GA-based multi-objective optimization of active nonlinear quarter car suspension system—PID and fuzzy logic control

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

Multi-Objective Optimization of Nonlinear Quarter Car Suspension System - PID and LQR Control

This paper presents modeling, control and optimization of a nonlinear quarter car suspension system. A mathematical model of nonlinear quarter car along with seat and driver is developed and simulated in Matlab/Simulink® environment. Input road condition is taken as class C road and vehicle travelling at 80kmph. Active control of suspension system is achieved using PID and LQR control actions. Instead of guessing and or trial and error method to determine the PID and LQR control parameters, a GA based optimization algorithm is implemented. The optimization function is modeled as multi-objective problem comprising of frequency weighted RMS acceleration, VDV, suspension space, tyre deflection and controller force. It is observed that optimized parameters gives better control as compared to the classical parameters and passive suspension system. Further simulations are carried out on suspension system with seat and driver model. The PID controller gives better ride comfort by reducing RMS head acceleration and VDV. Results are presented in time and frequency domain

Multi-objective optimization of active suspension predictive control based on improved PSO algorithm

The design and control for active suspension is of great significance for improving the vehicle performance, which requires considering simultaneously three indexes including ride comfort, packaging requirements and road adaptability. To find optimal suspension parameters and provide a better tradeoff among these three performances, this paper presents a novel multi-objective particle swarm optimization (MPSO) algorithm for the suspension design. The mathematical model of quarter-car suspension is first established, and it integrates the hydraulic servo actuator model. Further a model predictive controller is designed for the suspension by using the control strategies of multi-step forecast, rolling optimization and online correction of predictive control theory. To use vehicle body acceleration, tire deflection and suspension stroke to represent the above three performances respectively, a multi-objective optimization model is constructed to optimize the suspension stiffness and damping coefficients. The MPSO algorithm includes extra crossover operations, which are applied to find the Pareto optimal set. The rule to update the Pareto pool is that the newly selected solutions must have two better performances compared with at least one already existed in the Pareto pool, which ensures that each solution is non-dominated within the Pareto set. Finally, numerical simulations on a vehicle-type example are done under B-level road surface excitation. Simulation results show that the optimized suspension can effectively reduce the vertical vibrations and improve the road adaptability. The model predictive controller also shows high robustness with vehicle under null load, half load and full load. Therefore, the proposed MPSO algorithm provides a new valuable reference for the multi-objective optimization of active suspension control

Investigation of a non-linear suspension in a quarter car model

This thesis presents the study of a quarter car model which consists of a two-degree-of-freedom (2 DOF) with a linear spring and a nonlinear spring configuration. In this thesis, the use of non-linear vibration attachments is briefly explained, and a survey of the research done in this area is also discussed. The survey will show what have been done by the researches in this new field of nonlinear attachments. Also, it will be shown that this topic was not extensively researched and is a new type of research where no sufficient experimental work has been applied. As an application, a quarter car model was chosen to be investigated. The aim of the Thesis is to validate theoretically and experimentally the use of nonlinear springs in a quarter car model. Design the new type of suspension and insert it in the experimental set up, built from the ground up in the laboratory. A novel criterion for optimal ride comfort is the root mean square of the absolute acceleration specified by British standards ISO 2631-1997. A new way to reduce vibrations is to take advantage of nonlinear components. The mathematical model of the quarter-car is derived, and the dynamics are evaluated in terms of the main mass displacement and acceleration. The simulation of the car dynamics is performed using Matlab® and Simulink®. The realization of vibration reduction through one-way irreversible nonlinear energy localization which requires no pre-tuning in a quarter car model is studied for the first time. Results show that the addition of the nonlinear stiffness decreases the vibration of the sprung mass to meet optimal ride comfort standards. As the passenger is situated above the sprung mass, any reduction in the sprung mass dynamics will directly have the same effect on the passenger of the vehicle. The future is in the use of a nonlinear suspension that could provide improvement in performance over that realized by the passive, semi active and active suspension. The use of a quarter car model is simple compared to a half car model or a full car model, furthermore in the more complex models you can study the heave and the pitch of the vehicle. For the initial study of the nonlinear spring the quarter car model was sufficient enough to study the dynamics of the vehicle. Obtaining an optimum suspension system is of great importance for automotive and vibration engineer involved in the vehicle design process. The suspension affects an automobile’s comfort, performance, and safety. In this thesis, the optimization of suspension parameters which include the spring stiffness and damper coefficient is designed to compromise between the comfort and the road handling. Using Genetic algorithm an automated optimization of suspension parameters was executed to meet performance requirements specified. Results show that by optimizing the parameters the vibration in the system decreases immensely

Reduction of a Vehicle Multibody Dynamic Model Using Homotopy Optimization

The original publication is available at: Hall, A., Uchida, T., Loh, F., Schmitke, C., & Mcphee, J. (2013). Reduction of a Vehicle Multibody Dynamic Model Using Homotopy Optimization. Archive of Mechanical Engineering, LX(1). https://doi.org/10.2478/meceng-2013-0002Despite the ever-increasing computational power of modern processors, the reduction of complex multibody dynamic models remains an important topic of investigation, particularly for design optimization, sensitivity analysis, parameter identification, and controller tuning tasks, which can require hundreds or thousands of simulations. In this work, we first develop a high-fidelity model of a production sports utility vehicle in Adams/Car. Single-link equivalent kinematic quarter-car (SLEKQ, pronounced “sleek”) models for the front and rear suspensions are then developed in MapleSim. To avoid the computational complexity associated with introducing bushings or kinematic loops, all suspension linkages are lumped into a single unsprung mass at each corner of the vehicle. The SLEKQ models are designed to replicate the kinematic behaviour of a full suspension model using lookup tables or polynomial functions, which are obtained from the high-fidelity Adams model in this work. The predictive capability of each SLEKQ model relies on the use of appropriate parameters for the nonlinear spring and damper, which include the stiffness and damping contributions of the bushings, and the unsprung mass. Homotopy optimization is used to identify the parameters that minimize the difference between the responses of the Adams and MapleSim models. Finally, the SLEKQ models are assembled to construct a reduced 10-degree-of-freedom model of the full vehicle, the dynamic performance of which is validated against that of the high-fidelity Adams model using four-post heave and pitch tests.The authors gratefully acknowledge the financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the NSERC/Toyota/Maplesoft Industrial Research Chair program

Applying Neural Networks for Tire Pressure Monitoring Systems

A proof-of-concept indirect tire-pressure monitoring system is developed using neural net- works to identify the tire pressure of a vehicle tire. A quarter-car model was developed with Matlab and Simulink to generate simulated accelerometer output data. Simulation data are used to train and evaluate a recurrent neural network with long short-term memory blocks (RNN-LSTM) and a convolutional neural network (CNN) developed in Python with Tensorflow. Bayesian Optimization via SigOpt was used to optimize training and model parameters. The predictive accuracy and training speed of the two models with various parameters are compared. Finally, future work and improvements are discussed

The Enabler: A reevaluation of design concepts and construction of a scaled model

The basic objective of the student's work this quarter was to make an in depth examination of the design concepts used on the lunar vehicle 'The Enabler'. Several changes were made to the vehicle including a redesigned wheel, a more compact boom and a reduced articulation angle. The vehicle's final dimensions were determined through an optimization process by defining mathematical equations for several of the vehicle's defined objectives. These included the ability to scale a one meter object, traverse a one meter crevice, and maintain a wheel-to-wheel clearance of three inches while at maximum articulation. The final dimensions of the vehicle were used to construct an approximate 1/4 scale model of the chassis and wheels. The boom, however, was constructed on a 1/5 scale (from the original design). This was due to the redesign of the boom and the limitations of the constructing material and PVC fittings

Equivalent air spring suspension model for quarter-passive model of passenger vehicles

This paper investigates the GENSIS air spring suspension system equivalence to a passive suspension system. The SIMULINK simulation together with the OptiY optimization is used to obtain the air spring suspension model equivalent to passive suspension system, where the car body response difference from both systems with the same road profile inputs is used as the objective function for optimization (OptiY program). The parameters of air spring system such as initial pressure, volume of bag, length of surge pipe, diameter of surge pipe, and volume of reservoir are obtained from optimization. The simulation results show that the air spring suspension equivalent system can produce responses very close to the passive suspension system

Comparison of H∞ and μ-synthesis Control Design for Quarter Car Active Suspension System using Simulink

To improve road dealing with and passenger consolation of a vehicle, a suspension system is supplied. An active suspension system is taken into consideration better than the passive suspension system. In this paper, an active suspension system of a linear quarter vehicle is designed, that's issue to exclusive disturbances on the road. Since the parametric uncertainty within the spring, the shock absorber and the actuator has been taken into consideration, robust control is used. H∞ and µ-Synthesis controllers of are used to improve using consolation and road dealing with potential of the vehicle, in addition to confirm the sturdy stability and overall performance of the system. In the H∞ design, we designed a driving force for passenger consolation and to preserve the deflection of the suspension small and to reduce the disturbance of the road to the deflection of the suspension. For the µ synthesis system, we designed a controller with hydraulic actuator and uncertainty model. We designed a MATLAB / SIMULINK model for the active suspension system with the H∞ and µ-synthesis controllers we tested the use of 4 road disturbance inputs (bump, random, sinusoidal pavement and slope) for deflection of the suspension, body acceleration and body travel for passive, active suspension with controller and active suspension without controller. Finally, we evaluate the H∞ and µ-synthesis controllers with a Simulink model for suspension deflection, body acceleration and body travel simulation, and the result suggests that both designs offer correct overall performance, however the H∞ controller has superior overall performance as compared to the µ-synthesis controller