Skip to main content
SpringerLink
Log in

Observer-Based Proportional-Integral Controller Design for a Class of Uncertain Switched Systems

  • Research paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Electrical Engineering Aims and scope Submit manuscript

Abstract

In this paper, we studied the observer-based proportional-integral (PI) control problem for a class of switched systems with uncertainties. By choosing the appropriate Lyapunov function, a sufficient condition is given to stabilize the switched systems by PI controller and observer when the system states are not accessible. The main results are proposed and proved by linear matrix inequality technique. In order to approximate the relative equation with satisfactory accuracy, we describe the relevant design problem as a semidefinite programming by regular convex optimization. A simulation result is given to show the effectiveness of the algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Aouaouda S, Chadli M, Shi P, Karimi HR (2015) Discrete-time H−/H∞ sensor fault detection observer design for nonlinear systems with parameter uncertainty. Int J Robust Nonlinear Control 25(3):339–361

    Article  MathSciNet  MATH  Google Scholar 

  • Ates A, Alagoz BB, Yeroglu C (2017) Master-slave stochastic optimization for model-free controller tuning. Iran J Sci Technol Trans Electr Eng 41(2):153–163

    Article  Google Scholar 

  • Azeloglu CO, Sagirli A, Edincliler A (2016) Vibration mitigation of nonlinear crane system against earthquake excitations with the self-tuning fuzzy logic PID controller. Nonlinear Dyn 84(4):1915–1928

    Article  Google Scholar 

  • Bagherzadeh MA, Ghaisari J, Askari J (2015) Exponential stability of uncertain switched linear systems. Iran J Sci Technol Trans Electr Eng 39(E1):79–91

    Google Scholar 

  • Cherrat N, Boubertakh H, Arioui H (2018) Adaptive fuzzy PID control for a class of uncertain MIMO Nonlinear systems with dead-zone inputs’ nonlinearities. Iran J Sci Technol Trans Electr Eng 42(1):21–39

    Article  Google Scholar 

  • Chiu CS, Chiang TS (2017) H ∞ output-feedback fuzzy proportional-integral control of fully delayed input/output systems. ISA Trans 66:22–31

    Article  Google Scholar 

  • Grant M, Boyd S, Ye Y (2006) Disciplined convex programming. Springer, New York

    Book  MATH  Google Scholar 

  • Guo L, Wang H (2005) Generalized discrete-time PI control of output PDFs using square foot B-spline expansion. Automatica 41(1):159–162

    Article  MathSciNet  MATH  Google Scholar 

  • He S, Liu F (2011) Robust stabilization of stochastic Markovian jumping systems via proportional-integral control. Sig Process 91(11):2478–2486

    Article  MATH  Google Scholar 

  • He Z, Xie W (2016) Control of non-linear switched systems with average dwell time: interval observer-based framework. IET Control Theory Appl 10(1):10–16

    Article  MathSciNet  Google Scholar 

  • He W, Chen Y, Yin Z (2016) Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans Cybern 46(3):620–629

    Article  Google Scholar 

  • He S, Song J, Liu F (2017) Robust finite-time bounded controller design of time-delay conic nonlinear systems using sliding mode control strategy. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/tsmc.2017.2695483 (in press)

    Google Scholar 

  • He S, Ai Q, Ren C, Dong J, Liu F (2018) Finite-time resilient controller design of a class of uncertain nonlinear systems with time-delays under asynchronous switching. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/tsmc.2018.2798644 (in press)

    Google Scholar 

  • Kao Y, Xie J, Wang C, Karimi HR (2015) A sliding mode approach to H ∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems. Automatica 52:218–226

    Article  MathSciNet  MATH  Google Scholar 

  • Kommuri S, Defoort M, Karimi HR, Veluvolu K (2016) A robust observer-based sensor fault-tolerant control for PMSM in electric vehicles. IEEE Trans Ind Electron 63(12):7681–9671

    Article  Google Scholar 

  • Lee SW, Yoo SJ (2017) Adaptive-observer-based output-constrained tracking of a class of arbitrarily switched uncertain non-affine nonlinear systems. Nonlinear Anal Hybrid Syst 24:69–82

    Article  MathSciNet  MATH  Google Scholar 

  • Li X, Xiang Z (2014) Observer design of discrete-time impulsive switched nonlinear systems with time-varying delays. Appl Math Comput 229:327–339

    MathSciNet  MATH  Google Scholar 

  • Li Z, Gao H, Karimi HR (2014) Stability analysis and H∞ controller synthesis of discrete-time switched systems with time delay. Syst Control Lett 66(1):82–93

    MathSciNet  MATH  Google Scholar 

  • Li Y, Ma T, Zhao B (2015) Neural network control for the probe landing based on proportional integral observer. Math Probl Eng 2015:1–10

    MathSciNet  MATH  Google Scholar 

  • Li H, Gao Y, Shi P, Lam HK (2016) Observer-based fault detection for nonlinear systems with sensor fault and limited communication capacity. IEEE Trans Autom Control 61(9):2745–2751

    Article  MathSciNet  MATH  Google Scholar 

  • Liu X (2016) Optimization design on fractional order PID controller based on adaptive particle swarm optimization algorithm. Nonlinear Dyn 84(1):379–386

    Article  MathSciNet  Google Scholar 

  • Liu Y, Niu Y, Zou Y (2014) Non-fragile observer-based sliding mode control for a class of uncertain switched systems. J Franklin Inst 351(2):952–963

    Article  MathSciNet  MATH  Google Scholar 

  • Liu Y, Wang Z, He X, Zhou D (2017a) A class of observer-based fault diagnosis schemes under closed-loop control: performance evaluation and improvement. IET Control Theory Appl 11(1):135–141

    Article  MathSciNet  Google Scholar 

  • Liu X, Ho DWC, Song Q, Cao J (2017b) Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances. Nonlinear Dyn 90(3):2057–2068

    Article  MathSciNet  MATH  Google Scholar 

  • Liu J, Lam J, Shen M (2017c) Non-fragile multivariable PID controller design via system augmentation. Int J Syst Sci 48(10):2168–2181

    Article  MathSciNet  MATH  Google Scholar 

  • Lu R, Shi P, Su H, Wu Z, Lu JQ (2018) Synchronization of general chaotic neural networks with nonuniform sampling and packet missing: a switched system approach. IEEE Trans Neural Netw Learn Syst 29(3):523–533

    Article  MathSciNet  Google Scholar 

  • Luan X, Zhao S, Liu F (2013) H ∞ control for discrete-time Markov jump systems with uncertain transition probabilities. IEEE Trans Autom Control 58(6):1566–1572

    Article  MathSciNet  MATH  Google Scholar 

  • Luan X, Huang B, Liu F (2018a) Higher order moment stability region for Markov jump systems based on cumulant generating function. Automatica 93:389–396

    Article  MathSciNet  MATH  Google Scholar 

  • Luan X, Shi P, Liu F (2018b) Given-time multiple frequency control for Markov jump systems based on derandomization. Inf Sci 451–452:124–142

    MathSciNet  Google Scholar 

  • Mahmoud MS (2009) Switched delay-dependent control policy for water-quality systems. IET Control Theory Appl 3(12):1599–1610

    Article  MathSciNet  Google Scholar 

  • Ren Y, Sun G, Feng Z (2017) Observer-based stabilization for switched positive system with mode-dependent average dwell time. ISA Trans. https://doi.org/10.1016/j.isatra.2017.07.010

    Google Scholar 

  • Shen M, Yan S, Tang Z, Gu Z (2015) Finite-time H ∞ filtering of Markov jump systems with incomplete transition probabilities: a probability approach. IET Signal Proc 9(7):572–578

    Article  Google Scholar 

  • Shen H, Zhu Y, Zhang L, Park JH (2017) Extended dissipative state estimation for Markov jump neural networks with unreliable links. IEEE Trans Neural Netw Learn Syst 28(2):346–358

    Article  MathSciNet  Google Scholar 

  • Stiver JA, Antsaklis PJ (2015) Modeling and analysis of hybrid control systems. IEEE Conf Decis Control 4(11):3748–3751

    Google Scholar 

  • Su Y, Zheng C (2017) PID control for global finite-time regulation of robotic manipulators. Int J Syst Sci 48(3):547–558

    Article  MathSciNet  MATH  Google Scholar 

  • Su X, Liu X, Shi P, Yang R (2017) Sliding mode control of discrete-time switched systems with repeated scalar nonlinearities. IEEE Trans Autom Control 62(9):4604–4610

    Article  MathSciNet  MATH  Google Scholar 

  • Sui S, Li Y, Tong S (2016) Observer-based adaptive fuzzy control for switched stochastic nonlinear systems With partial tracking errors constrained. IEEE Trans Syst Man Cybern Syst 46(12):1605–1617

    Article  Google Scholar 

  • Sulikovski B, Galkowski K, Rogers E (2008) PI output feedback control of differential linear repetitive processes. Automatica 44(5):1442–1445

    Article  MathSciNet  MATH  Google Scholar 

  • Tao J, Wu Z, Su H, Wu Y, Zhang D (2018) Asynchronous and resilient filtering for Markovian jump neural networks subject to extended dissipativity. IEEE Trans Cybern. https://doi.org/10.1109/tcyb.2018.2824853

    Google Scholar 

  • Valerion D, Sa da Costa J (2006) Tuning of fractional PID controllers with Ziegler-Nichols-type rules. Signal Process 86(10):2771–2784

    Article  MATH  Google Scholar 

  • Wang Y, Xie L, de Souza CE (1992) Robust control of a class of uncertain nonlinear systems. Syst Control Lett 19(2):139–149

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J, Chen M, Shen H (2017) Event-triggered dissipative filtering for networked semi-Markov jump systems and its applications in a mass-spring system model. Nonlinear Dyn 87(4):2741–2753

    Article  MathSciNet  MATH  Google Scholar 

  • Wei Y, Qiu J, Karimi HR (2017) Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults. IEEE Trans Circuits Syst I Regul Pap 64(1):170–181

    Article  Google Scholar 

  • Wu L, Wang Z (2009) Guaranteed cost control of switched systems with neutral delay via dynamic output feedback. Int J Syst Sci 40(7):717–728

    Article  MathSciNet  MATH  Google Scholar 

  • Wu Z, Cui M, Shi P, Karimi HR (2013) Stability of stochastic nonlinear systems with state-dependent switching. IEEE Trans Autom Control 58(8):1904–1918

    Article  MathSciNet  MATH  Google Scholar 

  • Xu Y, Lu R, Shi P, Li H, Xie S (2016) Finite-time distributed state estimation over sensor networks with Round-Robin protocol and fading channels. IEEE Trans Cybern. https://doi.org/10.1109/tcyb.2016.2635122

    Google Scholar 

  • Yang D, Zhao J (2016) Observer-based H ∞ resilient control for a class of switched LPV systems and its application. Int J Syst Sci 47(15):3656–3667

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang L, Wang S, Karimi HR, Jasra A (2015) Robust finite-time control of switched linear systems and application to a class of servomechanism systems. IEEE ASME Trans Mechatron 20(5):2419–2485

    Google Scholar 

  • Zhao X, Shi P, Yin Y (2017) New results on stability of slowly switched systems: a multiple discontinuous Lyapunov function approach. IEEE Trans Autom Control 62(7):3502–3509

    Article  MathSciNet  MATH  Google Scholar 

  • Zong G, Wang R, Zheng W, Hou L (2015) Finite-time H ∞ control for discrete-time switched nonlinear systems with time delay. Int J Robust Nonlinear Control 25(6):914–936

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No. 61673001), the Foundation for Distinguished Young Scholars of Anhui Province (No. 1608085J05) and the Key Support Program of University Outstanding Youth Talent of Anhui Province (No. gxydZD201701).

Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing (Ministry of Education), School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, China

    Jun Dong, Qilong Ai & Shuping He

Authors
  1. Jun Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qilong Ai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuping He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuping He.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dong, J., Ai, Q. & He, S. Observer-Based Proportional-Integral Controller Design for a Class of Uncertain Switched Systems. Iran J Sci Technol Trans Electr Eng 43 (Suppl 1), 303–312 (2019). https://doi.org/10.1007/s40998-018-0139-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40998-018-0139-4

Keywords

Search

Navigation