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Design of robust optimal proportional–integral–derivative controller based on new interval polynomial stability criterion and Lyapunov theorem in the multiple parameters' perturbations circumstance

Design of robust optimal proportional–integral–derivative controller based on new interval polynomial stability criterion and Lyapunov theorem in the multiple parameters' perturbations circumstance

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  • Author(s): X.H. Li 1, 2 ; H.B. Yu 1 ; M.Z. Yuan 1 ; J. Wang 3
    • View affiliations
    • Affiliations: 1: Key Laboratory of Industrial Informatics, Shen Yang Institute of Automation, Chinese Academy of Sciences, Shen Yang, People's Republic of China
      2: Key Laboratory of Industrial Informatics, Graduate School of Chinese Academy of Sciences, Beijing, People's Republic of China
      3: NHI Group, Shen Yang Heavy Machinery, TBM Company, Shen Yang, People's Republic of China
  • Source: Volume 4, Issue 11, November 2010, p. 2427 – 2440
    DOI:  10.1049/iet-cta.2009.0424 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

Based on the new interval polynomial stability criterion and Lyapunov theorem, a robust optimal proportional–integral–derivative (PID) controller is proposed here to design for different plants that contain the perturbations of multiple parameters. A new stability criterion of the interval polynomial is presented to determine whether the interval polynomial belongs to Hurwitz polynomial. The robust optimal PID controller is acquired through minimising an augmented integral squared error (AISE) performance index. The robust optimal control problem is transformed into a non-linear constraint optimisation (NLCO) problem by applying new polynomial stability criterion and Lyapunov approach. The robust optimal PID parameters are obtained from solving the NLCO problem. The robustness and performances of the proposed method and other different tuning methods are compared. The ability of the proposed PID tuning method and other tuning methods to reject disturbances is discussed as well. The simulation results are presented to demonstrate the effectiveness of the proposed method and show better robustness of the robust optimal PID controller.

Inspec keywords: robust control; Lyapunov methods; polynomials; optimal control; three-term control; control system synthesis; nonlinear control systems; performance index; optimisation

Other keywords: multiple parameter perturbations circumstance; PID controller; PID tuning method; nonlinear constraint optimisation problem; interval polynomial stability criterion; Lyapunov theorem; augmented integral squared error performance index; Hurwitz polynomial; robust optimal proportional-integral-derivative controller

Subjects: Optimal control; Optimisation techniques; Nonlinear control systems; Control system analysis and synthesis methods; Stability in control theory; Algebra

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