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Control limitations for unstable plants

Control limitations for unstable plants. Sigurd Skogestad Kjetil Havre Truls Larsson Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) N 7491 Trondheim, Norway IFAC World Congress, Barcelona, July 2002.

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Control limitations for unstable plants

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  1. Control limitations for unstable plants Sigurd Skogestad Kjetil Havre Truls Larsson Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) N 7491 Trondheim, Norway IFAC World Congress, Barcelona, July 2002

  2. Previous work: Performance limitation for unstable plant when combined with unstable (RHP) zero • “Presence of unstable (RHP) poles impose a lower limit on the system bandwidth which may be incompatible with the upper limit imposed by RHP-zeros and time delays” • Boyd and Desoer (1985) • Doyle (1986), Doyle, Francis and Tannenbaum (1992) • Middleton (1991) • Kwakernaak (1995) • Seron, Braslavsky and Goodwin (1997) • Åstrøm (1997) • Havre and Skogestad (1998), Skogestad and Postlethwaite (1996) Unstable pole by itself: Any fundamental limitations?

  3. Outline • Previous work: RHP-pole and RHP-zero • Introductory example: Control of G=1/(s-10) with P-controller • Minimum input usage in terms of H2 and H-infinity norms • Inverse response in input • Examples • Conclusion

  4. Feedback control system

  5. P PI Introductory example Note inverse response for input (u)

  6. Introductory example…. RHP- Pole RHP- zero

  7. Introductory example…. Minimum input energy for Kc=20(with closed-loop pole move to mirror image)

  8. Introductory example…. Fast response possible with large Kc (and large u)

  9. Inverse response for bicycle caused by underlying instability

  10. Performance limitation for unstable plant Stabilization: Requires the active use of manipulated inputs Obervations from simulations: • Input usage: Large inputs may be required • Inverse response for input Quantify effect on control performance!

  11. “unavoidable”

  12. Example SISO

  13. Proof (SISO case)

  14. Conclusion input usage: • Instability requires active use of inputs • Quantified by lower bound on norm of KS u = KS (r – Gd d – n) • Stabilization may be impossible with constraints on input u

  15. y1 G1 G2 u y2 2. Performance limitation for stabilized plant Unstable plant: G Primary output Secondary measurement (for stabilization) P Stabilized plant: r2 y1 u G1 G2 K2 y2 Question: Does original instability (in G2) impose limitations on the use of r2 to control y1 (for the stabilized plant P)

  16. Answer: • Instability detectable in y1 (i.e. G1 contains the instability): No performance limitation for y1 • Instability not detectable in y1 (G1 stable): “New” plant P has unstable zero located at unstable pole Performance limitation for fory1 Special (and common) case: Control objective at the input y1 = u

  17. Challenge for potential World Championship in bicycle tilting (y1 = u)

  18. Application: Anti-slug control Two-phase flow (liquid and vapor) Slug (liquid) buildup

  19. Input u = Primary output y1 SP PIC MV Slug-catcher PT PT Measurement y2 Anti slug-control - control structure Undesired slug flow (limit cycle) unless feedback control is used to stabilize a steady flow regime (desired, but open-loop unstable)

  20. Anti slug control – experimental data (Statoil/SINTEF) Pressure (y2) Controller ON OFF INPUT u Density

  21. Conclusion • RHP-pole: Performance limitations at the plant input (u) • Minimum input usage • RHP-zero: Performance limitations at the plant output (y) • Minimum output variation See also the home page of Sigurd Skogestad: http://www.chembio.ntnu.no/users/skoge/

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