Abstract
Active brake control systems are able to use more accurate control designs on the real-time knowledge of wheel slip such as tire braking forces and external momentums. A multi-objective Pareto type optimization approach is used to evaluate the inconsistent points of the optimization design namely those of minimizing the directional deviation while achieving maximum braking forces on wheels. Moreover, the optimal target slip values defined by the braking purposes like as shorter stopping distance and stability increment by keeping the vehicle in the straight line. This gets by the control of the longitudinal and lateral slip dynamics of each wheel concerning to the road conditions. A controller is optimally brought up by manipulating optimal control law with weights of two control inputs with mathematical and probabilistic characterization. The first-passage probability of critical response levels is used to directly control the vehicle directional stability. An impressive simulation technique based on Monte Carlo method named asymptotic sampling is applied to define the required first-passage probabilities and the Latin Hypercube sampling is used to design of experiments and to cover the design space. Afterwards, a Pareto-type optimization approach is applied to a trade-off between the inconsistent points of the optimization design. The simulation is conducted by the validated vehicle model and the results are indicated that the probability-based control design is represented as a preferable braking performance in comparison with the other systems for braking in sever conditions.
Highlights
Newly engineering science has benefited from probability knowledge with the safety approach
The probability with safety approach incorporated with decision making are an intellectual method to analyze the engineering situations regarded as problems with uncertain input and output parameters and affects the outcomes while the action or process is not as anticipated [3], [10], [11]
Accountability of structural safety is necessary, and it can be provided by means of probability and decision making
Summary
Engineering science has benefited from probability knowledge with the safety approach. It has shown that the control systems with wheel slip design are more proper to adjust the braking forces besides their adaptability to different vehicles, operating and road conditions [52], [54], [55]. The objective is formulated using an efficient computationally method conducted on probabilitybased design optimization of the active braking by wire system (especially EHB) on split-μ roads through developing Pareto based control system concerning enhancing the stopping distance and maneuverability of braking. (1) and (4) are the longitudinal tire forces Fxi, lateral tire forces Fyf , Fyr and brake disk-pad friction coefficient μb which it is hard to measure by physical sensors Estimation of these unknown variables is possible by augmenting them as state variables in the state equation. The tire forces are defined by assuming there is no coupling relationship between the tire forces in the longitudinal and lateral directions as follows: Cxisi (Cxisi) μFzi (Cxisi) (μFzi)
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