From Bruce Abbott (2017.11.15.1435 EST)]
[From Erling Jorgensen (2017.11.15 1212 EST)]
Erling Jorgensen (2017.11.15 0925 EST)
Martin Taylor 2017.11.1511.29
EJ: Just a clarification.
EJ: But in a hierarchical PCT arrangement for controlling Position, don’t all of these implementing layers below that relationship level of Position become pursuit tracking tasks in their own right, since references for changing each of those implementing perceptions are also being generated?
MT: Not pursuit tracking, which implies chasing an ever-changing target. Here, only the reference values for the perceptions are being varied.
EJ: As I am visualizing it, the ever-changing reference values are the target that the perceptions are chasing. That is why a tracking task is a paradigmatic model for examining control, regardless of the type of control involved. It may represent relational position, degree of loudness when listening to music, an acceptable rate of return on an investment, the extent to which one’s sense of self is being portrayed genuinely. All of those are matching tasks, where a current perception is chasing a preferred reference for that perception.
EJ: If the perception is being pushed away from an already acceptable preference state, we call that compensatory tracking. But if the reference signal is leading the way in a changing manner, isn’t that pursuit tracking? I realize the distinction is a little artificial, because control is never perfect, so adjustments are common with either method.
BA: Technically speaking, pursuit tracking involves “pursuing” a variable that is external to the control system, such as the position of a target on a screen. We can set a reference for the distance between the target and the cursor and then move the cursor in a way that reduces that distance. (As Bill Powers noted, the reference distance does not have to be zero, although it typically is. For example, you could try to keep the cursor 1 cm below the target.)
BA: On the other hand, when the reference is varying over time, the control system will attempt to make the perception match the reference, making the perception “pursue” the reference. Control systems designed to do this are called “servomechanisms,” or “servos” for short.
BA: As for hierarchical control, a nice example is provided by the inverted pendulum demo that was created for LCS III. It implements a three-level hierarchy: A deviation of the pendulum bob from its reference position changes the reference of a velocity control. Deviations from this reference determine the reference for an acceleration control. The output of the acceleration control is a force, which acts on the cart and accelerates it according to the cart’s mass. Acceleration of the cart acts through the pendulum’s rod to accelerate the bob.
BA: This arrangement produces some interesting and perhaps unexpected behavior. In the demo, the user can move the bob position reference along the X axis. If before the change the bob had been balanced in the inverted position, what would you expect to happen? If the new reference position is to the right of the bob’s current position, one would think that the system would begin by accelerating the cart in that direction. However, the vertical rod would fail to transfer this motion to the bob, so the cart would begin to move out from beneath the bob. This would cause the bob to begin falling toward the left, and this motion would then be increased by the horizontal component of the force acting on the bob through its connection to the cart. The pendulum would simply fall over.
BA: But this is not what happens! Instead, one observes the cart accelerating to the left. The bob is no longer directly over the cart; instead, the pendulum is starting to lean to the right. As the rightward lean reaches a certain angle, the cart reverses direction, moving rightward at just the right speed to keep the bob at about that angle. As the cart catches up the new reference position, it speeds up slightly. This allows the cart to get under the bob again and then pass it, so that the pendulum is now leaning slightly leftward. In this position a breaking force is applied to the cart, slowing the movements of both the bob and cart. As the bob comes to a stop at the new reference position, so does the cart, directly under the bob and thus in position to keep the inverted pendulum balanced. The system will now move the cart slightly left or right as needed to offset the effect of any disturbance to bob position.
BA: On the surface it looks as though a relatively complex set of “if-then” commands have been executed to produce the observed movements, (e.g., if the reference moves right, then initially move the cart to the left.) In fact it is all accomplished without any such programming, simply through the actions of the pendulum’s hierarchical control system.
BA: Bill’s Little Man demo implements a similar hierarchical system to move Little Man’s finger into the target triangle. The bell-shaped pattern of velocities that emerges when the arm moves from one target position to another is no doubt a byproduct of this hierarchical control. (For example, to prevent overshoot, one must begin to apply a breaking force to the appropriate parts of the arm well before the finger-tip arrives at the target. As the finger closes in on the target position, the positional error diminishes, reducing the velocity reference, reducing the acceleration reference, reducing the force exerted by the muscles that are driving the arm in the direction of the target.)
BA: It should be noted that this form of hierarchical control is not identical to the hierarchy of perceptions described by HPCT. If perception of a position is a Level 1 (intensity) perception, it cannot then be said that velocity belongs to Level 2, otherwise velocity would have to qualify as a sensation and be “composed” of two or more Level 1 intensities, and so on. However, the hierarchical control principle is enforced: The next level up sets the reference for the level below, and the outputs of the lower level act as the means by which the level above it controls its own perception.
Bruce