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New Observer-Based Controller Design for Delayed Systems Subject to Input Saturation and Disturbances

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Iranian Journal of Science and Technology, Transactions of Electrical Engineering Aims and scope Submit manuscript

Abstract

A new methodology to design an \({H}_{\infty }\) observer-based controller for discrete-time delayed systems subject to input saturation and \({\mathcal {L}}_{2}\)-norm disturbances is proposed, motivated by a benchmark problem. The stabilizing observer-based controller gains are obtained from an LMI formulation using a Lyapunov–Krasovskii functional, free weighting matrices, and an effective approach to overcome the obstacle of the bilinearity. To select the most adequate controller, an iterative optimization algorithm is developed to maximize the set of admissible initial conditions. The proposed results are illustrated by a practical application using the quadruple tank process to visualize different control theory notions and phenomena in laboratory conditions.

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References

  • Azam SNM (2017) Linear discrete-time state space realization of a modified quadruple tank system with state estimation using Kalman filter. J Phys Conf Ser 783(1):012031

    Google Scholar 

  • Ben WS, Boubaker O, Lungu M, Mobayen S (2018) Full and reduced-order unknown input observer design for linear time-delay systems with multiple delays. Math Probl Eng 2018:1–13

    MathSciNet  MATH  Google Scholar 

  • Boutat-Baddas L, Osorio-Gordillo G-L, Darouach M (2019) \(\text{ H }_{\infty }\) dynamic observers for a class of nonlinear systems with unknown inputs. Int J Control. https://doi.org/10.1080/00207179.2019.1600031

    Article  Google Scholar 

  • Chakrabarty A, Corless M (2019) Estimating unbounded unknown inputs in nonlinear systems. Automatica 104:57–66

    Article  MathSciNet  Google Scholar 

  • Cao Y-Y, Lin Z, Hu T (2002) Stability analysis of linear time-delay systems subject to input saturation. IEEE Trans Circuits Syst 49(2):233–240

    Article  MathSciNet  Google Scholar 

  • Chang XH, Zhang L, Park JH (2015) Robust static output feedback \(\text{ H }_{\infty }\) control for uncertain fuzzy systems. Fuzzy Sets Syst 273:87–104

    Article  MathSciNet  Google Scholar 

  • El Fezazi N (2019) An observer-based controller for congestion control in data networks. J Control Autom Electr Syst 30(5):645–656

    Article  Google Scholar 

  • El Fezazi N, El Haoussi F, Tissir EH, Alvarez T (2017) Design of robust \(\text{ H }_{\infty }\) controllers for congestion control in data networks. J Frankl Inst 354(17):7828–7845

    Article  MathSciNet  Google Scholar 

  • El Fezazi N, El Haoussi F, Tissir EH, Bender FA, Alvarez T (2019a) Multiclass AQM on a TCP/IP router: a control theory approach. Int J Robust Nonlinear Control 29(6):1719–1733

    Article  MathSciNet  Google Scholar 

  • El Fezazi N, Tissir EH, El Haoussi F, Bender FA, Husain AR (2019b) Controller synthesis for steer-by-wire system performance in vehicle. Iran J Sci Technol Trans Electr Eng. https://doi.org/10.1007/s40998-019-00204-8

    Article  Google Scholar 

  • El Haiek B, El Aiss H, Hmamed A, El Hajjaji A, Tissir EH (2018) A new approach to robust observer-based control of one-sided Lipschitz nonlinear systems. IET Control Theory Appl 13(3):333–342

    Article  Google Scholar 

  • El Haoussi F, Tissir EH, Tadeo F, Hmamed A (2011) Delay-dependent stabilisation of systems with time-delayed state and control: application to a quadruple-tank process. Int J Syst Sci 42(1):41–49

    Article  MathSciNet  Google Scholar 

  • Hajiani P, Poshtan J (2014) Abrupt and incipient fault detection and compensation for a 4-tank system benchmark. Turk J Electr Eng Comput Sci 22(5):1287–1297

    Article  Google Scholar 

  • Hajmohammadi R, Mobayen S (2019) An efficient observer design method for singular discrete-time systems with time delays and nonlinearity: LMI approach. Sci Iran 26(3):1690–1699

    Google Scholar 

  • Hu W, Huang Y, Huang W, Chen S (2019) Observer and controller design for state-delay Takagi–Sugeno fuzzy systems subjected to unknown time-varying output delays. In: 12th Springer international conference on intelligent robotics and applications, Shenyang, China, vol 11743, pp 169–180

  • Huong DC, Thuan MV (2018) Design of unknown-input reduced-order observers for a class of nonlinear fractional-order time-delay systems. Int J Adapt Control Signal Process 32(3):412–423

    Article  MathSciNet  Google Scholar 

  • Jafari E, Binazadeh T (2019) Observer-based improved composite nonlinear feedback control for output tracking of time-varying references in descriptor systems with actuator saturation. ISA Trans 91:1–10

    Article  Google Scholar 

  • Johansson KH (2000) The quadruple-tank process: a multivariable laboratory process with an adjustable zero. IEEE Trans Control Syst Technol 8(3):456–465

    Article  MathSciNet  Google Scholar 

  • Johansson KH, Nunes JLR (1998) A multivariable laboratory process with an adjustable zero. In: IEEE international American control conference, Philadelphia, USA, vol 4, pp 2045–2049

  • Johansson KH, Horch A, Wijk O, Hansson A (1999) Teaching multivariable control using the quadruple-tank process. In: 38th IEEE international conference on decision and control, Phoenix, USA, vol 1, pp 807–812

  • Lamrabet O, Tissir EH, El Haoussi F (2019) Anti-windup compensator synthesis for sampled-data delay systems. Circuits Syst Signal Process 38(5):2055–2071

    Article  MathSciNet  Google Scholar 

  • Lien CH (2004) Robust observer-based control of systems with state perturbations via LMI approach. IEEE Trans Autom Control 49(8):1365–1370

    Article  MathSciNet  Google Scholar 

  • Liu W, Ma Q, Zhou G, Zhao J (2019) Adaptive dynamic surface control using disturbance observer for nonlinear systems with input saturation and output constraints. Int J Syst Sci 50(9):1784–1798

    Article  MathSciNet  Google Scholar 

  • Malikov AI (2019) State and unknown inputs observers for time-varying nonlinear systems with uncertain disturbances. Lobachevskii J Math 40(6):769–775

    Article  MathSciNet  Google Scholar 

  • Nguyen CM, Trinh H (2016) Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay. Appl Math Comput 286:57–71

    MathSciNet  MATH  Google Scholar 

  • Nguyen CM, Pathirana PN, Trinh H (2019) Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances. Appl Math Comput 353:42–53

    MathSciNet  MATH  Google Scholar 

  • Pal VC, Negi R, Kumar J (2015) An observer based dynamic output feedback controller for discrete system with input saturation and time varying delay. Int J Control Theory Appl 8(4):1383–1394

    Google Scholar 

  • Pal VC, Kumar J, Negi R, Pati A (2017) \({\text{H}}_{\infty }\) control of discrete time delayed systems in presence of actuator saturation. In: 3rd IEEE international Indian control conference, Guwahati, India, pp 295–302

  • Pham T-P, Sename O, Dugard L (2019) Unified \({\rm H}_{\infty }\) observer for a class of nonlinear Lipschitz systems: application to a real ER automotive suspension. IEEE Control Syst Lett 3(4):817–822

    Article  Google Scholar 

  • Qiu J, Sun K, Wang T, Gao H (2019) Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2019.2895560

    Article  Google Scholar 

  • Thuan MV, Huong DC, Sau NH, Ha QT (2019) Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems. Trans Inst Meas Control. https://doi.org/10.1177/0142331219856190

    Article  Google Scholar 

  • Trinh H, Huong DC, Nahavandi S (2019) Observer design for positive fractional-order interconnected time-delay systems. Trans Inst Meas Control 41(2):378–391

    Article  Google Scholar 

  • Wang H, Chen B, Lin C, Sun Y (2019) Observer-based adaptive fuzzy tracking control for a class of MIMO nonlinear systems with unknown dead zones and time-varying delays. Int J Syst Sci 50(3):546–562

    Article  MathSciNet  Google Scholar 

  • Wei Y, Zheng WX, Xu S (2015) Robust output feedback control of uncertain time-delay systems with actuator saturation and disturbances. J Frankl Inst 352(5):2229–2248

    Article  MathSciNet  Google Scholar 

  • Yang Y, Lin C, Chen B (2019) Nonlinear \(\text{ H }_{\infty }\) observer design for one-sided Lipschitz discrete-time singular systems with time-varying delay. Int J Robust Nonlinear Control 29(1):252–267

    Article  MathSciNet  Google Scholar 

  • Zhan T, Ma S, Liu X, Chen H (2019) Impulsive observer design for a class of switched nonlinear systems with unknown inputs. J Frankl Inst 356:6757–6777

    Article  MathSciNet  Google Scholar 

  • Zhou X, Li C, Huang T, Xiao M (2015) Fast gradient-based distributed optimisation approach for model predictive control and application in four-tank benchmark. IET Control Theory Appl 9(10):1579–1586

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. LESSI, Department of Physics, Faculty of Sciences Dhar El Mehraz, University Sidi Mohammed Ben Abdellah, BP 1796, Fes-Atlas, Morocco

    Nabil El Fezazi, Ouarda Lamrabet & El Houssaine Tissir

  2. IASCM, Department of Mathematic and Informatics, Polydisciplinary Faculty, BP 300, 62700, Selouane, Nador, Morocco

    Fatima El Haoussi

Authors
  1. Nabil El Fezazi
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  2. Ouarda Lamrabet
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  3. Fatima El Haoussi
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  4. El Houssaine Tissir
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Correspondence to Nabil El Fezazi.

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El Fezazi, N., Lamrabet, O., El Haoussi, F. et al. New Observer-Based Controller Design for Delayed Systems Subject to Input Saturation and Disturbances. Iran J Sci Technol Trans Electr Eng 44, 1081–1092 (2020). https://doi.org/10.1007/s40998-019-00298-0

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  • DOI: https://doi.org/10.1007/s40998-019-00298-0

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