Background: The primary function of a suspension system is to isolate the vehicle body from road irregularities thus providing the ride comfort and to support the vehicle and provide stability. The suspension system has to perform conflicting requirements; hence, a passive suspension system is replaced by the active suspension system which can supply force to the system. Active suspension supplies energy to respond dynamically and achieve relative motion between body and wheel and thus improves the performance of suspension system. Methods: This study presents modelling and control optimization of a nonlinear quarter car suspension system. A mathematical model of nonlinear quarter car is developed and simulated for control and optimization in Matlab/ Simulink® environment. Class C road is selected as input road condition with the vehicle traveling at 80 kmph. Active control of the suspension system is achieved using FLC and PID control actions. Instead of guessing and or trial and error method, genetic algorithm (GA)-based optimization algorithm is implemented to tune PID parameters and FLC membership functions' range and scaling factors. The optimization function is modeled as a multi-objective problem comprising of frequency weighted RMS seat acceleration, Vibration dose value (VDV), RMS suspension space, and RMS tyre deflection. ISO 2631-1 standard is adopted to assess the ride and health criterion. Results: The nonlinear quarter model along with the controller is modeled and simulated and optimized in a Matlab/Simulink environment. It is observed that GA-optimized FLC gives better control as compared to PID and passive suspension system. Further simulations are validated on suspension system with seat and human model. Parameters under observation are frequency-weighted RMS head acceleration, VDV at the head, crest factor, and amplitude ratios at the head and upper torso (AR_h and AR_ut). Simulation results are presented in time and frequency domain. Conclusion: Simulation results show that GA-based FLC and PID controller gives better ride comfort and health criterion by reducing RMS head acceleration, VDV at the head, CF, and AR_h and AR_ut over passive suspension system.

Graphical abstract

This paper presents the modeling and optimization of quarter car suspension system using Macpherson strut. A mathematical model of quarter car is developed, simulated and optimized in Matlab/Simulink ® environment. The results are validated using test rig. The suspension system parameters are optimized using a genetic algorithm for objective functions viz. vibration dose value (VDV), frequency weighted root mean square acceleration (hereafter called as RMS acceleration), maximum transient vibration value, root mean square suspension space and root mean square tyre deflection. ISO 2631-1 standard is adopted to assess ride and health criterion. Results shows that optimum parameters provide ride comfort and health criterions over classical design. The optimization results are experimentally validated using quarter car test setup. The genetic algorithm optimization results are further extended to the artificial neural network simulation and prediction model. Artificial neural network model is carried out in Matlab/Simulink ® environment and Neuro Dimensions. Simulation, experimental and predicted results are in close correlation. The optimized system reduces the values of VDV by 45%. Also, RMS acceleration is reduced by 47%. Thus, the optimized system improved ride comfort by reducing RMS acceleration and improved health criterion by reducing the VDV. Finally ANN can be used for predicting the optimum suspension parameters values with good agreement.

In this paper, a genetic algorithm (GA) based in an optimization approach is presented in order to search the optimum weighting matrix parameters of a linear quadratic regulator (LQR). A Macpherson strut quarter car suspension system is implemented for ride control application. Initially, the GA is implemented with the objective of minimizing root mean square (RMS) controller force. For single objective optimization, RMS controller force is reduced by 20.42 % with slight increase in RMS sprung mass acceleration. Trade-off is observed between controller force and sprung mass acceleration. Further, an analysis is extended to multi-objective optimization with objectives such as minimization of RMS controller force and RMS sprung mass acceleration and minimization of RMS controller force, RMS sprung mass acceleration and suspension space deflection. For multi-objective optimization, Pareto-front gives flexibility in order to choose the optimum solution as per designer's need.Keywords: Genetic algorithm (GA), MacPherson strut, quarter car, linear quadratic regulator (LQR), optimization. RESUMENEn este artículo se presenta un algoritmo genético (GA) basado en un enfoque de optimización con el fin de encontrar los parámetros de la matriz de ponderación del regulador lineal cuadrático (LQR). Se implementa un sistema de suspensión Macpherson para la aplicación del control de amortiguación. Inicialmente el GA se implementa con el objetivo de minimizar la raíz cuadrada media (RMS) del controlador de fuerza. Para la optimización de un único objetivo, el controlador RMS de la fuerza se reduce en un 20,42 % con un ligero aumento en la aceleración RMS de la masa suspendida. Se observa equilibrio entre el control de fuerza y la aceleración de la masa suspendida. Además, el análisis se extiende a la optimización multiobjetivo con objetivos como la minimización del control RMS de la fuerza y de la aceleración debida a la masa suspendida y la minimización del control RMS de la fuerza, RMS surgida por la aceleración de la masa y la deflexión del espacio de la suspensión. Para la optimización multiobjetivo el Pareto-frontal facilita elegir la solución óptima según la necesidad del diseñador.Palabras clave: Algoritmo genético (AG), suspensión MacPherson, cuarto de coche, regulador lineal cuadrático (LQR), optimización.

This paper presents a time domain performance analysis of LQR and Hoo control strategy implemented to a quarter car suspension model The performance analysis is carried out on the basis of body trave� body acceleration and suspension deflection criteria. The simulation results show that LQR controller performs better to improve vehicle ride comfort.