feedback and feedforward

When we move to catch a ball, we must interpret our view of the ball's movement to estimate its future trajectory. Our attempt to catch the ball incorporates this anticipation of the ball's movement in determining our own movement. As the ball gets closer, or exhibits spin, we may find it departing from the expected trajectory, and we must adjust our movements accordingly. This is an example of the visual system providing inputs to a controller (our brain) which must generate control signals to cause some system (our musculature) to behave in some desired way (to catch the ball). Feedforward anticipates the relation between system and environment to determine a course of action; feedback monitors discrepancies which can be used to refine the actions. In general terms, therefore, a control problem is to choose the input to some system in such a way as to cause its output to behave in some desired way, whether to stay near a set reference value (the regulator problem), or to follow close upon some desired trajectory (the tracking problem). A control signal defined by its intended effect may not achieve that effect either because of the effect of disturbances upon the system, or because of inaccuracy in the controller's knowledge of the controlled system. Feedback is then required to compare actual and intended performance, so that a compensatory change in the input may be determined. Overcompensation yields instability; undercompensation yields poor adjustment to ''. Thus, not only is feedback necessary, but it must be properly apportioned if the controller is to obtain smooth coordinated behaviour.

It is important to note that feedback can only be used effectively if the controller is 'in the right ballpark' in his (or its) model of the controlled system. However, in the real world the exact values of the parameters describing a system are seldom available to the controller, and may actually change (compare short-term loading effects on muscles and longer-term ageing effects and weight changes). To adapt to such changes, the outer, feedback, loop of Fig. 1 must be augmented by an identification algorithm. The job of this algorithm is to monitor the output of the controlled system continually and to compare it with the output that would be expected on the basis of the current estimated state, the current estimated parameters, and the current control signals. On the basis of this data, the identification algorithm can identify more and more accurate estimates of the parameters that define the controlled system, and these updated parameters can then be supplied to the controller as the basis for his (or its) state estimation and control computations.

If the controlled system, or the disturbances to it, are sufficiently slowly time-varying for the identification procedure to make accurate estimates of the (system plus disturbance) parameters more quickly than they actually change, the controller will be able to act efficiently, despite the fluctuations in the system dynamics. The controller, when coupled to an identification procedure, is precisely what is often referred to as an 'adaptive controller': it adapts its control strategy to changing estimates of the dynamics of the controlled system.

Marvin Minsky (1961) has observed that it may also be necessary for the identification procedure to generate some of the input to the controlled system — in other words, to apply test signals to try out various hypotheses about the parameters of the controlled system — trading off the loss of control caused by an inaccurate estimate of the parameters against the degradation resulting from the controller intermittently relinquishing control.

Note that the identification algorithm can only do its job if the controller is of the right general class. It is unlikely that a controller adapted for guiding the arm during ball catching will be able, simply as a result of parameter adjustment, properly to control the legs in the performance of a waltz. Thus the adaptive control system of Fig. 1 (controller plus identification procedure) is not to be thought of as a model of the brain; rather each such control system is a model of a brain 'unit' which can be activated when appropriate. We may think of it as a synergy. An important problem in analysing human movement is that of the coordinated phasing in and out of the brain's various synergies (control systems).


Fig. 1. To render a controller adaptive, an identification algorithm monitors control signals and feedback signals to provide the controller with updated estimates of the parameters that describe the controlled system.
Feedforward is that strategy whereby a controller monitors a system's environment directly, and applies appropriate compensatory signals to the controlled system — rather than waiting for feedback on how changes in the environment have affected the system before giving compensatory signals. The advantage is speed — such changes may be compensated before they have any noticeable effect on the system — but the cost is paid in controller complexity: for the controller must have an accurate model of the effect of all such disturbances upon the system, if it is to compute controls which will indeed effect the necessary compensations.

Feedforward generates large control signals which rapidly correct large discrepancies from the desired output. The resultant change in output may be too fast for long-latency feedback paths to play a major effect.

Feedback and feedforward are separate control strategies and thus may have separate structural embodiments, as shown in Fig. 2 (which does not show the identification algorithms that may provide the adaptive components for each strategy). Note that feedforward is 'pulse activated' in the hypothetical scheme of Fig. 2. It is activated when the error is not small. If well calibrated, the feedforward controller will, with a single brief time pattern of control, return the system to the 'right ballpark', i.e. making the error small enough for feedback control to function effectively. The system should thus have a 'refractory period' based on the time constants of the controlled system — it should not generate a second control signal before the control system has had time to respond fully to the first control signal. The reader should note what at first appears to be a semantic trick. The sample of the system's output is called 'feedback' when fed to the feedback controller, yet is called 'actual output sample' when fed to the feedforward controller. This looks like a way of avoiding the admission that feedforward requires feedback! But the difference is, in fact, a genuine one. A feedforward controller will, in general, need to know the actual state of the controlled system before generating its control signal, but need not monitor that output while the control signal is actually emitted. By contrast, the feedback controller continually monitors the error signal in generating its controls. As suggested by our ball-catching example, the situation in Fig. 2 might be refined so as to have the feedforward controller monitor the relation between the actual trajectory and a predicted trajectory, changing strategy if the discrepancy or error exceeds a threshold. But, again, we have a discrete-activation form of feedforward.


Fig. 2. Discrete-activation feedforward — one of various possible configurations in which feedback and feedforward controls are explicitly separated. Here feedforward is active for large errors to get the controlled system 'into the right ballpark', while feedback provides 'fine-tuning' in the presence of small errors. The dashed lines marked 'required' indicate the supply of necessary activation if the system supplied is to function. Non-dashed lines indicate 'data flow'.
Fig. 3 shows a different strategy, which appears to describe better the control of muscle. Here, the control neuron must maintain a specific level of firing to hold a limb in a desired position — there is a functional relation between a desired output (e.g. muscle length) and a necessary input (e.g. maintained tension). In this case, the feedforward would be co-activated with the feedback system, so that feedforward sets and maintains the control level specified by the functional relationship, while feedback compensates for minor departures.


Fig. 3. Co-activation feedforward — one of various possible configurations in which feedback and feedforward are explicitly separated. Here the feedforward controller continually supplies a control signal which can maintain the output of the controlled system 'in the right ballpark', while the feedback controller utilizes error feedback to provide the necessary fine-tuning to compensate for inaccuracy in the feedforward controller's model of the controlled system, as well as for disturbances. Such a mode of control is appropriate only when the controlled system has a functional relation between maintained input and maintained output.


(Published 1987)

See also biofeedback; cybernetics, the history of.

— Michael A. Arbib

Bibliography
• Feldman, A. G. (1966). 'Functional tuning of the nervous system with control of movement or maintenance of a steady posture — II. Controllable parameters of the muscles'. Biophysics, 11.
• Greene, P. H. (1969). 'Seeking mathematical models of skilled actions'. In Brodsky, R. (ed.), Biomechanics.
• MacKay, D. M. (1966). 'Cerebral organization and the conscious control of action'. In Eccles, J. C. (ed.), Brain and Conscious Experience.
• Minsky, M. L. (1961). 'Steps towards artificial intelligence'. Proceedings of the Institute of Radio Engineers, 49.

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