A negative group delay model for feedback-delayed manual tracking performance
- 210 Downloads
We propose that feedback-delayed manual tracking performance is limited by fundamental constraints imposed by the physics of negative group delay. To test this hypothesis, the results of an experiment in which subjects demonstrate both reactive and predictive dynamics are modeled by a linear system with delay-induced negative group delay. Although one of the simplest real-time predictors conceivable, this model explains key components of experimental observations. Most notably, it explains the observation that prediction time linearly increases with feedback delay, up to a certain point when tracking performance deteriorates. It also explains the transition from reactive to predictive behavior with increasing feedback delay. The model contains only one free parameter, the feedback gain, which has been fixed by comparison with one set of experimental observations for the reactive case. Our model provides quantitative predictions that can be tested in further experiments.
KeywordsMotor control Tracking Dynamical modeling Negative group delay Synchronization
We would like to thank the reviewers for their thoughtful comments.
Compliance with ethical standards
The experiment, published in Stepp (2009), was approved by the University of Connecticut Institutional Review Board and conducted in accordance with the Declaration of Helsinki.
Conflict of interest
The authors declare that they have no conflict of interest.
- Bariska, A. (2008). Time Machine, Anyone? https://www.dsprelated.com/blogimages/Andor Bariska/NGD/ngdblog. Pdf.
- Brillouin, L. (1960). Wave Propagation and Group Velocity (Pure and Applied Physics (Vol. 8)). New York: Academic Press.Google Scholar
- Dajani, H. R., & Lam, J. C. H. (2008). Prediction of pulsatile physiological signals using a negative group delay circuit. In Proceedings of the 1st WSEAS International Conference on Biomedical Electronics and Biomedical Informatics (pp. 91–96).Google Scholar
- Langenberg, U., Kessler, K., Hefter, H., Cooke, J. D., Brown, S. H., & Freund, H. J. (1992). Effects of delayed visual feedback during sinusoidal visuomotor tracking. European Journal of Neuroscience Society of Neuroscience Abstract Supplement, 5, 209–209.Google Scholar
- Lee, E. B. (1994). Approximation of linear input/output delay differential systems. In L. Markus, K. D. Elworthy, W. N. Everitt, & E. B. Lee (Eds.), Differential equations, dynamical systems, and control science: A festschrift in honor of Lawrence Markus - Lecture Notes in Pure and Applied Mathematics (pp. 659–682, Vol. 152). New York: M. Dekker.Google Scholar
- Milton, J., Meyer, R., Zhvanetsky, M., Ridge, S., & Insperger, T. (2016). Control at stability’s edge minimizes energetic costs: expert stick balancing. J R Soc Interface, 13(119), 20160212. doi: 10.1098/rsif.2016.0212.
- Milton, J. G. (2011). The delayed and noisy nervous system: implications for neural control. Journal of Neural Engineering, 8(6), 065005.Google Scholar
- Nijhawan, R. (2008). Visual prediction: psychophysics and neurophysiology of compensation for time delays. Behavioral and Brain Sciences, 31(2), 179–198; discussion 198–239.Google Scholar
- Smith, K. U. (1962). Delayed Sensory Feedback and Behavior. Philadelphia: W.B. Saunders Co..Google Scholar
- Smith, O. J. M. (1959). A controller to overcome dead time. ISA. Journal, 6(2), 28–33.Google Scholar
- Voss, H. U. (2001b). Dynamic long-term anticipation of chaotic states. Physical Review Letters, 87(1), –014102.Google Scholar
- Voss, H. U. (2002). Fast response by synchronization. In K.-H. Hoffmann (Ed.), 2nd caesarium - Coupling of Biological and Electronic Systems, Bonn (Germany), 2002 (pp. 119–126). Berlin: Springer.Google Scholar
- Voss, H. U. (2016a). The leaky integrator with recurrent inhibition as a predictor. Neural Computation, 28(8), 1498–1502.Google Scholar
- Voss, H. U. (2016b). Signal prediction by anticipatory relaxation dynamics. Physical Review E, 93, 030201(R).Google Scholar
- Voss, H. U. (2016c). A simple predictor based on delay-induced negative group delay. arxiv.org/abs/1606.07791, 1–13.