Vehicle Suspension Control Research Articles

Optimisation of Internal Model Control Performance Indices for Autonomous Vehicle Suspension

Autonomous vehicles (AVs) have grown in popularity and acceptability due to their unique capacity to reduce pollution, road accidents, human error, and traffic congestion. Vehicle suspension is an important component of a car chassis since it affects the performance of vehicle dynamics. As a result, enhancing suspension performance and stability is critical in order to achieve a more pleasant and safer car. Although there are several suspension control methods, they all suffer from fixed gain characteristics that are prone to nonlinearities, disturbances, and the inability to be tuned online. This research provides a comparison of Internal Model Control (IMC) performance metrics for vehicle suspension control. The IMC approach was tuned using the Genetic Algorithm and the Particle Swarm Optimisation algorithms. The performance of each of these schemes was analysed and compared in order to determine the approach with the best performance in terms of AV suspension control. The performance of the system response was compared to that of the traditional IMC. According to the comparison analysis, the optimized IMC systems had lower IAE, ITAE, ISE, rising time, and settling time values than the traditional IMC. Furthermore, there were no overshoots in any of the controllers.

Simultaneous Suspension Control and Energy Harvesting Through Novel Design and Control of a New Nonlinear Energy Harvesting Shock Absorber

Simultaneous vibration control and energy harvesting of vehicle suspensions have attracted significant research attention over the past decades. However, existing energy harvesting shock absorbers (EHSAs) are mainly designed based on the principle of linear resonance, thereby compromising suspension performance for high-efficiency energy harvesting and being only responsive to narrow bandwidth vibrations. In this paper, we propose a new EHSA design -- inerter pendulum vibration absorber (IPVA) -- that integrates an electromagnetic rotary EHSA with a nonlinear pendulum vibration absorber. We show that this design simultaneously improves ride comfort and energy harvesting efficiency by exploiting the nonlinear effects of pendulum inertia. To further improve the performance, we develop a novel stochastic linearization model predictive control (SL-MPC) approach in which we employ stochastic linearization to approximate the nonlinear dynamics of EHSA that has superior accuracy compared to standard linearization. In particular, we develop a new stochastic linearization method with guaranteed stabilizability, which is a prerequisite for control designs. This leads to an MPC problem that is much more computationally efficient than the nonlinear MPC counterpart with no major performance degradation. Extensive simulations are performed to show the superiority of the proposed new nonlinear EHSA and to demonstrate the efficacy of the proposed SL-MPC.

Research on Finite Element Structure of Vehicle Suspension Control Arm Based on Neural Network Sensing Control

To improve the adaptive control of the neural network under the influence of vehicle suspension control, the neural network control method is proposed. The specific content of the method analyzes the nonlinear properties of vehicle suspensions, proposes neural network-based adaptive control strategies, and develops neural network-based nonlinear algorithms and neural identifiers. Genetic algorithms perform predictive control of rear suspension through a compensation network. The experimental results show that the model structure is order n = m = 2 , the AN1 network node is 4-6-1, the AN2 network node is 5-4-1, the AN3 network node is 6-4-1, and the learning correction rate is α = 0.90 . In the actual simulation calculation, the number of nodes in the hidden layer of the network is increased, and the minimum number of nodes is chosen to determine the structure of the network, since the control effect obtained is not fundamentally changed. The suspension, which is controlled by the neural network’s adaptive control, has a vibration-reducing effect and is more effective by increasing the control of the rear suspension. The neural network has been shown to be able to effectively control the vehicle’s control arm.

Adaptive sliding mode-based active disturbance rejection control for vehicle suspension control

This article presents an adaptive sliding mode-based active disturbance rejection control strategy for the quarter car active suspension control. The suspension system is problematic for its nonlinearities from the dampers, springs, and irregular excitation from the road surface. This study considers this complex behavior and nonlinear characteristics of the suspension system and uses an adaptive sliding mode control law and an extended state observer to estimate and eliminate them from the controlled system. The central concept is to combine the advantages of adaptive sliding mode control to accurately track the reference trajectory with the ability of active disturbance rejection control to reject the parameter uncertainties and external disturbances. The proposed control scheme is verified in simulation studies with parameter uncertainties, nonlinearities, and external disturbances. The simulation results show that the proposed control scheme can significantly improve vehicles’ ride comfort and road-handling ability, owing to the extended state observer’s estimation capability. A comparison of the proposed strategy is also presented with a linear active disturbance rejection control and a conventional proportional–integral–derivative controller. Simulation results show that adaptive sliding mode-based active disturbance rejection improves the robustness against modeling errors, nonlinearities, and disturbances.

Active vehicle suspension control using road preview model predictive control and radial basis function networks

Active suspension systems in road vehicles are applied in order to mitigate the road-induced chassis vertical accelerations more effectively than standard passive suspensions, thus increasing comfort and handling. Such systems are greatly assisted by road preview schemes, consisting of special sensors usually based on laser scanners (e.g. LiDAR sensors), which detect road irregularities ahead of the vehicle and feed this information to a control system, designed to manipulate the active suspension accordingly. In this paper, a model predictive controller (MPC) with road preview incorporating radial basis function (RBF) models, is presented as a control scheme for a full car active suspension system. The employed RBF models can efficiently approximate the nonlinear behavior of the suspension system, thus improving performance over linear MPC methods. Special care is taken to alleviate the increased computational complexity entailed in the RBF models, in order to ensure that online implementation of the controller is feasible. The proposed scheme is evaluated on a detailed simulated full car model under various road excitation types, while making use of a realistic approach for incorporating LiDAR road scanner noise. Comparisons to a passive suspension system, as well as a standard MPC controller with a fully linear plant model, demonstrate the performance potential of using RBF prediction models in a road preview MPC context.

Experimental Validation of LQR Weight Optimization Using Bat Algorithm Applied to Vibration Control of Vehicle Suspension System

To deal with multiple constraints of vehicle active suspension system (ASS) including road handling and passenger safety, this paper presents an optimal linear quadratic regulator (LQR) approach which employs bat algorithm (BA) for selection of optimal state and input penalty matrices of LQR. We formulate the conflicting control objectives of ASS, namely, ride comfort and passenger safety as a multi-constraint optimization problem and employ the BA for weight selection of LQR. The key advantage of the proposed approach is that the local optima problem is avoided by utilizing the frequency tuning and random walk technique in BA. The performance of the proposed approach is experimentally tested using hardware in loop (HIL) testing on a quarter car ASS for realistic road profiles. Moreover, the performance is benchmarked against grey wolf optimization tuned LQR. Experimental results assessed based on ISO 2631 standards highlight the significant improvement in the ride comfort and passenger safety.

Symmetry Control of Comfortable Vehicle Suspension Based on H∞

Suspension is an important part of intelligent and safe transportation; it is the balance point between the comfort and handling stability of a vehicle under intelligent traffic conditions. In this study, a control method of left-right symmetry of air suspension based on H∞ theory was proposed, which was verified under intelligent traffic conditions. First, the control stability caused by the active suspension control system running on uneven roads needs to be ensured. To address this issue, a 1/4 vehicle active suspension model was established, and the vertical acceleration of the vehicle body was applied as the main index of ride comfort. H∞ performance constraint output indicators of the controller contained the tire dynamic load, suspension dynamic stroke, and actuator control force limit. Based on the Lyapunov stability theory, an output feedback control law with H∞-guaranteed performance was proposed to constrain multiple targets. This way, the control problem was transformed into a solution to the Riccati equation. The simulation results showed that when dealing with general road disturbances, the proposed control strategy can reduce the vehicle body acceleration by about 20% and meet the requirements of an ultimate suspension dynamic deflection of 0.08 m and a dynamic tire load of 1500 N. Using this symmetrical control method can significantly improve the ride comfort and driving stability of a vehicle under intelligent traffic conditions.

Proposal of Data-Based Preview Controller for Active Vehicle Suspension

Proposal of Data-Based Preview Controller for Active Vehicle Suspension

Fuzzy SMC Method for Active Suspension Systems with Non-ideal Inputs Based on a Bioinspired Reference Model

This paper copes with robust control of vehicle suspension in a simpler way, with guaranteed performance and less energy consumption. To this end, a fuzzy SMC method for active suspension system based on bionic nonlinear dynamics is designed. Unlike existing results, the proposed control method effectively exploits the beneficial nonlinear stiffness and damping of the biomimetic reference model, resulting in energy-saving performance. At the same time, some practical problems are fully considered, including input saturation, dead zone, unknown/uncertain dynamics, as well as external interference. Theoretical analysis and simulation results illustrate that the designed fuzzy SMC method based on bionic dynamics could effectively suppress the vibration of the active suspension system, improve ride comfort as well reduce energy consumption

Suspension System Control Based on Type‐2 Fuzzy Sliding Mode Technique

This paper presents a new method of intelligent control for vehicle suspension. First, the suspension system is modeled with all the details, and then based on the obtained model, the sliding mode control is designed for it. The controller parameters and coefficients are calculated and updated by a type‐2 fuzzy system. The chattering phenomenon is eliminated with a unique technique. In order to evaluate the performance of the proposed control system, two‐model uncertainty of the road is applied. Simulations have been performed for both active and passive modes. The simulation results show the high efficiency of the proposed control system.

Feasibility of a Neural Network-Based Virtual Sensor for Vehicle Unsprung Mass Relative Velocity Estimation.

With the automotive industry moving towards automated driving, sensing is increasingly important in enabling technology. The virtual sensors allow data fusion from various vehicle sensors and provide a prediction for measurement that is hard or too expensive to measure in another way or in the case of demand on continuous detection. In this paper, virtual sensing is discussed for the case of vehicle suspension control, where information about the relative velocity of the unsprung mass for each vehicle corner is required. The corresponding goal can be identified as a regression task with multi-input sequence input. The hypothesis is that the state-of-art method of Bidirectional Long–Short Term Memory (BiLSTM) can solve it. In this paper, a virtual sensor has been proposed and developed by training a neural network model. The simulations have been performed using an experimentally validated full vehicle model in IPG Carmaker. Simulations provided the reference data which were used for Neural Network (NN) training. The extensive dataset covering 26 scenarios has been used to obtain training, validation and testing data. The Bayesian Search was used to select the best neural network structure using root mean square error as a metric. The best network is made of 167 BiLSTM, 256 fully connected hidden units and 4 output units. Error histograms and spectral analysis of the predicted signal compared to the reference signal are presented. The results demonstrate the good applicability of neural network-based virtual sensors to estimate vehicle unsprung mass relative velocity.

Optimized Fuzzy Skyhook Control for Semi-Active Vehicle Suspension with New Inverse Model of Magnetorheological Fluid Damper

To improve the performance of vehicle suspension, this paper proposes a semi-active vehicle suspension with a magnetorheological fluid (MRF) damper. We designed an optimized fuzzy skyhook controller with grey wolf optimizer (GWO) algorithm base on a new neuro-inverse model of the MRF damper. Because the inverse model of the MRF damper is difficult to establish directly, the Elman neural network was applied. The novelty of this study is the application of the new inverse model for semi-active vibration control and optimization of the semi-active suspension control method. The calculation results showed that the new inverse model can accurately calculate the required control current. The fuzzy skyhook control method optimized by the grey wolf optimizer (GWO) algorithm was established based on the inverse model to control the suspension vibration. The simulation results showed that the optimized fuzzy skyhook control method can simultaneously reduce the amplitude of vertical acceleration, suspension deflection, and tire dynamic load.

Vibration control of vehicle suspension with magneto-rheological variable damping and inertia

To avoid the limitation of conventional vehicle magnetorheological (MR) suspension, a variable damping and inertia device is applied in the vehicle suspension with MR technology. A semi-active adaptive MR inerter (AMRI) is discussed. A quarter car suspension model with an AMRI installed in parallel with a double-ended MR damper (D-MRD) is considered. First, the vehicle suspension with variable damping and inertia is analyzed. The prototype of D-MRD and MR variable inertia flywheel (MRVIF) are fabricated and tested respectively. Then, the control model of D-MRD and MRVIF is developed on the basis of test data. An improved Fuzzy PID controller for the semi-active suspension with D-MRD and AMRI is formulated. Numerical simulation is investigated to validate the proposed variable damping and inertia device. The results demonstrate that the performance of the semi-active suspension with D-MRD and AMRI can achieve much better ride comfort than the semi-active suspension with only D-MRD or AMRI.

Deep Learning-Based Estimation of the Unknown Road Profile and State Variables for the Vehicle Suspension System

The vehicle suspension control unit serves as a critical component to the vehicle system, as it ensures the steering stability and sound ride quality of the vehicle. To effectively realize control strategies, it is essential to foreknowledge the road profile and the suspension system's internal state variables. While the mentioned variables are not practically measurable using commercial sensors, it is necessary to estimate the desired variables by utilizing observer systems. Conventional means have mainly employed model-based approaches, in which model uncertainties and high computational cost pose limitations for practical implementation. Herein, we propose a data-driven deep learning method as an alternative because no explicit physical modeling is required, and evaluation is computationally cheap. We first propose a novel encoder-decoder structured recurrent neural network model with a two-phase attention mechanism to estimate the unknown road profile and four state variables of the vehicle suspension system. Based on a simulated data set, we assess the proposed model's qualitative and quantitative results and demonstrate that our model can achieve highly accurate estimation results with fast computation time. Besides, we validate our black-box model's reliability by comparing its interpretation with the suspension system's actual physical characteristics. Furthermore, we compare the proposed model with existing baseline methods, and the results show that our proposed deep learning model significantly outperforms the baseline. Lastly, we experiment with our network's autoregressive capability and demonstrate the feasibility of estimating a sequence of future values, which has not been presented in previous works.

Hardware in the Loop Testing of Adaptive Inertia Weight PSO-Tuned LQR Applied to Vehicle Suspension Control

This paper presents an adaptive inertia weight particle swarm optimization (AIWPSO) employed for solving the multiobjective weight optimization problem of LQR applied for the vehicle active suspension system (ASS). To meet the competing control objectives of ASS including the ride comfort, road handling, and suspension travel, the state feedback controller design for ASS is formulated as an optimization problem and an improved PSO is employed for finding the optimal weights of the linear-quadratic regulator (LQR). Specifically, for solving the premature convergence of the particles and imbalance between exploration and exploitation capabilities of PSO, an adaptive inertia weight that updates the velocity of the particles based on the success rate is used. The efficacy of the AIWPSO-tuned LQR is experimentally tested on a quarter-car ASS plant using the hardware in loop (HIL) testing for an uneven road surface. Experimental results highlight that, compared to conventional PSO-tuned LQR, the proposed scheme can significantly minimize the vehicle body acceleration due to irregular road profile while guaranteeing the minimum tire friction for passenger safety. The ISO 2361-1 standards adopted to evaluate the ride and health criteria substantiate that the proposed scheme reduces the vibration dose value by 25.34% for a bumpy road profile. Moreover, the cumulative power spectral density (CPSD) of vehicle body acceleration assessed in both low- and high-frequency regions manifests the significant improvement in the ride comfort.

Reducing wheel wear from the perspective of rail track layout optimization

Wheel wear (W-wear) is one of the most critical issues affecting vehicle-track performances and operating costs. Currently, the works on W-wear behavior and W-wear reduction are mainly based on four aspects: wheel-rail (WR) tribology, WR profile, vehicle structure design and active control of vehicle suspensions. Little attention has been paid to the effects of track layout parameters, such as superelevation, gauge, and cant. To supplement the existing research, this work aims to investigate the relationship between W-wear and track layout parameters and ultimately reduce W-wear through optimizing track layout parameters. The framework consists of a series of steps. Firstly, a multibody dynamics simulation (MBS) model of an Sgnss wagon with 55 degrees of freedom (DOFs) is built. Then, taking a 375-m-radius curve as a case, the influence of track layout parameter (superelevation, gauge, and cant) on W-wear and vehicle derailment safety is investigated based on Kriging surrogate model (KSM). Finally, based on optimized results obtained by KSM and particle swarm optimization (PSO), two optimal regions and three reasonable suggestions concerning the layout of a 375-m-radius curve are given from the perspective of reducing W-wear. This study is promising for the parameter setting of those dedicated lines, on which the train speed is usually fixed, such as metro, light rail, and tram.

Pointwise‐constrained optimal control of a semiactive vehicle suspension

SummaryThis article presents an optimal control strategy (OCS) for semiactive vehicle suspensions with road profile sensors. The suspension is modeled as a quarter‐car model with a magnetorheological (MR) damper. The OCS main objective is to minimize the fourth‐power acceleration of the sprung mass. In addition, three pointwise constraints of the model are taken into account when the optimal control problem is solved: suspension travel limits (upper and lower) and tyre vertical force. In order to deal with a large number of constraints, we implement the gradient optimization method based on the method of moving asymptotes routine, which shows very good performance reaching optimal controls while satisfying the constrains. The solution has been compared with two passive MR damper configurations (low and high damping) as well as Skyhook and Balance control strategies for three different road inputs. Results show that OCS fulfills the constraints and reduces the sprung mass acceleration peak and the root‐mean‐quad acceleration up to 59%, in comparison to passive strategies.

Fuzzy adaptive nonlinear stochastic control for vehicle suspension with electromagnetic actuator

This work solves the stability problem of a vehicle suspension with stochastic disturbance by designing an adaptive controller. The model of a quarter vehicle subjected to noise excitation is considered. The stochastic perturbance is realized by the roughness of the road and the vehicle moving with constant velocity. In the control design procedure, fuzzy logic systems are used to approximate unknown nonlinear functions. Meanwhile, the mean value theorem is employed to ensure the existence of the affine virtual control variables and control input. The backstepping technique is applied to construct the ideal controller. On the basis of Lyapunov stability theory, the proposed control method proves that the displacement and speed of the vehicle is reduced to a level ascertained by a true “desired” conceptual suspension reference model. Finally, the effectiveness of the proposed method is verified by simulation of electromagnetic actuator servo system.

Invariant Sets in Saturated and Robust Vehicle Suspension Control

This manuscript introduces a new robust control design of car active suspension systems using ellipsoidal techniques. The impact of road irregularities is regarded as an external disturbance. The suggested controller meets the following objectives: optimal passenger comfort, actuator control force limit satisfaction, effective disturbance rejection, and robustness against changes in passengers’ load. The passenger load variations cause system uncertainty that is modeled as norm-bounded. A new sufficient condition is established based on the invariant ellipsoid method and the linear matrix inequalities optimization to guarantee robust stability and performance for the system. Time-domain model of road roughness based on trigonometric functions is studied. The performance of the proposed controller is tested using a quarter-car model with an active suspension system. Comparative simulation with other techniques, e.g., H∞ and regional pole placement, is given. Actuator dynamics and system nonlinearities are modeled and included in the design at the end.

A Semi-active Vehicle Suspension Control Strategy Based on Negative Stiffness Characteristics

A suspension is an indispensable part of a vehicle. It is of great significance for passengers’ comfort and vehicle stability. This paper proposes a semi-active vehicle suspension model with negative stiffness, and analyzes the effect of negative stiffness characteristics upon vehicle response. When analyzing the performance of semi-active vehicle suspension, a quarter vehicle suspension model is established, and the space state model is built for numerical simulation. After contrasting and analyzing the response of semi-active passive suspension with negative stiffness and semi-active suspension controlled by Skyhook damping algorithm, we conclude that semi-active suspension with negative stiffness decreases the vibration speed of the vehicle body and the deflection of the tire in the low-frequency stage, and improves the smoothness and stability of the suspension. Hence, the negative stiffness characteristic is beneficial to improve the comfort and stability of the vehicle.