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Pole Path Assignment of Constrained SISO Affine Nonlinear Systems

  • M. KaheniEmail author
  • M. Hadad Zarif
  • A. Akbarzadeh Kalat
  • M. Sami Fadali
Research Paper
  • 16 Downloads

Abstract

This paper proposes a feedback linearization control scheme for affine nonlinear systems with a constrained control signal where a fast response is required. Instead of placing the linearized system poles at exact locations, ray-like paths in the left hand plane are selected where the poles can freely vary to efficiently exploit the admissible input signal range to increase the speed of response. A stability test for the proposed method is derived via the multivariable circle criterion and the Kalman–Yakubovich–Popov lemma. Simulation results demonstrate how the method significantly increases the speed of response in spite of the input constraints compared to fixed pole placement.

Keywords

Desired pole path Feedback linearization Nonlinear control Variable structure control Time optimal control 

References

  1. Adamy J, Flemming A (2004) Soft variable-structure controls: a survey. Automatica 40:1821–1844MathSciNetCrossRefGoogle Scholar
  2. Ahmadizadh S, Zarei J, Karimi HR (2014) Robust unknown input observer design for linear uncertain time delay systems with application to fault detection. Asian J Control 16:1–14MathSciNetCrossRefGoogle Scholar
  3. Angeli D, Mosca E (2002) Lyapunov-based switching supervisory control of nonlinear uncertain systems. IEEE Trans Autom Control 47:500–505MathSciNetCrossRefGoogle Scholar
  4. Arefi MM, Zarei J, Karimi HR (2014) Adaptive output feedback neural network control of uncertain non-affine Systems with unknown control direction. J Frankl Inst 351:4302–4316MathSciNetCrossRefGoogle Scholar
  5. Bazzi S, Shammas E, Asmar D (2017) Relaxing nonholonomic constraints to eliminate chattering from time-optimal control solutions. IEEE Robot Autom Lettrs 2:1817–1824CrossRefGoogle Scholar
  6. Blondel VD, Tsitsiklis JN (1999) Complexity of stability and controllability of elementary hybrid systems. Automatica 35:479–489MathSciNetCrossRefGoogle Scholar
  7. Boyuan L, Haipingand D, Weihua L (2016) Optimal distribution control of non-linear tire force of electric vehicles with in-wheel motors. Asian J Control 18:69–88MathSciNetCrossRefGoogle Scholar
  8. Bretl T (2012) Minimum-time optimal control of many robots that move in the same direction at different speeds. IEEE Trans Robot 28:351–363CrossRefGoogle Scholar
  9. Chadli M, Karimi HR (2013) Robust observer design for unknown inputs Takagi–Sugeno models. IEEE Trans Fuzzy Syst 21:158–164CrossRefGoogle Scholar
  10. Choi Y-M, Jeong J, Gweon D-G (2006) A novel damping scheduling scheme for proximate time optimal servomechanisms in hard disk drives. IEEE Trans Magn 42:468–472CrossRefGoogle Scholar
  11. Cortes J, Svikovic V, Alou P, Oliver JA, Cobos JA (2015) \({v^1}\) concept: designing a voltage-mode control as current mode with near time-optimal response for buck-type converters. IEEE Trans Power Electron 30:5829–5841Google Scholar
  12. Dinuzzo F, Ferrara A (2009) Higher order sliding mode controllers with optimal reaching. IEEE Trans Autom Control 54:2126–2136MathSciNetCrossRefGoogle Scholar
  13. Farhadi A (2017) Sub-optimal control over AWGN communication network. Eur J Control 37:27–33MathSciNetCrossRefGoogle Scholar
  14. Ghasemi R, Sun J, Kolmanovsky IV (2009) Neighboring extremal solution for nonlinear discrete-time optimal control problems with state inequality constraints. IEEE Trans Autom Control 54:2674–2679MathSciNetCrossRefGoogle Scholar
  15. Gholipour R, Khosravi A, Mojallali H (2015) Multi-objective optimal backstepping controller design for chaos control in a rod-type plasma torch system using bees algorithm. Appl Math Model 39:4432–4444MathSciNetCrossRefGoogle Scholar
  16. Hung JY, Gao W, Hung JC (1993) Variable structure control: a survey. IEEE Trans Ind Electron 40:2–22CrossRefGoogle Scholar
  17. Incremona GP, Rubagotti M, Ferrara A (2017) Sliding mode control of constrained nonlinear systems. IEEE Trans Autom Control 62:2965–2972MathSciNetCrossRefGoogle Scholar
  18. Jing Wu PLR, Sun X, Martin RR (2016) Improving shape from shading with interactive tabu search. J Comput Sci Technol 31:450–462CrossRefGoogle Scholar
  19. Kaheni M, Hadad Zarif M, Akbarzadeh Kalat A, Sami Fadali M (2018) Soft variable structure control of linear systems via desired pole paths. Inf Technol Control 47:447–456Google Scholar
  20. Kaheni M, Hadad Zarif M, Akbarzadeh Kalat A, Sami Fadali M (2020) Radial pole paths SVSC for linear time invariant multi input systems with constrained inputs. Asian J Control 22:1–9Google Scholar
  21. Kamal S, Bandyopadhyay B (2015) High performance regulator for fractional order systems: a soft variable structure control approach. Asian J Control 17:1342–1346MathSciNetCrossRefGoogle Scholar
  22. Kandukuri ST, Klausen A, Karimi HR, Robbersmyr KG (2016) A review of diagnostics and prognostics of low-speed machinery towards wind turbine farm-level health management. Renew Sustain Energy Rev 53:697–708CrossRefGoogle Scholar
  23. Khalil HK (2001) Nonlinear systems, 3rd edn. Prentice-Hall, Englewood CliffsGoogle Scholar
  24. Kirk DE (2004) Optimal control theory: an introduction. Dover Publications, New YorkGoogle Scholar
  25. Kommuri SK, Defoort M, Karimi HR, Veluvolu KC (2016) A robust observer-based sensor fault-tolerant control for PMSM in electric vehicles. IEEE Trans Ind Electron 63:7671–7681CrossRefGoogle Scholar
  26. Liu X (2016) Optimization design on fractional order PID controller based on adaptive particle swarm optimization algorithm. Nonlinear Dyn 84:379–386MathSciNetCrossRefGoogle Scholar
  27. Liu Y, Zhang C, Gao C (2012) Dynamic soft variable structure control of singular systems. Comm Nonlinear Sci Numer Simul 17:3345–3352MathSciNetCrossRefGoogle Scholar
  28. Liu Y, Kao Y, Gu S, Karimi HR (2015a) Soft variable structure controller design for singular systems. J Frankl Inst 352:1613–1626MathSciNetCrossRefGoogle Scholar
  29. Liu Y, Gu S, Kao Y, Tang S (2015b) Soft variable structure controller design for constrained systems based on s-class functions. Neural Comput Appl 26:705–711CrossRefGoogle Scholar
  30. Marden M (1949) The geometry of the zeros of a polynomial in a complex variable, 1st edn. American Mathematical Society, ProvidencezbMATHGoogle Scholar
  31. Morari M, Baotic M, Borrelli F (2003) Hybrid systems modeling and control. Eur J Control 9:177–189CrossRefGoogle Scholar
  32. Morse AS (1996) Supervisory control of families of linear set-point controllers part I. Exact matching. IEEE Trans Autom Control 41:1413–1431CrossRefGoogle Scholar
  33. Pontryagin LS (1987) Mathematical theory of optimal processes. CRC Press, Boca RatonGoogle Scholar
  34. Poonawala HA, Spong MW (2017) Time-optimal velocity tracking control for differential drive robots. Automatica 85:152–157MathSciNetCrossRefGoogle Scholar
  35. Serikitkankul P, Seki H, Hikizu M, Kamiya Y (2005) Adaptive near time-optimal seek control of a disk drive actuator. IEEE Trans Magn 41:2869–2871CrossRefGoogle Scholar
  36. Shorten RN, Narendra KS (2003) On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form. IEEE Trans Autom Control 48:618–621MathSciNetCrossRefGoogle Scholar
  37. Sira-Ramirez H, Ahmad S, Zribi M (1992) Dynamical feedback control of robotic manipulators with joint flexibility. IEEE Trans Syst Man Cybern 22:736–747CrossRefGoogle Scholar
  38. Slotine JJ, Li W (1991) Applied nonlinear control. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  39. Utkin V (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control 22:212–222MathSciNetCrossRefGoogle Scholar
  40. Utkin V (1984) Variable structure systems—present and future. Autom Remote Control 44:1105–1120MathSciNetzbMATHGoogle Scholar
  41. Wei Q, Liu D, Lin Q, Song R (2017) Discrete-time optimal control via local policy iteration adaptive dynamic programming. IEEE Trans Cybern 47:3367–3379CrossRefGoogle Scholar
  42. Xu R, Liu Y, Gao C, Wang S (2014) Soft variable structure control with differential equation for generalized systems. In: The 26th Chinese control and decision conference (2014 CCDC), Changsha, pp 530–535Google Scholar
  43. Young KD, Utkin VI, Ozguner U (1999) A control engineer’s guide to sliding mode control. IEEE Trans Control Syst Technol 7:328–342CrossRefGoogle Scholar
  44. Yuan M, Chen Z, Yao B, Zhu X (2017) Time optimal contouring control of industrial biaxial gantry: a highly efficient analytical solution of trajectory planning. IEEE/ASME Trans Mechatron 22:247–257CrossRefGoogle Scholar
  45. Zaslavski AJ (2015) Structure of approximate solutions of discrete time optimal control Bolza problems on large intervals. Nonlinear Anal Theory Methods Appl 122(123):23–55MathSciNetCrossRefGoogle Scholar
  46. Zhakatayev A, Rubagotti M, Varol HA (2017) Time-optimal control of variable-stiffness-actuated systems. IEEE/ASME Trans Mech 22:1247–1258CrossRefGoogle Scholar
  47. Zhao X, Yang H, Karimi HR, Zhu Y (2016) Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay. IEEE Trans Cybern 46:1337–1349CrossRefGoogle Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of Electrical Engineering and RoboticsShahrood University of TechnologyShahroodIran
  2. 2.Electrical and Biomedical Engineering DepartmentUniversity of Nevada RenoRenoUSA

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