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Mr. John Smith

Job title



Developing and implementing vehicle active safety systems, e.g. electronic stability control (ESC), can significantly reduce the number of crashes, despite the increasing traffic density. However, any failure of a component or instrument of the electronic safety systems, e.g. sensor reading or motor failure, affects the vehicle’s dynamic response. In x-bywire and especially in braking-by-wire systems the performance degradation due to a failure becomes even more critical due to the lack of mechanical connection between driver’s pedal input and tires. In this study the fault tolerance of a hybrid braking system consisting out of an electric regenerative braking system –an electric motor installed at the front axle- and an electrohydraulic braking system acting on all wheels is considered. The main subject of the present paper is the development of a fault tolerant integrated Vehicle Dynamics Control (VDC) system based on the State Dependent Riccati Equation (SDRE) technique. In SDRE the nonlinear dynamics of the system is factorized into the state vector and the product of a matrix valued function that depends on the state itself. In doing so, the nonlinearities of the system are fully captured bringing the nonlinear system to a linear like structure having state-dependent coefficient (SDC) matrices. The nonlinear regulator is derived by minimizing an objective function which is formulated as a weighted integral of the system response and the actuators effort. By following an augmented penalty approach the method allows to implement adaptive terms in the objective function which can be used to improve system performance against failures. The proposed optimized VDC system is based on a 3 DOF vehicle model with a nonlinear combined slip Pacejka tire model and the SDRE technique. An extended linearization scheme of the system’s state space equations on the basis of the Pacejka tire model is developed and a suboptimal controller is computed at each time increment by solving efficiently an Algebraic Riccati Equation. The proposed control strategy has been evaluated in simulation utilizing a 14 Degrees Of Freedom nonlinear vehicle model in Matlab/Simulink environment. The simulation analysis later is validated experimentally by implementing the control system on a real time dSpace platform in a driving car. The performance of the controller will be shown for the mu-split braking manoeuvre considering three controller configurations. In the first configuration the VDC performance is evaluated for the nominal condition (no failure). In the second configuration the controller is tested in case of a failure without failure detection by the supervisory controller. In the third coniguration the controller is tested in case of failure with failure detection by the supervisory controller. The results show that the proposed controller can optimally stabilize the vehicle in nominal condition. In the case of failure the results demonstrate that if the fault detection and diagnosis module provides appropriate feedback for the supervisory controller the performance of the proposed VDC system is close to the nominal one and in the case of no failure detection, the system is still robust enough to stabilize the vehicle however at the cost of slower response. Last but not least it is shown that recuperation of energy is possible even in critical for safety situations. The main limitation of the proposed method is that it uses a very simple fault diagnosis module. Furthermore, it is assumed that the failure is isolated and doesn’t affect the reliability and performance of other system’s components. The SDRE method allows to design integrated vehicle dynamic controllers using a detailed description of the vehicle’s nonlinear state dynamics. Furthermore, as the objective function in the SDRE technique can be function of the state of the system, it is possible to systematically design a reconfigurable and robust controller in case of a system’s component failure. For the first time the application of SDRE using a penalty augmented approach in case of a failure is presented and proven to be effective. The problem of designing an optimal and fault tolerant vehicle dynamic control system based on the SDRE technique has been presented. The proposed system has been tested in simulation and experimentally and has been proven capable to stabilize the vehicle with an optimized braking force distribution.

Kanarachos, Stratis*; Alirezaei, Mohsen; Scheepers, Bart; Jansen, Sven; Maurice, Jan-Pieter,

Design And Evaluation Of A Fault Tolerant Brake By Wire System Based On The
State Dependent Riccati Equation Technique

EB2013-ACC-001 • Paper • EuroBrake 2013 • Braking within Advanced Chassis Control Systems (ACC)


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