In cybernetics, hierarchical control systems have a “higher-level” control system which provides set points to (possibly multiple) “lower-level” control systems, which the lower-level systems then seek. For example, a reaction-wheel-robot attitude-control system might plan a maneuver and then command reaction-wheel control systems to seek particular velocities for their respective reaction wheels.
It occurs to me that under some circumstances it makes sense to send more than just a set point. For example, if the central control system for a robot arm commands the servo in each of its joints to a particular position, the force the servo applies to reach that position will depend on the difficulty of the movement — the mechanical impedance, as they say, and may reach a very high level if unexpected impedance is encountered, perhaps because a research assistant’s head is unexpectedly in the way of the arm. It is possible for the central control system to pay attention to these error signals and send new commands under those circumstances, but this puts stringent demands on the response time of the central control system.
It might make more sense to command the lower-level control with not just a set point but also a gradient, including a derivative with respective to any of a variety of variables — in the above case, it might be the force. In particular, the derivative of position with respect to force is simply the mechanical compliance, so this amounts to commanding not just a position but also a compliance.
Under some circumstances the commanded compliance (or other analogous gradient) would be achieved by electronic or other active feedback control — position sensors feeding back to motor-control systems, for example — but in other cases it could be achieved wholly or partly through passive means.
For example, a “brushless DC motor” or a stepper motor has a variable stationary holding torque determined by the armature current when the motor is stopped; moreover, an analogous kind of control is possible when the motor is moving as well by controlling what percentage of the time the windings are carrying current that tends to slow down the rotation rather than no current; and a tendon-actuated system, such as parts of the humans’ bodies, will be stiffer when both the extensor and retractor tendons are under tension (“muscle tone”) than when both of them are relaxed.
In other cases, mechanical compliance can be usefully altered by taking advantage of redundant degrees of control. Holding chopsticks close to the base rather than close to the tip, for example, is a technique for increasing mechanical compliance and thus making it easier to pick up food.
In an electronic context, this “variable compliance” might amount to things like a varying gain on an amplifier, a variable DC bias on a varactor, or a bias current on a secondary winding that varies the permeability of a magnetic core, as in a magamp.
The variables whose values the lower-level control uses to perturb the set point are not necessarily directly related to the control mechanism. For example, it sometimes makes sense for a hand computer display to brighten when the hand computer senses increased ambient light, even if the human using it doesn’t command it to brighten; a quadcopter rotor might reduce the setpoint of its speed if a local accelerometer indicates that it’s accelerating upwards; and so on. In general, the idea is for the lower-level control loop to have a set point that is a locally-linear approximation to the potentially more complex and time-varying function used by the higher-level loop to figure out what set point to send to the lower-level loop.
It is observable that the humans use mechanisms such as these at several levels in their motor control; this is demonstrated, for example, by attempting to use a mouse rotated 180° or to write legibly in a mirror.
Controlling the gradients of such “reflexive” low-level control loops can dramatically reduce the demands on the high-level control, in particular often permitting much higher communication and processing latency before the whole system begins to unintentionally oscillate. Also, it can allow the high-level control loop to send commands that suppress, excite, or control oscillations in the lower-level control loop (such as human voices producing higher pitches and the humans doing that freaky thing where they vibrate their eye irises sideways), also reducing the demands on the stability of that lower-level control loop.
Beyond just the gradient of the set point, it might make sense for the high-level control loop to alter other parameters of the low-level control loop; for example, if it’s a PID controller, it might make sense to alter the gains of the P, I, and D components depending on circumstances. With modern electronics it is possible to get subnanosecond response times from analog electronic control loops and trivial to get submicrosecond response times.
Note that a PD controller (a PID controller with no I term) will also perturb its operating point according to the plant’s response — linearly so if the plant is linear — and this can limit the force the robot arm exerts on the research assistant’s head. So in a sense this is a special case of the more general concept I’m describing; but it is missing the crucial ability for the higher-level control loop to set the compliance separately from the set point, and it can only work at all in that context if the robot actuator is working against a spring or something.
It isn’t necessary for the lower-level setpoint perturbation to be linear. It might be whatever nonlinear function is most convenient to compute (for example, using the exponential Ebers–Moll response of BJTs) or it might be a precision higher-degree approximation, as in mechanical naval fire control computers.