Stabilizing PID controllers for a single-link biomechanical model with position, velocity, and force feedback

Journal of Biomechanical Engineering

Volumn 126, Issue 6, 2004, Pages 838-843

  Iqbal, Kamran ^a   Roy, Anindo ^a  

^a University of Arkansas   (United States)

Author keywords

Delayed Feedbacks; Hermite Biehler Theorem; Linear Matrix Inequality; PID Control; Single link Biomechanical Model

Indexed keywords

APPROXIMATION THEORY; CONTROL EQUIPMENT; FEEDBACK; MATRIX ALGEBRA; MUSCLE; NEUROLOGY; PENDULUMS; PHYSIOLOGY; TENDONS; THREE TERM CONTROL SYSTEMS; TRANSFER FUNCTIONS; VISCOELASTICITY;

CENTRAL NERVOUS SYSTEM (CNS); GOLGI TENDON ORGANS (GTO); MUSCLE SPINDLE (MS); PROPORTIONAL-INTEGRAL-DERIVATIVE (PID) CONTROLLERS;

BIOMECHANICS;

ALGORITHM; ARTICLE; BIOMECHANICS; BODY MOVEMENT; BODY POSTURE; CENTRAL NERVOUS SYSTEM FUNCTION; EXPERIMENTAL MODEL; FEEDBACK SYSTEM; FORCE; MUSCLE CONTRACTION; MUSCLE SPINDLE; MUSCULOSKELETAL SYSTEM; POSITION; TENDON RECEPTOR; VELOCITY; VISCOELASTICITY;

ADAPTATION, PHYSIOLOGICAL; BIOMECHANICS; COMPUTER SIMULATION; FEEDBACK; HUMANS; LOWER EXTREMITY; MODELS, BIOLOGICAL; MOVEMENT; MUSCLE CONTRACTION; MUSCULOSKELETAL EQUILIBRIUM; POSTURE; PROPRIOCEPTION; STRESS, MECHANICAL;

EID: 14344262525     PISSN: 01480731     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1824134     Document Type: Article

References (32)

1. Kataria, A., Ozbay, H., and Hemami, H., 1999, "Point to Point Motion of Skeletal Systems with Multiple Transmission Delays," Proc. IEEE Conf. on Robotics and Auto., Detroit, MI, Vol. 1, pp. 53-58.
2. Bobbert, A. E., and Schenau van Ingen, G. J., 1988, "Coordination in Vertical Jumping," J. Biomech., 21, pp. 249-262.
3. Golliday, C. L. J., and Hemami, H., 1976, "Postural Stability of the Two-degree-of-freedom Biped by General Linear Feedback," IEEE Trans. Autom. Control, 21, pp. 74-79.
4. Pandy, M. G., Zajac, F. E., Sim, E., and Levine, W. S., 1990, "An Optimal Control Model for Maximum-height Human Jumping," J. Biomech., 23, pp. 1185-1198.
5. Hemami, H., and Katbab, A., 1982, "Constrained Inverted Pendulum Model of Evaluating Upright Postural Stability," J. Dyn. Syst., Meas., Control, 104, pp. 343-349.
6. Horak, F. B., and Nashmer, L. M., 1986, "Central Programming of Postural Movements: Adaptation to Altered Support-surface Configurations," J. Neurophysiol., 55, pp. 1369-1381.
7. Camana, P. C., Hemami, H., and Stockwel, C. W., 1977, "Determination of Feedback for Human Posture Control Without Physical Intervention," J. Cybernetics, 7, pp. 199-225.
8. Hemami, H., and Ozbay, H., 2000, "Modeling and Control of Biological Systems with Multiple Afferent and Efferent Transmission Delays," J. Rob. Syst., 17, pp. 609-622.
9. Hemami, H., Weimer, F. C., Robinson, C. S., Stockwell, C. W., and Cvetkovic, S., 1978, "Biped Stability Considerations with Vestibular Models," IEEE Trans. Autom. Control, 23, pp. 1074-1079.
10. Iqbal, K., and Pai, Y. C., 2000, "Predicted Region of Stability for Balance Recovery: Motion at the Knee Joint can Improve Termination of Forward Movement," J. Biomech., 33, pp. 1619-1627.
11. Pai, Y. C., and Iqbal, K., 1999, "Simulated Movement Termination for Balance Recovery: Can Movement Strategies be Sought to Maintain Stability even in the Presence of Slipping or Forced Sliding?" J. Biomech., 32, pp. 779-786.
12. Bhattacharyya, S. P., Chapellat, H., and Keel, L., 1995, Robust Control: The Parametric Approach, Prentice-Hall, Englewood Cliffs, NJ, Chap. 1, pp. 38-53.
13. Ho, M., Datta, A., and Bhattacharyya, S. P., 2000, "Generalizations of the Hermite-Biehler Theorem: The Complex Case," Linear Algebr. Appl., 320, pp. 23-36.
14. Datta, A., Ho, M., and Bhattacharyya, S. P., 1999, Synthesis and Design of PID Controllers, Springer, Berlin, Chap. 3, pp. 25-49.
15. Ho, M., Datta, A., and Bhattacharyya, S. P., 2000, "A New Approach to Feedback Design," Technical Report, Department of Electrical Engineering, Texas A&M University, College Station, TX.
16. Roy, A., and Iqbal, K., 2003, "PID Controller Design for First-Order-Plus-Dead-Time Model via Hermite-Biehler Theorem," Proc. American Control Conference, Denver, Colorado, Vol. 3, pp. 5286-5291.
17. Van der Helm, F., and Rozendaal, L., 2000, "Musculoskeletal Systems with Intrinsic and Proprioceptive Feedback," in Biomechanics and Neural Control of Movement and Posture, edited by J. M. Winters, and P. E. Crago, Springer, New York, Chap. 11, pp. 164-174.
18. Brown, I. E., and Loeb, G. E., 2000, "A Reductionist Approach to Creating and Using Neuromusculoskeletal Models," in Biomechanics and Neural Control of Movement and Posture, edited by J. M. Winters, and P. E. Crago, Springer, New York, Chap. 10, pp. 148-163.
19. Stroeve, S. H., 1998, "Impedance Characteristics of a Neuromusculoskeletal Model of the Human Arm: I. Posture Control," in Neuromuscular Control of Arm Movements, Ph.D. thesis, Delft University of Technology, Delft, The Netherlands, Chap. 5, pp. 86-90.
20. Stroeve, S., 1999, "Impedance characteristics of a neuromusculoskeletal model of the human arm. I. Posture control," Biol. Cybern., 81, No. 5-6, pp. 475-495.
21. Rozendaal, L. A., 1997, "Stability of the Shoulder: Intrinsic Muscle Properties and Reflexive Control," Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
22. Baker, G. A., Jr., 1965, "The Theory and Application of The Fadé Approximant Method," in Advances in Theoretical Physics, edited by K. A. Brueckner, Academic, New York, Vol. 1. pp. 1-58.
23. Jones, G. A., and Jones, J. M., 1998, "Bézout's Identity," in Elementary Number Theory, Springer, Berlin, Chap. 1. pp. 7-11.
24. Ho, M., Datta, A., and Bhattacharyya, S. P., 1999, "Generalizations of the Hermite-Biehler Theorem," Linear Algebr. Appl., 302, pp. 135-153.
25. Roy, A., and Iqbal, K., 2003, "PID Controller Stabilization of a Single-Link Biomechanical Model with Multiple Delayed Feedbacks," Proc. IEEE Conf. on Systems, Man, and Cyb., Washington, D.C., Vol. 1, pp. 642-647.
26. Johansson, R., Magnusson, M., and Akesson, M., 1988, "Identification of Human Postural Dynamics," IEEE Trans. Biomed. Eng., 35, No. 10, pp. 858-869.
27. Peterka, R. J., 2002, "Sensorimotor Integration in Human Postural Control," J. Neurophysiol., 88, pp. 1097-1118.
28. He, J., Levine, W. S., and Loeb, G. E., 1991, "Feedback Gains for Correcting Small Perturbations to Standing Posture," IEEE Trans. Autom. Control, 36, No. 3, pp. 322-332.
29. Barin, K., 1989, "Evaluation of a General Model of Human Postural Dynamics and Control in the Sagittal Plane," Biol. Cybern., 61, pp. 37-50.
30. Sinkjaer, T. S., Toft, E., Andreassen, S., and Hornemann, B. C., 1988, "Muscle Stiffness in Human Ankle Dorsiflexors: Intrinsic and Reflex Components," J. Neurophysiol., 60, pp. 1110-1121.
31. Brooks, V., 1986, The Neural Basis of Motor Control, Oxford University Press, Oxford Chap. 4.
32. Hidler, J., and Rymer, W. Z., 1999, "A Simulation Study of Reflex Instability in Spasticity: Origins of Clonus," IEEE Trans. Rehabil. Eng., 7, No. 3, pp. 327-340.