A Rationale for Human Operator Pulsive Control Behavior

Abstract

When performing tracking tasks which involve demanding controlled elements such as those with K/s 2 dynamics, the human operator often develops discrete or pulsvie control outputs. Although such pulsive control behavior has been linked to the necessity for low-frequency lead equalization on the part of the human operator, no satisfactory model-based explanation of pulsive behavior has been offered to date. A dual-loop model of the human operator is discussed, the dominant adaptive feature of which is the explicit appearance of an internal model of the manipulator-controlled element dynamics in an inner feedback loop. Using this model, a rationale for pulsive control behavior is offered which is based upon the assumption that the human attempts to reduce the computational burden associated with time integration of sensory inputs. It is shown that such time integration is a natural consequence of having an internal representation of the K/s 2 -controlled element dynamics in the dual-loop model. A digital simulation is discussed in which a modified form of the dual-loop model is shown to be capable of producing pulsive control behavior qualitively comparable to that obtained in experiment. d e e d J k K K e m m n e s Pu 5 r» a. tpi T Nomenclature disturbance -(m + d), error Y d e, displayed error imaginary unit integer exponent appearing in Y p . controlled element gain gain appearing in Y p = frequency, rad/s = neuromuscular frequency, rad/s system undamped natural pY. , = gain appearing in Y p . , s = gain appearing in crossover approximation to Y d Y c -controlled element output due to control activity = human operator's estimate of m, s ~ l = injected error remnant = Laplace variable = lead time constant appearing in Y p , s = washout time constant appearing in Y n . , s "in = "e-Um = output of Y p -output of Y pe -output of Yp= force output of neuromuscular system = manipulator dynamics = human operator's model of manipulator-controlled element dynamics = controlled element dynamics = display dynamics = human operator single-loop describing function = outer-loop equalization dynamics in dual-loop human operator model = inner-loop equalization dynamics in dual-loop human operator model = human operator neuromuscular dynamics = nonlinear element in dual-loop human operator model = manipulator output = neuromuscular system damping ratio = parameters which determine characteristics of Y pu = relative correlated output = root-mean-square value of variable x = time delay, s = power spectral density of variable x

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