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Universidad Nacional Autónoma de México

Universidad Nacional Autónoma de México. Analysis of Steady State Behavior of Second Order Sliding Mode Algorithm I. Boiko, L. Fridman, R. Iriarte. To show. Universidad Nacional Autónoma de México. In the presence of an actuactor the transient process may converges to a periodic motion.

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Universidad Nacional Autónoma de México

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  1. Universidad Nacional Autónoma de México Analysis of Steady State Behavior of Second Order Sliding Mode AlgorithmI. Boiko, L. Fridman, R. Iriarte

  2. To show Universidad Nacional Autónoma de México • In the presence of an actuactor the transient process may converges to a periodic motion. Frequency Domain Analysis of Super Twisting Algorithm (STA) Also • To analyze parameters of the periodic solution. • To compare the periodic solution of system driven by STA and first order SM controllers.

  3. Universidad Nacional Autónoma de México Higher Order Sliding Mode Algorithms • Twisting IEEE TAC June 2004 • Super Twisting STA

  4. Finite time convergence Plants with relative degree two Relay control law Finite time convergence Plants with relative degree one Continuous control law Twisting Supertwisting Universidad Nacional Autónoma de México Caractheristics of TA and STA

  5. Universidad Nacional Autónoma de México

  6. Universidad Nacional Autónoma de México Super Twisting Algorithm Structure ρ = 0.5 (square root)

  7. Universidad Nacional Autónoma de México u2 plot of Super Twisting Algoritm

  8. Universidad Nacional Autónoma de México

  9. Universidad Nacional Autónoma de México Methods of analysis • Poincaré maps • Describing functions analysis • . . .

  10. Universidad Nacional Autónoma de México Advantages/Disadvantagesof methods • Poincaré maps • Sufficient conditions satisfied • Complicated (requires the knowledge of the general solutions of the equations) A D

  11. Universidad Nacional Autónoma de México Advantages/Disadvantagesof methods • Describing function analysis • Easy to use • Necessary conditions satified only • Approximated method (low pass filtering hypothesis is nedded) • Works with one nonlinearity (modification is done) A D D A R R

  12. Universidad Nacional Autónoma de México DF of the super twisting algorithm Harmonic balance equation

  13. Universidad Nacional Autónoma de México

  14. Universidad Nacional Autónoma de México Plots of -1/N(Ay,); 1 > 2 > 3 > 4

  15. Universidad Nacional Autónoma de México Example

  16. Universidad Nacional Autónoma de México Negative reciprocal of DF –N-1(Ay) and the Nyquist plot W(j)

  17. Universidad Nacional Autónoma de México Negative reciprocal of DF –N-1(Ay) and the Nyquist plot W(j) (zoomed)

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  21. Universidad Nacional Autónoma de México Conclusions • It was shown that for a plant plus actuactor with relative degree more than one a periodic motion may occur in the systems with the STA. • An algorithm to obtain the parameters of this motion was given. • The comparison between periodic solution parameters for the SAME plants and SAME actuator with UNIT control amplitude for the systems driven by first order sliding modes and STA was done.

  22. Universidad Nacional Autónoma de México Future trends • Universal chattering test. • Frequency shapping. • Robustness properties of systems with actuators driven by STA algorithms.

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