Global search optimization algorithm for vehicle active suspension

Automotive suspension system provides comfort by isolation ground vibration from passenger. An active system consists of vehicle mass, spring, damper and actuator. The response of vehicle is measured by the amplitude and frequency of its vertical displacement. The response depends on the parameters such as vehicle mass, spring stiffness, damping coefficient, force and time. The equation of motion relating the response with the parameters is complex. The solution can be obtained either by analytical, numerical and/or experimental methods. The analytical method is limited to simple cases, whereas experimental method is costly. Hence, numerical method, namely, the Direct Transcription (DT) and Global Search (GS) can be used. In the present work the GS method is used. The results are compared with analytical, DT and experimental. The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. Formally, global optimization seeks global solution of a constrained optimization model. Nonlinear models are ubiquitous in many applications, e.g., in advanced engineering design, co-design problems, biotechnology, data analysis, environmental management, financial planning, process control, risk management, scientific modeling, and others. Their solution often requires a global search approach. Spring stiffness and damping coefficient were determined using GS optimization approach with a control input force was applied directly to the active suspension system.A design methodology for optimizing the passive suspension parameters was developed and illustrated on 1/4 car model. The dynamics of the suspension system were analyzed as the control force value is increased gradually. The optimization numerical results were simulated in time and frequency domains. A very important results of the research was that there are fundamental trade-offs between ride quality and road holding that are independent of suspension type or design due to the value of the damping ratio. GS Simulations in time and frequency domains were conducted comparing the optimized passive and active suspensions under the same performance index and single bump sinusoidal road profile. It was shown that the active suspension can provide significant performance improvements over the passive suspension and comparable to the active suspension obtained by DT in terms of spring stiffness and damping coefficient. An experimental test rig was to validate the optimal numerical results and the dynamic responses in frequency domain. The analytical simulations were investigated. It was found that the optimal active suspension system in the absence of the control force showed less sprung mass acceleration overshoot and settling time, compared to optimal passive suspension system and DT model. In the frequency domain, the frequency response in terms of natural frequency obtained for GS is 1.26 Hz, DT is 1.35 Hz and experimental is 1.32 Hz. The percentage error between experiment and GS is 4.18% and between experiment and DT is 2.6%. For magnitude, GS gave 5.63 dB, DT gave 8.56 and experiment is 13.12 dB. The difference between GS and experiment is 57.1% and DT and experiment is 0.348%.

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