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UNAM

UNAM. Dr. Leonid Fridman. NEW TRENDS IN SLIDING CONTROL MODE. L. Fridman Universidad Nacional Autónoma de México División de Posgrado, Facultad de en Ingeniería Edificio ‘A’, Ciudad Universitaria C.P. 70-256, México D. F. lfridman@verona.fi-p.unam.mx 14 MAYO DE 2004. f(x,t). u. x.

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UNAM

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  1. UNAM Dr. Leonid Fridman NEW TRENDS IN SLIDING CONTROL MODE L. Fridman Universidad Nacional Autónoma de México División de Posgrado, Facultad de en Ingeniería Edificio ‘A’, Ciudad Universitaria C.P. 70-256, México D. F. lfridman@verona.fi-p.unam.mx 14 MAYO DE 2004

  2. f(x,t) u x 0 UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control Given a system

  3. UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control

  4. UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control Motivations Given a system Problem formulation: Design control function u to provide asymptotic stability in presence of bounded uncertain term , that contains model uncertainties and external disturbances. f(x,t) u x 0

  5. x(0) UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control Basics of Sliding Mode Control • Desired compensated error dynamics (sliding surface): • The purpose of the Sliding Mode Controller (SMC) is to drive a system's trajectory to a user-chosen surface, named • sliding surface, and to maintain the plant's state trajectory on this surface thereafter. The motion of the system on the sliding surface is named • sliding mode. The equation of the sliding surface must be selected such that the system will exhibit the desired (given) behavior in the sliding mode that will not depend on unwanted parameters (plant uncertainties and external disturbances).

  6. UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control x 1. Sliding surface design 2 reaching phase x(0) x 1 sliding phase 2. SMC design Sliding mode existence condition Equivalent control

  7. UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control More than Robustness- (insensitivity!!!!) to disturbances and uncertainties WHY Sliding mode control? WHEN Sliding mode control? Control plants that operate in presence of unmodeled dynamics, parametric uncertainties and severe external disturbances and noise: aerospace vehicles, robots, etc.

  8. UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control Numerical example: Features: 1. Invariance to disturbance 2. High frequency switching

  9. UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control Continuous and smooth sliding mode control 1. Continuous approximation via saturation function signs sat(s/e) 1 s e s -1 Numerical example:

  10. UNAM Dr. Leonid Fridman Intuitive theory of Sliding mode control Simulations Features: 1. Invariance to disturbance is lost to some extend 2. Continuous asymptotic control

  11. UNAM Dr. Leonid Fridman Second order Sliding mode control 1. Twisting Algorithm Features: 1.Convergence in finite time for and 2.Robustness INSENSITIVITY!!!! 3.Convergence

  12. UNAM Dr. Leonid Fridman New trends in sliding mode control Chattering avoidance whit Twisting Algorithm (continuous control) Features: 1.Convergence in finite time for and 2.Robustness 3.Convergence

  13. UNAM Dr. Leonid Fridman Continuous Second order Sliding mode control 2. Super Twisting Algorithm Features: 1. Invariance to disturbance 2. Continuous control

  14. UNAM Dr. Leonid Fridman Sliding mode observers/differentiators 3. Second Order ROBUST TO NOISE Sliding Mode Observer

  15. UNAM Dr. Leonid Fridman Higher order Sliding mode control 4. High order slides modes controllers of arbitrary order Features: 1.Convergence in finite time for 2.Robustness 3.Convergence 4.r-Smooth control

  16. UNAM Dr. Leonid Fridman Higher order Sliding mode control High order slides modes controllers of arbitrary order

  17. UNAM Dr. Leonid Fridman CHATTERING ANALISYS • Frecuency Methods modifications. Boiko, Castellanos LF IEEE TAC2004 • Universal Chattering Test. Boiko, Iriarte, Pisano, Usai, LF • Chattering Shaping. Boiko, Iriarte, Pisano, Usac, LF Frequency analysis

  18. (s,x) S PLANT ACTUATOR S UNAM Dr. Leonid Fridman CHATTERING ANALISYS Singularly Perturbed Approach Integral Manifold Averaging LF IEEE TAC 2001 LF IEEE TAC 2002 Second Order Sliding Mode Controllers

  19. UNAM Dr. Leonid Fridman UNDERACTUATEDSYSTEMS SMC + H_{∞} Fernando Castaños & LF SMC + Optimal multimodel Poznyak, Bejarano & LF

  20. UNAM Dr. Leonid Fridman OBSERVATION & IDENTIFICATION VIA 2 -SMC • Uncertainty identification • Parameter identification • Identification of the time variant parameters J. Dávila & LF

  21. UNAM Dr. Leonid Fridman RELAY DELAYED CONTROL Countable set of periodic solutions=sliding modes Shustin, E. Fridman LF 93 Set of Steady modes

  22. UNAM Dr. Leonid Fridman CONTROL OF OSCILLATIONS AMPLITUDE Only Is accessible FFS 93------ s(t-1) is accessible Strygin, Polyakov, LF IJC 03, IJRNC 04

  23. UNAM Dr. Leonid Fridman APPLICATIONS • Investigation and implementation of 2-SMC • Shaping of Chattering parameters

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