Sprung Mass Acceleration Research Articles

Road-classification-based sprung-mass adaptive suspension control system

The road-classification-based sprung-mass adaptive suspension control system (RBSA) is established to improve the ride comfort under the condition that the road grade and sprung mass changed simultaneously. First, a linearized optimal control method for the Macpherson suspension is derived based on mechanical equations, and the reliability of the method is verified by experiments. Second, based on the optimal control theory and multi-objective optimization algorithm, the RBSA control system is established. The controller parameters can be automatically adjusted by the RBSA control system according to the road roughness grade and sprung mass acceleration under different sprung mass and road excitation conditions, and the vibration of the suspension is optimal under different conditions. Finally, the correctness and superiority of the control system are verified by simulation and experiment and by comparing with passive suspension, ordinary active suspension, and preview suspension with fixed sprung mass. The results of simulation and experiment show that the sprung mass acceleration of the RBSA control system is smaller than that of the comparing group, and the ride comfort can be effectively improved.

A Variable Horizon Model Predictive Control for Magnetorheological Semi-Active Suspension with Air Springs.

To improve the characteristics of traditional model predictive control (MPC) semi-active suspension that cannot achieve the optimal suspension control effect under different conditions, a variable horizon model predictive control (VHMPC) method is devised for magnetorheological semi-active suspension with air springs. Mathematical models are established for the magnetorheological dampers and air springs. Based on the improved hyperbolic tangent model, a forward model is established for the magnetorheological damper. The adaptive fuzzy neural network method is used to establish the inverse model of the magnetorheological damper. The relationship between different road excitation frequencies and the control effect of magnetorheological semi-active suspension with air springs is simulated, and the optimal prediction horizons under different conditions are obtained. The VHMPC method is designed to automatically switch the predictive horizon according to the road surface excitation frequency. The results demonstrate that under mixed conditions, compared with the traditional MPC, the VHMPC can improve the smoothness of the suspension by 2.614% and reduce the positive and negative peaks of the vertical vibration acceleration by 11.849% and 6.938%, respectively. Under variable speed road conditions, VHMPC improved the sprung mass acceleration, dynamic tire deformation, and suspension deflection by 7.191%, 7.936%, and 22.222%, respectively, compared to MPC.

Quasi-static modeling of a full-channel effective magnetorheological damper with shunt and bending magnetic circuit

Magnetorheological dampers (MRD) are widely used in vibration control due to their rapid response and adjustable damping forces. However, conventional MRD designs with closed rectangular magnetic circuits suffer from limited effective working lengths and inadequate damping force for vehicle suspensions. To address this, a novel full-channel effective MRD with shunt and bending magnetic circuit (FEMRD_SB) is proposed. This design increases the effective working length of the damping channel by incorporating a bending motion in the magnetic circuit. Magnetic circuit shunting is integrated to mitigate magnetic leakage during bending, improving energy utilization efficiency. To better meet the practical needs of vehicle suspension, a quasi-static mathematical model aiming to explain the mechanical properties of the damper is investigated. Traditional models often overlook the uneven distribution of magnetic fields, which leads to poor modeling accuracy. To improve the precision of the quasi-static model, a multiphysical field coupling quasi-static modeling method is proposed. This method, utilizing the Takagi–Sugeno fuzzy neural network establishes the relationship between magnetic field and displacement, facilitating the integration of magnetic, flow, and solid fields for more precise modeling outcomes. Simulations and experiments validate the effectiveness of the FEMRD_SB and the quasi-static model. The real-vehicle experiments demonstrate that the FEMRD_SB effectively suppresses the sprung mass acceleration of a vehicle, improving the vehicle’s ride comfort.

Adaptive neural network backstepping control for the magnetorheological semi-active air suspension system with uncertain mass and time-varying input delay

Aiming at rejecting external disturbance induced by the random road profile, this paper proposes an adaptive robust control strategy to address the control problem of semi-active air suspension system installed with magnetorheological dampers (MRD) for enhancing ride comfort and handling performance. To effectively depict the inherent nonlinear dynamics of the adjustable air spring, a radial basis function neural network (RBFNN) model is trained by the experimental data offline, and an adaptive learning algorithm is introduced to maintain the modeling accuracy. Moreover, to handle the prevalent sensitive parameter variation (such as sprung mass), a nonlinear estimator is designed to estimate the uncertain sprung mass. Furthermore, a delay compensator is integrated into the control law to mitigate the impact of the time-varying input delay caused by the actuator of MRD to restrain the chattering phenomena. Additionally, the stability of the closed-loop system is rigorously proven by employing a Lyapunov–Krasovskii functional, guaranteeing the boundedness of both tracking error and estimation error. Simulation results are displayed and analyzed, illustrating the feasibility and efficiency of the proposed control strategy in depressing the sprung mass acceleration and tire deflection, showing its significance in both control performance enhancement and chattering elimination.

A simulation study on visual preview control of vehicle magnetorheological suspension

Abstract At present, the boom in intelligent vehicles, especially automotives, has brought magnetorheological (MR hereinafter) suspensions into further focus. Generally, traditional MR suspensions work with acceleration sensors to respond with a non-negligible time delay issue due to the inductive property of MR damper (MRD hereinafter), which hinders their full performance especially at high-speed driving with a powerless “blind zone”. To address this issue, this study proposes a simulation study on visual preview control for vehicle MR suspension based on MPC (Model Predictive Control), since the road preview is able to compensate the time delay due to the future road information perceived in advance. First, a camera with a computer vision algorithm is employed to preview road information of target type, target size and distance to wheels. Besides, the error correction of radial and tangential distortions of camera lens are investigated, and the trajectory of wheels are predicted by a cycloid model because MR suspension only needs to respond to the road targets that the wheels will pass over. Further, the area in front of the vehicle is divided into a recognition zone and action zone, and the road targets within action zone (<1.5 m) are calculated more precisely for a prepared immediate response from the MR suspension. Then, the performance of a simulating vehicle MR suspension is investigated through a joint simulation by the automotive simulation software CarSim and the model-solving Simulink. The evident results show that the MR suspension with visual preview control performs the best in ride comfort (mean square values of sprung mass acceleration is 82% and 52% lower compared to a passive suspension and a MR suspension with skyhook control, respectively). Therefore, the visual preview control strategy of MR suspension is able to enhance the performance on the discrete road conditions.

Integrating of LMIs with Buckingham Π theorem for control of uncertain oscillating systems

This paper introduces a novel framework for robust controller synthesis in oscillating systems by synergistically combining generalized linear matrix inequalities (GLMIs) with the Buckingham Π theorem. The primary goal is to enhance the design of robust controllers for systems with uncertain parameters through the exploitation of dimensionless groups derived from the Buckingham Π theorem. By establishing a dimensionless state-space representation, the proposed approach demonstrates adaptability to a broad spectrum of similar systems. The LMI-based formulation facilitates the systematic design of controllers capable of effectively mitigating the impact of parametric uncertainties. Simulation results for an uncertain inverted pendulum and a vehicle active suspension system validate the superior performance of the proposed method compared to conventional control techniques, such as MPC, LQG, SMC, PID, and LQR. For the uncertain inverted pendulum system, the proposed robust control scheme achieves a cart position stabilization in 5.35 s and pendulum stabilization in 6.3 s, which is faster than standard control algorithms. In the context of the vehicle active suspension system, the performance indices for sprung mass acceleration, suspension deflection, and tire deflection are 0.19, 0.47, and 0.07, respectively. These values indicate significant reductions when compared to conventional passive suspension systems and standard robust control methodologies.

Active suspension hierarchical control with parameter uncertainty and external disturbance of electro-hydraulic actuators

In order to improve the ride comfort and handling stability of the electro-hydraulic active suspension system, a hierarchical control strategy is proposed. For the active suspension system with body mass uncertainty and safety constraints, an enhanced constraint adaptive backstepping controller is designed to generate the target force of body vertical motion. When dealing with constraints, nonlinear filters are introduced, backstepping technology and quadratic Lyapunov function are used to combine the control target and domain constraints, and the vertical displacement of the body and the suspension deflection control index are synthesized into a single controlled variable, so that the control variable converging to zero meets the suspension dynamic displacement limit. The ride comfort and safety of the active suspension system are improved. Secondly, stability analysis is conducted on the zero dynamic error system to ensure that all safety performance indicators are bounded. The effects of external disturbances, parameter uncertainties and modelling errors on the force tracking accuracy of asymmetric cylinder electrohydraulic systems are addressed. A backstepping dynamic surface control method based on a nonlinear perturbation observer is proposed, which estimates the composite perturbation terms such as modelling error and external perturbation, and uses the estimated value of the nonlinear observer to design a feedforward compensating control term to offset the effect of the composite perturbation on the system performance. In addition, the dynamic surface control method is used to calculate the derivative of the target force input, which avoids the derivative explosion phenomenon and reduces the computational complexity of the system. Simulation test results show that this method reduces the computational complexity of the system and improves the control performance. And under random and bumpy road conditions, the root-mean-square value of sprung mass acceleration performance index is reduced by 48.354 % and 72.677 % compared with passive suspension, which improves the ride comfort of the vehicle.

Research on a Variable Universe Control Method and the Performance of Large Sprayer Active Suspension Based on an Artificial Fish Swarm Algorithm–Back Propagation Fuzzy Neural Network

In view of the typical requirements of large high-clearance sprayers, such as those operating in poor road conditions for farmland plant protection and at high operation speeds, reducing the vibration of sprayer suspension systems has become a research hotspot. In this study, the hydro-pneumatic suspension (HPS) of large high-clearance sprayers was taken as the object, and a variable universe T-S fuzzy controller with real vehicle vibration data as input was proposed to control suspension motion in real time. Different from traditional semi-active suspension, based on the characteristics of variable universe extension factors, a training method combining the artificial fish swarm algorithm and the back propagation algorithm was used to establish a fuzzy neural network controller with precise input to optimize the variable universe. Then, the time-domain and frequency-domain response characteristics of HPS were analyzed by simulating the special road conditions typical of farmland. Finally, the field performance of the sprayer equipped with the new controller was tested. The results show that the error rate of the AFSA-BP algorithm in training the FNN could be reduced to 3.9%, and compared with a passive suspension system, the T-S fuzzy controller improved the effects of spring mass acceleration, pitch angle acceleration, and roll angle acceleration by 18.3%, 23.3%, and 27.7%, respectively, verifying the effectiveness and engineering practicality of the active controller in this study.

Research on Inertial Force Attenuation Structure and Semi-Active Control of Regenerative Suspension

To improve the energy recovery ability of the energy-regenerative suspension, a transmission is generally used to increase the motor speed, but this results in a significant increase in the equivalent inertial mass of the suspension. The research on energy-regenerative suspension has been ongoing for more than 20 years, but there have been few product applications, mainly due to the failure to solve the problem of the deterioration of suspension performance caused by equivalent inertial mass. This paper proposes a new suspension configuration with the suspension shock absorber connected to a high-frequency vibration reduction structure and establishes a vibration transmission model. Through frequency domain analysis, it has been conclusively proven that the new-configuration can significantly reduce both the sprung mass acceleration and relative dynamic load of the energy regenerative suspension. On the basis of frequency domain analysis, a scheme based on PWM control of the dissipation resistance value of the energy regenerative suspension is proposed, and through bench comparison experiments, it has been verified that the new-configuration suspension can eliminate the oscillation of the damping force curve of the shock absorber and significantly improve the suspension performance. Further experiments show that using the skyhook semi-active control algorithm the new-configuration suspension can further reduce the sprung mass acceleration and relative dynamic load.

Integration of Skyhook Control in a Quarter Car with Magnetorheological (MR) Damper

Semi-active suspension (SAS) systems attenuate vibrations with minimal power Consumption and is usually paired with magnetorheological (MR) dampers which are a type of variable damper that produces high damping forces with no mechanical movement. This paper presents the analysis of a Skyhook controller in a quarter car test rig equipped with MR damper to reduce vibration peaks when excited by a sinusoidal signal which simulates the unevenness of road surfaces. The viability of Skyhook control in mitigating vibration was examined from the experiments. The study discovered that there was an improvement of 12.72% by Skyhook control when compared to passive damping based on the sprung mass acceleration of both damping modes. The Skyhook controller surpassed passive damping and was deemed a success in vibration control.

Time Domain Analysis of Ride Comfort and Energy Dissipation Characteristics of Automotive Vibration Proportional–Integral–Derivative Control

<div>A time domain analysis method of ride comfort and energy dissipation characteristics is proposed for automotive vibration proportional–integral–derivative (PID) control. A two-degrees-of-freedom single wheel model for automotive vibration control is established, and the conventional vibration response variables for ride comfort evaluation and the energy consumption vibration response variables for energy dissipation characteristics evaluation are determined, and the Routh stability criterion method was introduced to assess the impact of PID control on vehicle stability. The PID control parameters are tuned using the differential evolution algorithm, and to improve the algorithm’s adaptive ability, an adaptive operator is introduced, so that the mutation factor of differential evolution algorithm can change with the number of iterations. The PID control parameter optimization method presented in this article is versatile and can be used to optimize PID control parameters under different conditions. This article provides the results of PID control parameter optimization under different conditions. Based on PID control and its parameter tuning, a time domain solution method for two types of vibration response variables, their root mean square values, and the average power of energy consumption vibration of automotive vibration PID control is proposed. Two kinds of simulation test schemes are designed under urban driving conditions, which are commonly used Class B road and pulse road, with a commonly used vehicle speed of 60 km/h. The ride comfort and energy dissipation characteristics of passive suspension and PID control are compared. The results show that introducing energy consumption vibration response variables as a supplement to the conventional vibration response variables is beneficial for expanding the research and application scope of the automotive vibration and its control; with the sprung mass acceleration deviation as the control input, PID control can effectively improve the vehicle ride comfort, but it makes the vibration energy dissipation characteristics worse.</div>

P-Bifurcation Analysis of a Quarter-Car Model With Inerter-Based Pendulum Vibration Absorber: A Wiener Path Integration Approach

Abstract In this theoretical study, a recently developed inerter-based pendulum vibration absorber (IPVA) coupled with energy harvesting capabilities is applied to the quarter car model with class C road conditions (ISO 8608). The impact of varying the pendulum length parameter on power harvesting, ride comfort (sprung mass acceleration), and road handling is investigated. It is discovered that P-bifurcation of the probability density function (PDF), can simultaneously occur with enhanced output power (40% improvements), low sprung mass acceleration (60% improvements), and better road handling (60% improvements) when compared with the linear benchmark system. To predict this bifurcation, a Wiener path integration (WPI) method coupled with curvature checking is developed for the PDF. An efficient bifurcation detection algorithm is developed which leads to the prediction of monomodal, bimodal, and rotation PDF regions in the noise intensity-electrical damping plane. Using Monte Carlo simulations (MCS), the performance metrics were then compared against the optimal linear benchmark for varying driving speed on a class F road while varying the electrical damping so that the system is at or near P-bifurcation. Energy transfer into the electrical domain and power harvested are shown to be up to 43% and 20% higher than for the optimized linear system, respectively. Electrical efficiency considerations show that generator selection is also a factor. Ride comfort and road handling still saw improvements of at least 59%. Finally, the new algorithm effectively reduces an exhaustive MCS for various parameter configurations when qualitative changes in the PDF are linked to performance.

Optimal Control Method of Semi-Active Suspension System and Processor-in-the-Loop Verification

This study presents an implementation of a proportional–integral–derivative (PID) controller utilizing particle swarm optimization (PSO) to enhance the compromise on road holding and ride comfort of a quarter car semi-active suspension system (SASS) through simulation and experimental study. The proposed controller is verified with a processor-in-the-loop (PIL) approach before real-time suspension tests. Using experimental data, the magnetorheological damper (MR) is modeled by an artificial neural network (ANN). A series of experiments are applied to the system for three distinct bump disturbances. The algorithm performance is evaluated by various key metrics, such as suspension deflection, sprung mass displacement, and sprung mass acceleration for simulation. The phase plane method is used to prove the stability of the system. The experimental results reveal that the proposed controller for the SASS significantly improves road holding and ride comfort simultaneously.

Superposition of populations in multi-objective evolutionary optimization of car suspensions

The design of the suspension model of road cars is extremely important for both driver comfort and safety. Road traffic injuries are currently the eighth leading cause of death worldwide and are predicted to become the seventh leading cause of death by 2030, according to the World Health Organization (WHO). Among other factors, road infrastructure is one of the most important factors to consider when designing the suspension model, especially as autonomous driving becomes more popular. In addition, there is a growing need to test and study the impact of road roughness and pavement type on autonomous vehicles (AVs). This work provides the following contributions: a platform for suspension system optimization–flexible, highly parameterizable and rich in applications. Our solution implements, tests and optimises the 2, 3 and 4 degrees of freedom (DOF) quarter-car models (QCM) with linear seat suspension and the 5 DOF half-car model (HCM), respectively, based on random road profiles generated according to ISO 8608 standards. In addition, many multi-objective optimization (MOO) algorithms have been implemented and applied in isolation to see their comparative performance (in terms of Pareto fronts, hypervolume, coverage, spread, and epsilon), but most importantly we have also introduced a meta-optimization technique by super-positioning Non-dominated Sorting Genetic Algorithm II and Strength Pareto Evolutionary Algorithm 2, where each of the algorithms, running concurrently, produces a percentage of the total number of individuals in a generation, percentage that is calculated according to the solution quality of the individuals in the previous generation. The experimental results were obtained by simulating the optimal configurations generated by the MOO heuristic algorithms on different categories of cars (small/medium). Finally, the Taguchi method and regression analysis were used to evaluate the effects of specific parameters on system responses such as sprung mass acceleration and displacement. The Taguchi simulation was performed to experimentally validate the results obtained by metaheuristic optimization methods.

Optimal nonlinear polynomial control of a quarter-vehicle suspension system under harmonic and random road excitations

The present paper proposes an optimal polynomial control strategy for a quarter-vehicle suspension system based on dynamic programming. The optimal control objective is to decrease the responses of sprung mass acceleration, suspension deformation and road excitation, which are reflected in the performance index. The optimal control force is obtained through the principle of dynamic programming, and the form of the optimal control force mainly depends on the form of the cost function. The optimal nonlinear polynomial control (NPC) force is derived by selecting the cost function in polynomial form. The linear feedback matrix and nonlinear feedback matrix in the NPC force are determined by the Riccati equation and Lyapunov equation, respectively. The root mean square (RMS) responses of the sprung mass acceleration, suspension deformation and road load of driving vehicles under deterministic and random road surfaces are calculated. The numerical results showed that the proposed NPC strategy has a better control effect over the traditional linear quadratic regulator (LQR), especially on the peak reduction of sprung mass acceleration. Finally, the optimal control force is divided into active control force and passive control force. The energy input of the optimal control force can be reduced by only inputting the active control force.

Vibration analysis and adaptive model predictive control of active suspension for vehicles equipped with non-pneumatic wheels

In this paper, an adaptive controller is proposed for an active suspension system to achieve optimal compromise performance for vehicles equipped with non-pneumatic wheels under different road conditions. Firstly, the effective vertical stiffness of the non-pneumatic wheel (NPW) was identified through the static force-deflection tests. Then, the effect of the variations in NPW stiffness and mass on the vibration responses was investigated using a quarter-vehicle model. In order to coordinate the ride comfort and handling performance of the vehicle for different road excitations, an adaptive controller was synthesized using the model predictive control (MPC) theory together with an H ∞ state observer. The control gains for different control objectives were determined using a genetic algorithm (GA). Simulations indicate that the proposed controller can adapt to different road excitations and effectively enhance the dynamic performance of the vehicle. Specifically, by applying adaptive control, the root-mean-square (RMS) value of sprung mass acceleration (SMA) and the dynamic wheel load (DWL) coefficient are reduced by 19.4% and −9.3% on Class B roads and 12.4% and 3.8% on Class C roads, respectively, which is superior to the modified skyhook control (19.4% and −11.8% on Class B roads, and 19.3% and −12.3% on Class C roads). The effectiveness of simulation results was subsequently verified through hardware-in-the-loop experiments.

Comfort-Oriented Semi-Active Suspension Configuration with Inerter-Based Network Synthesis

This paper presents a comfort-oriented semi-active suspension system composed of a network-synthesized passive section and a controllable section based on a semi-active inerter. Firstly, the semi-active suspension system is divided into a passive part and a controllable part. For the passive part, first-order and second-order robust positive real controllers are designed. The problem with H2 cost is considered, and the bilinear matrix inequalities (BMI) are solved using an iterative method to obtain two admittance functions. The admittance functions are physically realized as two mechanical networks composed of mechanical passive elements such as inerter, spring, and damper (ISD). Then, the parameters of these mechanical elements in those networks are optimized by Particle Swarm Optimization (PSO). Secondly, a semi-active inerter based on Sky-hook control is introduced for the semi-active part of the suspension system. Finally, the semi-active ISD suspension structure is verified by a quarter vehicle model. The simulation results show that the first-order and second-order suspension systems optimize the RMS of the spring mass acceleration by 14.2% and 23.9%, respectively, as compared to traditional suspension systems. Furthermore, frequency-domain analysis also shows that both suspension systems effectively reduce the value of spring mass acceleration in the low-frequency band.

Hybrid Particle Swarm Optimization Genetic LQR Controller for Active Suspension

In this paper, a hybrid particle swarm optimization genetic algorithm LQR controller is used on a quarter car model with an active suspension system. The proposed control algorithm is utilized to overcome the shortcoming that the weight matrix Q and matrix R determined by experience in the traditional LQR control method. The proposed hybrid control method makes it possible to achieve the optimal control effect. A full-order state observer is proposed to observe the state of active suspension. A quarter car active suspension model and road input model are presented at first, and the LQR controller based on the hybrid particle swarm optimization genetic algorithm is utilized in the active suspension system control. Sprung mass acceleration, suspension deflection, and tire dynamic load are selected as the control effect evaluation index. Next, simulation results are presented. According to the results, compared with the passive suspension and active suspension with a traditional LQR control, there is an obvious reduction in the sprung mass acceleration, deflection, and tire dynamic load with an optimized controller under case 1 and case 2. Simultaneously, the system state fed back by the full-order state observer can effectively reflect the true state of the active suspension system.

Study on Adaptive Sliding Mode Fault-tolerant Control of 1/4 Vehicle Electromagnetic Suspension

An adaptive sliding mode fault-tolerant manage approach is proposed to remedy the trouble of actuator acquire failure of the electromagnetic hybrid energetic suspension device and the hassle of automobile manipulate balance degradation induced by using the nonlinear pressure of spring and damper. The failure thing is chosen to symbolize the actuator fault size, and the actuator fault parameter mannequin is established. Combining sliding mode manipulate with adaptive control, an adaptive sliding mode fault-tolerant controller for lively suspension primarily based on an correct mannequin is designed. Based on the Lyapunov balance theory, the steadiness of the machine is proved; and the Gravity search algorithm (GSA) and linear matrix inequality (LMIS) are used to optimize the sliding floor parameters, and the most beneficial answer is chosen in accordance to the health function. The simulation effects exhibit that in contrast with passive suspension, the root capability rectangular values of sprung mass acceleration, suspension dynamic deflection, and tire dynamic load underneath adaptive sliding mode fault-tolerant manipulate approach decrease by way of 41.7%, 38.4%, and 36.5% respectively. It suggests that the designed adaptive sliding mode fault-tolerant controller is right and can enhance car experience comfort.

Simulation Study of Semi-active Suspension Fuzzy Adaptive PID Control System

This work develops a mathematical model of a quarter car suspension system with two degrees of freedom and suggests a fuzzy adaptive PID controller by assessing the drawbacks of conventional control methods. The three PID parameters are automatically modified by fuzzy control, and the PID parameters are adjusted in real time. The Matlab/Simulink platform is used to create the relevant simulation model. The simulation results demonstrate the superiority of the fuzzy adaptive PID control system suggested in this study by demonstrating a reduction in the Sprung Mass Acceleration by 17.85%, the Suspension Working Space by 14.42%, and the Dynamic Tyre Load by 9.48%.