Point to point motion of skeletal systems with multiple transmission delays

Biological systems are highly nonlinear, have at least one pair of muscles actuating every degree of freedom at any joint, and possess neural transmission delays in their feedforward (efferent) and feedback (afferent) paths. This nonlinear time delay system, involved in movement and continuous interaction with the environment, is precise, stable, and very adaptive. The problem of trajectory tracking control of a three-link sagittal model of the shank, thigh and trunk is considered in this study. The controller is synthesized using the Q-parameterization method of controller design, for the class of stable nonlinear systems. The "free design" parameter is chosen to achieve certain performance and robustness objectives, the standard approach in H/sup /spl infin// control design. Performance of the system to a class of reference inputs and robustness issues pertaining to neglected nonlinearities, unmodeled dynamics and uncertainties in time delays, are addressed in the problem. Simulations are conducted to test the performance and feasibility of the controller for the task of squatting.

[1]  C. Desoer,et al.  On the stabilization of nonlinear systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[2]  Vasfi Eldem,et al.  Partial Disturbance Rejection with Internal Stability and $H_\infty$ Norm Bound , 1998 .

[3]  D. Wolpert,et al.  Is the cerebellum a smith predictor? , 1993, Journal of motor behavior.

[4]  Hitay Özbay,et al.  An Identification Procedure for Linear Continuous Time Systems with Jump Parameters , 1990 .

[5]  Antonio Camurri,et al.  Network models in Motor control and Music , 1997 .

[6]  Daniel M. Wolpert,et al.  The Cerebellum as a Predictive Model of the Motor System: A Smith Predictor Hypothesis , 1995 .

[7]  Hitay Özbay.  Active Control of a Thin Airfoil: Flutter Suppression and Gust Alleviation , 1993 .

[8]  Hitay Özbay,et al.  Comments on "Solutions to the combined sensitivity and complementary sensitivity problem in control systems , 1998, IEEE Trans. Autom. Control..

[9]  H. Ozbay,et al.  Effect of time delay in network traffic control , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[10]  Mladen Luksic,et al.  On the structure of H∞ controllers , 1990, 1990 American Control Conference.

[11]  Onur Toker,et al.  On suboptimal H∞ controllers for unstable distributed plants , 1993, 1993 American Control Conference.

[12]  Ruth F. Curtain,et al.  Dynamic stabilization of regular linear systems , 1997, IEEE Trans. Autom. Control..

[13]  Hitay Özbay,et al.  On input/output stabilization of singular integrodifferential systems , 1994 .

[14]  Hitay Özbay,et al.  On the synthesis of stable H∞ controllers , 1999 .

[15]  Hitay Özbay,et al.  Design of Multivariable H∞-Based Steering Controllers for Vehicles with Modeled Time Delays , 1998 .

[16]  H. Ozbay,et al.  A solution to the robust flow control problem for networks with multiple bottlenecks , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[17]  Hooshang Hemami,et al.  A marionette-based strategy for stable movement , 1993, IEEE Trans. Syst. Man Cybern..

[18]  H. Ozbay,et al.  Robust control of an aeroelastic system modeled by a singular integrodifferential equation , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[19]  Taesam Kang,et al.  Robust rate-based flow controllers for high-speed networks: the case of uncertain time-varying multiple time-delays , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[20]  Hitay Özbay,et al.  ON THE TWO-BLOCK H PROBLEM FOR A CLASS OF UNSTABLE DISTRIBUTED SYSTEMS , 1996 .

[21]  A. Pellionisz,et al.  Brain modeling by tensor network theory and computer simulation. The cerebellum: Distributed processor for predictive coordination , 1979, Neuroscience.

[22]  Hitay Özbay,et al.  H∞ Optimal Repetitive Control Design for Stable Plants , 1996 .

[23]  Onur Toker,et al.  Gap metric problem for MIMO delay systems: Parametrization of all suboptimal controllers , 1995, Autom..

[24]  H. Ozbay,et al.  Multi-objective controller design via optimal interpolation with an aircraft control application , 1996, Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Contro.

[25]  Hooshang Hemami,et al.  Modeling and control of biological systems with multiple afferent and efferent transmission delays , 2000, J. Field Robotics.

[26]  Glen R. Bachmann,et al.  Active Feedback Controller Design for a Thin Airfoil , 1993, 1993 American Control Conference.

[27]  Shivkumar Kalyanaraman,et al.  On Rate-Based Congestion Control in High Speed Networks: Design of an H1 Based Flow Controller for Single Bottleneck , 1998 .

[28]  H. Ozbay,et al.  Robust stabilization of an aero-elastic system , 1991, IEEE 1991 International Conference on Systems Engineering.

[29]  T. E. Peery,et al.  On Fixed Order Controllers for Delay Systems: Discrete Time Case , 1993, 1993 American Control Conference.

[30]  Fikret A. Aliev,et al.  Optimization of linear control systems : analytical methods and computational algorithms , 1998 .

[31]  E. Bizzi,et al.  Learning Newtonian Mechanics , 1997 .

[32]  Onur Toker,et al.  Mathematics of Control , Signals , and Systems Complexity Issues in Robust Stability of Linear Delay-Differential Systems * , 2005 .

[33]  O. Toker,et al.  On the complexity of purely complex μ computation and related problems in multidimensional systems , 1998, IEEE Trans. Autom. Control..

[34]  Hitay Ozbay,et al.  On the 1-block H∞ control problem for a class of MIMO distributed systems , 1991, 1991 American Control Conference.

[35]  Allen Tannenbaum,et al.  A solution to the standard H∞ problem for multivariable distributed systems , 1989 .

[36]  H. Ozbay,et al.  On the two block problem for unstable distributed systems , 1990, 29th IEEE Conference on Decision and Control.

[37]  H. Hemami,et al.  Control of constrained systems of controllability index two , 1980 .

[38]  Hooshang Hemami.  Execution of Voluntary Bipedal Movement with a Simple Afferent Processor , 1991 .

[39]  Malcolm C. Smith,et al.  On the optimal two block H∞ compensators for distributed unstable plants , 1992, 1992 American Control Conference.

[40]  H. Ozbay,et al.  Robustness analysis of controllers designed for active flutter suppression , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[41]  T. E. Peery,et al.  H∞ Optimal Repetitive Controller Design for Stable Plants , 1997 .

[42]  Allen Tannenbaum,et al.  Remarks on H" Optimization of Multivariate Distributed Systems , 1988 .

[43]  Hitay Özbay,et al.  Robust control design techniques for active flutter suppression , 1994 .

[44]  O. Toker,et al.  On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[45]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[46]  H. Ozbay,et al.  Suboptimal robustness in the gap metric for MIMO delay systems , 1994, Proceedings of 1994 American Control Conference - ACC '94.