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Inherent robust stability of driver support systems

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Abstract

Presented are the fact that the transfer function from the front steering angle to yaw rate is strictly positive real, irrespective of the uncertain mass and uncertain velocity, how to determine the positivity margin for this transfer function (some stabilization results are obtained), and how to check the positivity of a controller family. Furthermore, by exploiting the intrinsic structure of system equations and uncertainties, a nonconservative PID stabilization criterion for driver support systems is established. Some interesting results on positivity and connections of PID controllers are shown. Finally, some extreme point results on PID α-stabilization are obtained. These results give certain explanations and justifications for the simulation results performed at German Aerospace Research Center.

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References

  1. Ackermann, J.,Robust Control: Systems with Uncertain Physical Parameters, London: Springer-Verlag, 1993.

    MATH  Google Scholar 

  2. Kharitonov, V. L., Asymptotic stability of an equilibrium position of a family of systems of linear differential equations,Differential'nye Uravneniya, 1978, 14(11): 2086.

    MATH  MathSciNet  Google Scholar 

  3. Bartlett, A. C., Hollot, C. V., Huang, L., Root location of an entire polytope of polynomials: It suffices to check the edges,Mathematics of Control, Signals and Systems, 1988, 1(1): 61.

    Article  MATH  MathSciNet  Google Scholar 

  4. Tsypkin, Y., Polyak, B., Frequency domain criteria for robust stability of polytope of polynomials,IEEE Trans. on Automatic Control, 1991, 36(12): 1464.

    Article  MATH  MathSciNet  Google Scholar 

  5. Garloff, J., Wagner, D. G., Hadamard products of stable polynomials are stable,Journal of Mathematical Analysis and Applications, 1996, 202(8): 797.

    Article  MATH  MathSciNet  Google Scholar 

  6. Wang, L., Robust strict positive realness of transfer function families,Systems Science and Mathematical Sciences, 1994, 7 (4): 371.

    MATH  MathSciNet  Google Scholar 

  7. Wang, L., Robust stability of polynomial families with nonlinearly correlated perturbations: Boundary results with application, inProc. of European Control Conference, Brussels, 1997 (ed. Landau, F.), Paris: IEEE Press, 1997, 66–88.

    Google Scholar 

  8. Wang, L., Interval polynomial stability theory and its applications in testing the strict positive realness of transfer function families,IMA J. Mathematical Control and Information, 1996, 22(1): 19.

    Article  Google Scholar 

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Authors and Affiliations

  1. Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, 100871, Beijing, China

    Long Wang

  2. Robust Control Group, Institute of Robotics and System Dynamics, German Aerospace Research Center, D-82230, Wessling, Germany

    J. Ackermann

Authors
  1. Long Wang
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  2. J. Ackermann
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Additional information

Project supported by the National Major Basic Research and Development Program, the National Key Project of China and Alexander von Humboldt Foundation of Germany.

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Wang, L., Ackermann, J. Inherent robust stability of driver support systems. Sci. China Ser. E-Technol. Sci. 42, 437–448 (1999). https://doi.org/10.1007/BF02916753

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  • DOI: https://doi.org/10.1007/BF02916753

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