Computational methods for the optimization of the mapping of actuators and sensors in the control of flexible structures

In this work the problem of actuator and sensor mapping and controller design for the flexible structure control is approached as minimization of the residual deformations index norm of the closed-loop disturbance deformation path) over the set of nondestabilizing feedback controllers and over the set of possible actuator and sensor mappings. Computational load associated with this approach is reduced by restricting the search to the mapping areas where an inexpensive lower estimate of residual deformations index (derived as a part of this study) is less than the desired value of this index. Further improvement is achieved by including statistical description of the difference between the actual and the estimated performance index over the set of mappings, in order to adjust the level of the mapping acceptance / rejection in such a way that the number of rejected mappings is increased. Serial and parallel optimization procedures based on exhaustive search and genetic algorithms are discussed. These concepts and algorithms are applied to test cases of simply supported beam, the UCLA Large Space Structure, and a telescope mirror model: a hinged round plate.

[1]  Thomas L. Vincent,et al.  Controlling a Flexible Plate to Mimic a Rigid One , 1990 .

[2]  Anthony Skjellum,et al.  Using MPI - portable parallel programming with the message-parsing interface , 1994 .

[3]  Dean W. Sparks,et al.  Survey of experiments and experimental facilities for control of flexible structures , 1992 .

[4]  S. Chemishkian,et al.  Lower limits of deformation suppression in flexible structures , 1998, Proceedings of Thirtieth Southeastern Symposium on System Theory.

[5]  H. J. Robertson,et al.  Development of an active optics concept using a thin deformable mirror , 1970 .

[6]  A. Laub,et al.  Parallel algorithms for algebraic Riccati equations , 1991 .

[7]  François E. Cellier,et al.  Continuous system modeling , 1991 .

[8]  S. M. Joshi,et al.  Sensor-Actuator Placement for Flexible Structures with Actuator Dynamics , 1993 .

[9]  A. J. Laub,et al.  Hypercube implementation of some parallel algorithms in control , 1988 .

[10]  Lawrence A. Bergman,et al.  Robust Control of a Slewing Beam System , 1995 .

[11]  James E. Baker,et al.  Reducing Bias and Inefficienry in the Selection Algorithm , 1987, ICGA.

[12]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[13]  H. Baruh,et al.  Actuator placement in structural control , 1992 .

[14]  Eric Rogers,et al.  Parallel processing in a control systems environment , 1993 .

[15]  Thomas L. Vincent,et al.  Positioning and active damping of flexible beams , 1990 .

[16]  Michael L Delorenzo,et al.  Sensor and actuator selection for large space structure control , 1990 .

[17]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[18]  Richard Y. Chiang,et al.  Robust control toolbox , 1996 .

[19]  G. Stein,et al.  Inherent damping, solvability conditions, and solutions for structural vibration control , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[20]  Shankar P. Bhattacharyya,et al.  CONTROL of UNCERTAIN DYNAMIC SYSTEMS , 1991 .

[21]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[22]  Gilbert Syswerda,et al.  Uniform Crossover in Genetic Algorithms , 1989, ICGA.

[23]  J. Seinfeld,et al.  Optimal location of process measurements , 1975 .

[24]  A. Hamdan,et al.  Measures of Modal Controllability and Observability for First- and Second-Order Linear Systems , 1989 .