I think that, in order to get a good model of the driver you have to have a good model of the feedback connection from the last output the driver produces (torque force on the wheel) to the output that affects the controlled variable (position in the lane). This feedback function would include the amount of steering wheel movement per unit torque applied and the amount tire movement per steering wheel movement and the amount of car movement per tire movement, taking into account variations in resistance to this movement due to variations in road surface conditions.
So there’s a lot of physics between the driver’s output (muscle-produced torque) and the direction of the car relative to the lane lines (the controlled variable) and this physics probably involves integrals that reduce the amount of integration needed in the driver’s output function. This seems like exactly the kind of problem that you, Bruce, should be able to solve easily, physics expert that you are. Rupert and Adam should be able to help out as well.
I also think that Adam’s nice linear regression method for extracting the controller’s output gain (Ko) independent of the feedback gain (Kf) might help us learn how real controllers (such as a car driver) actually work. I’ve been doing a little work testing Adam’s model and I’ve found that it works quite well, even when the feedback function is non-linear (but monotonic).
Adam’s method, if it works for the kinds of behaviors I’ve modeled, would be a great contribution to PCT methodology because it would make it possible to separate the controller’s gain from feedback (environmental) gain. These two contributions to loop gain are confounded when I fit my models to data, resulting in some puzzling variations in the loop gain parameter. I’d like to know the degree to which these variations are the result of variations in environmental conditions (Kf) versus variations in conditions of the controller (Ko).
Best, Rick