical tool and using an ideal force sensor (sampled at 1Khz), I used an auto-correlation technique to identify the inherent delay in the force sensor of the tool. I have been working all day and I repeated this experiment several times and noticed the delay can fall anywhere between 0-60 ms (I suspect the great disparity would be due to the poor sampling on the force sensor of the tool).

By robotically displacing the end effect into and out of the tissue, I now have input/output data that I used to model a linear transfer. The plant acts as a 2-order stable, however to keep it simple - I modeled it as a first-order plus dead-time model (FOPDT) in order to implement the Smith predictor.

The Smith predictor had similar disturbance rejection performance as a ZN-tuned PID controller.

I have been looking into anticipative controllers. I actually modified the Smith predictor to handle periodic disturbances (since most tissue motion is periodic). It performs extremely well but has several limitations that I would like to stay away from.

The plant is acting as a 2nd-order response, however modelling it as a FOPDT, the “transient period” is approximately 300 ms.

A few questions:

  1. Using the autocorrelation technique I described. Is the delay I am getting due to poor sampling on the force sensor? or is it actual inhere delay in the system? or is it both?
  2. Are there any tools to help extrapolate the feedback loop in real-time to increase my “sampling”?
  3. Adaptive PID controllers? How to they stack up to undersampled/dead-time systems?
  4. Can Kalman filters be used anywhere in my application? I have no experience with them.


[Peter Nachtwey, Delta Computer Systems,,]

The main problem is that the force will rise or fall quickly if there are tracking error between the moving surface and the end effector. The force will rise or fall way too fast for control method stated.

Putting an big air bag between the moving surface and end effector will reduce the rate of force changes due to tracking errors. This will probably not be practical. In other words, the compliance of the system must be known. The mechanical engineer should know this if he is any good.
If contact is metal on metal then one should look up Young’s modulus.

I have done enough of these applications to know you are wasting your time trying to make this work.

Above is a snippet.

PNachtwey, Sometimes the best course of action is to stop doing what you are doing, right? :)