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An emergency braking controller based on extremum seeking with experimental implementation

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Abstract

An extremum seeking scheme is developed for maximizing the longitudinal tire forces of the road vehicles during emergency braking situations. If the road condition is known, then a conventional braking controller could generate required braking moment to track the slip set point which belongs to that road condition. However, estimating the road condition is not an easy task and it brings additional computation effort. Rather than that, a self optimization algorithm is presented in this paper without relying on road condition estimation. The developed controller searches optimum operation point for getting maximum friction force. Computer simulations show the effectiveness of the self optimization routine. To validate the real time applicability of the algorithm, an electromechanical braking test system is used for the experiments. Due to the limited measurements from the experimental system, force and moment observers are designed to calculate necessary control inputs for maximizing the friction potential, i.e. the braking force. Via the experimental study, it has been shown that the developed self optimizing controller is fast, accurate, and operable on a real braking system.

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Abbreviations

\(\beta (t)\) :

Time increasing function in self optimization algorithm

\(\gamma \) :

Positive constant in self optimization algorithm

\(\rho \) :

Positive constant in self optimization algorithm

\(\kappa \) :

Slip ratio

\(\lambda \) :

Variable in self optimization algorithm

\(\mu (\kappa )\) :

Friction function between wheels

\(\tau ,\,\tau _1,\,\tau _2\) :

Filter time constants of force and moment observers

\(\omega \) :

Tire rotational velocity (rad/s)

\(d_{1}\) :

Viscous friction coefficient of the upper wheel (Nm/rad/s)

\(d_{2}\) :

Viscous friction coefficient of the lower wheel (Nm/rad/s)

i :

Brake motor command

m :

Vehicle mass in simulation study (kg)

\(r_{1}\) :

Radius of the upper wheel (m)

\(r_{2}\) :

Radius of the lower wheel (m)

s :

Sliding surface variable

t :

Time variable (s)

u :

Longitudinal velocity of the vehicle in simulation study (m/s)

\(x_{1}\) :

Angular velocity of the upper wheel (rad/s)

\(x_{2}\) :

Angular velocity of the lower wheel (rad/s)

\({\hat{x}}_1\) :

Estimated angular velocity of the upper wheel (rad/s)

\({\hat{x}}_2\) :

Estimated angular velocity of the lower wheel (rad/s)

D :

Positive constant

\(F_{n}\) :

Normal force from the upper wheel to the lower wheel (N)

G :

Proportional controller constant

\(F_{x}\) :

Friction force (N)

\(I_\omega \) :

Moment of inertia of the wheel in simulation study (\(\hbox {kg}\,\hbox {m}^{2}\))

\(J_{1}\) :

Moment of inertia of the upper wheel (\(\hbox {kg}\,\hbox {m}^{2}\))

\(J_{2}\) :

Moment of inertia of the lower wheel (\(\hbox {kg}\,\hbox {m}^{2}\))

M :

Positive constant in self optimization algorithm

\(M_{1}\) :

Braking moment (Nm)

\(M_{\mathrm{des}}\) :

Desired braking moment (Nm)

\(M_{10}\) :

Static friction moment of the upper wheel (Nm)

\(M_{20}\) :

Static friction moment of the lower wheel (Nm)

\(M_{\mathrm{g}}\) :

Gravitational and shock absorber moment acting on the balance lever (Nm)

Q :

Positive constant in force observer

R :

Tire radius of the vehicle model in simulation study (m)

T :

Positive constant in moment observer

\(T_{b}\) :

Braking moment in simulation study (Nm)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Işık University, 34980, Şile, Istanbul, Turkey

    Erkin Dinçmen

  2. Department of Mechanical Engineering, Istanbul Technical University, Gümüşsuyu, Istanbul, Turkey

    Tunç Altınel

Authors
  1. Erkin Dinçmen
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  2. Tunç Altınel
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Corresponding author

Correspondence to Erkin Dinçmen.

Additional information

This work was supported by the Turkish National Research Council (TUBITAK) under Grant no: 112E267.

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Dinçmen, E., Altınel, T. An emergency braking controller based on extremum seeking with experimental implementation. Int. J. Dynam. Control 6, 270–283 (2018). https://doi.org/10.1007/s40435-016-0286-2

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  • DOI: https://doi.org/10.1007/s40435-016-0286-2

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