Active Suspension Control Research Articles

Event-triggered finite-time guaranteed cost control of uncertain active suspension vehicle system

The event-triggered finite-time guaranteed cost control problem is important for an uncertain active suspension vehicle system. Existing works on the design of finite-time controllers for active suspension systems have not been extended to the event-triggered finite-time guaranteed cost control problem for uncertain active suspension systems. In this paper, we investigate the problem of designing an event-triggered finite-time guaranteed cost controller for an uncertain active suspension system. A new event-triggered controller and a cost function are first defined. Then, some new sufficient conditions for designing an event-triggered state feedback controller are derived based on linear matrix inequalities to stabilise the closed-loop systems while guaranteeing an adequate cost level of performance. Finally, numerical results and simulations are given to illustrate the effectiveness of the proposed method.

Integrated Control of Intelligent Vehicle Driving Stability Using Three-Dimensional Phase Space

<div>To enhance vehicle dynamic stability during driving, we developed a three-dimensional phase space model that incorporates the sideslip angle of center of mass, yaw rate, and lateral load transfer rate. This model enabled real-time evaluation and active control of vehicle stability. First, longitudinal and lateral controllers were implemented to ensure precise vehicle trajectory. Second, a hierarchical control strategy was designed to actively manage the desired sideslip angle, yaw rate, and roll angle based on the vehicle’s destabilizing conditions, thereby maintaining the vehicle within a stable state space. We simulated and tested the stability analysis methods and integrated control strategies for both cars and trucks under DLC (double lane change) and CDC (circular driving condition) scenarios using joint simulations with CarSim/TruckSim and Simulink. The proposed integrated stability control strategy, which combined MPC-based trajectory tracking with direct yaw moment control and active suspension control, enhanced the vehicle’s directional and roll stability. This approach effectively mitigated vehicle instability under extreme conditions. Compared to the MPC lateral tracking control system, the performance of the integrated control system was significantly improved. In the DLC scenario, the maximum values of the sedan’s lateral deviation, sideslip angle, yaw rate, and vehicle roll angle decreased by 22.6%, 33.9%, 5.5%, and 1.2%, respectively. In the CDC scenario, the truck’s lateral acceleration, sideslip angle, yaw rate, and vehicle roll angle decreased by 7.5%, 46.8%, 8.2%, and 80%, respectively. Additionally, open-loop simulation tests were conducted under fishhook steering conditions for both passenger cars and trucks. The results further validated the effectiveness of the integrated control strategy, demonstrating its ability to significantly improve yaw rate and roll response, thereby enhancing overall vehicle stability under challenging driving conditions.</div>

Does the application of Jensen's integral inequality and LMIs confirm exponential stability in delayed systems with gapped gamma distribution through augmented Lyapunov function?

This study is dedicated to a comprehensive exploration aimed at advancing our understanding of stability within dynamic systems. The focus is particularly on the intricate domain of delayed systems characterized by gapped gamma distributions. The primary objective of this investigation revolves around evaluating the pragmatic application and efficacy of Jensen's integral inequality in combination with the powerful analytical tools provided by Linear Matrix Inequalities (LMIs). This evaluation is crucial for rigorously assessing exponential stability within these complex systems. Central to our investigative framework is the strategic deployment of augmented Lyapunov functions. These functions play a crucial role in unraveling the intricate stability properties of delayed systems featuring gapped gamma distributions, allowing for a nuanced examination of their inherent stability characteristics under various conditions. The mathematical formulation crafted in this exploration intricately captures the interplay between the distinctive attributes of the gapped gamma distribution and the complex dynamics of the loop traffic flow model within the overarching delayed system. This interconnection serves as the fundamental basis for the stability analysis, providing insights into the interdependence of these key elements. The noteworthy contribution of this study lies in the systematic construction of a robust analytical framework explicitly tailored for stability assessment. A comprehensive investigation is undertaken to elucidate critical aspects, including the convergence rate and the attainment of asymptotic stability within the considered delayed system. Additionally, a dedicated simulation section, focusing on Vehicle Active Suspension Control, has been incorporated to further validate and showcase the applicability of the proposed methodology.

Research on anti-rollover control of three-axle rescue vehicle based on active suspension and differential braking

Abstract. Due to its intricate operational environment, substantial mass, and elevated center of mass, the three-axle emergency rescue vehicle is more prone to rollover. This study aims to enhance the operational stability and mitigate rollover risks by establishing a rollover dynamic model with 11 degrees of freedom. Using the coupling characteristics of vehicle dynamics and tire force, an anti-rollover control strategy of the three-axle vehicle based on the cooperative work of differential braking and active suspension is proposed. According to the vehicle motion characteristics, the active suspension controller is built by using a fuzzy PID algorithm, and the differential braking controller is built by using the improved adaptive model predictive control algorithm. The step and fishhook tests of differential braking, active suspension control and joint control are carried out respectively. The simulation results show that the joint control strategy can effectively reduce the rollover tendency of the vehicle, and further improve the anti-rollover ability of the vehicle compared with the single system control.

Carbody swaying suppression for a high-speed rail vehicle by utilising active lateral suspension control

This study proposes the use of active lateral secondary suspension (ALS) to address low-frequency carbody swaying in high-speed rail vehicles under low wheel-rail conicity conditions. Field experiments reveal lateral acceleration exceeding 0.10 g at a dominant frequency of 1.4 Hz, with a Sperling index exceeding 3.0 during carbody swaying occurs. By integrating field-measured wheel/rail profiles and yaw damper parameters into a multibody dynamics model of vehicle system, the coupling between bogie hunting and carbody yaw and upper-center roll modes is identified as the root cause of swaying. Evaluating classic sky-hook ALS controls, damping control proves highly effective. Doubling the damping coefficient and blow-off force becomes essential when only half of the four actuators per vehicle are active. Stiffness control adjusts carbody suspension modal characteristics to prevent resonances with the bogie hunting mode, effectively suppressing swaying. In contrast, inerter control exhibits limited efficacy. Semi-active control, with optimised gain settings, can also alleviate swaying, with control system delay identified as a critical factor, suggesting a 100 ms limit for effective swaying suppression.

A low-complexity fixed-time prescribed performance control for uncertain full-vehicle active suspensions with hydraulic actuators

This paper addresses the low-complexity fixed-time prescribed performance control problem for uncertain full-vehicle active suspension systems. Different from existing results that ignore the dynamics of the actuator, this paper considers a hydraulic actuator in the controller design. To address the nonlinearities of hydraulic active suspension systems, a new low-complexity fixed-time prescribed performance control method is proposed. In this method, the function approximators (e.g. neural networks (NNs) and fuzzy systems (FSs)) are not needed, which means that the heavy computational costs are avoided. Furthermore, by developing a fixed-time performance function, the proposed method can ensure that the suspension motions converge to the prescribed range within a finite time. Based on the Lyapunov theorem and Extreme Value Theorem, the stability of the closed-loop suspension system is strictly proved. Finally, the comparative simulation results show that the proposed method effectively improves the attitude stability and ride comfort of the suspension system.

Simulation analysis of quarter car active suspension control based on QBP-PID

Simulation analysis of quarter car active suspension control based on QBP-PID

Vertical vibration control to the in-wheel-motor electric vehicles with static eccentricity based on a reinforcement learning method

The in-wheel-motor electric vehicle (IWM-EV) is hailed as the epitome of driving ingenuity within the realm of electric vehicles. Nonetheless, the intricate nature of its components, compounded by the intricate interplay of multiple force fields, poses a significant detriment to ride comfort. In the present study, an IWM-EV driven by a permanent magnet synchronous motor was employed as a representative case study. Initially, the calculations were conducted to determine the unbalanced magnetic force (UMF) in the presence of static eccentricity of the stator. Subsequently, the characteristics of UMF across different ratios of static eccentricity as well as different velocities in the time domains were analyzed. Furthermore, the road-electromagnetic-mechanical model was developed to investigate the influence of UMF on the vertical vibration of IWM-EV under static eccentricity, comparing it against the scenario devoid of UMF. Finally, a reinforcement learning control approach was adopted to regulate the active suspension system, comparing its efficacy with that of passive suspension and semi-active suspension (specifically, skyhook control). Through extensive simulations, the results demonstrated that the reinforcement learning control strategy derived from the road-electromagnetic-mechanical model outperforms the other two control strategies, exhibiting commendable resilience and adaptability across diverse road surfaces and velocities. This study unveiled the potential of RL methods in enhancing riding comfort through active suspension control.

Adaptive endocrine PID control for active suspension based on reinforcement learning

Adaptive endocrine PID control for active suspension based on reinforcement learning

Dynamic characteristic analysis and key parameter optimization of throttling orifice type air damping air spring

Abstract The unique hysteretic characteristic of rubber bellows and the nonlinear flow of internal airflow in the system results in the significant nonlinear dynamic characteristic of throttling orifice type air damping air springs (OADASs). To solve the problem of mathematical representation of dynamic characteristic and key parameters optimization of throttling OADAS, this paper comprehensively considers the hysteretic characteristic of rubber bellows under variable pressure, the nonlinear dynamic characteristic model and linear model of throttling OADAS are established based on the concepts of gas thermodynamics and fluid mechanics. The static and dynamic characteristic tests of the throttling OADAS are conducted, to verify the accuracy and effectiveness of the proposed model, and to reveal the influence laws of excitation amplitude, excitation frequency, and throttling orifice diameter on the quantitative characterization indexes. Finally, a complete throttling orifice diameter optimization method is proposed based on the eight-degree-of-freedom model of the entire vehicle. Optimization results illustrate that the RMS values of the vertical acceleration of the body and the vertical acceleration of the driver are decreased by 19.02% and 38.44%, respectively. Overall, the outcomes of this paper can provide the design idea and theoretical basis for air damping matching and active suspension control.

Delayed feedback active suspension control for chaos in quarter car model with jumping nonlinearity

Vehicles that operate on off-road terrain, such as rough and unpaved roads, sometimes suffer from severe vibrations. This vibration causes vehicle tires to lose contact with the supporting ground and subsequently collide with it. This jumping leads to nonlinear impact dynamics similar to those of a bouncing ball. In this study, a quarter car model with jumping nonlinearity is newly developed to represent the impact dynamics of an off-road vehicle under harsh terrain conditions. Subsequently, complicated vibrations, such as quasi-periodic and chaotic vibrations in the developed model, are identified using a bifurcation diagram and Lyapunov exponents. Additionally, delayed feedback (DF) control of the active suspension is designed for the developed model. The numerical results show that DF control is effective at eliminating chaos and reducing vibration levels. The noise robustness of the DF control is validated for sinus excitation and small random road noise. The results indicate that DF is effective even when road noise exists. Thus, this study demonstrates the feasibility of DF active suspension control for future suspension control design of the off-road vehicle.

Active suspension control using novel HB3C optimized LQR controller for vibration suppression and ride comfort enhancement

This article addresses the optimization of a Vehicle Active Suspension System (VASS) through the application of a Linear Quadratic Regulator (LQR) controller. The primary objective is to enhance ride comfort and ensure vehicle stability by addressing the divergent needs of vibration control. The research identifies key issues in existing optimization algorithms, namely, the exploration stage inefficiency in Big Bang Big Crunch Optimization (B3C) and the slow convergence rate in Coyote Optimization (CO). To overcome these challenges, a novel hybrid algorithm, Hybrid Coyote optimization based Big Bang Big Crunch (HB3C), is proposed. The research objective is to optimize the LQR weighting matrices using the HB3C algorithm, aiming for improved ride comfort and vehicle safety. The problem statement involves the inadequacies of existing algorithms in addressing the exploration and convergence issues. The motivation lies in enhancing the efficiency of VASS through optimal control, leading to better ride comfort and safety. The methodology involves integrating CO within a loop with B3C to compute the optimum reduction rate for the algorithm. Since, B3C algorithm’s success is highly dependent on selecting the ideal reduction rate. This hybrid approach is then applied to optimize the existing LQR weighting matrices. The results are evaluated in terms of time domain and frequency domain response analysis, with a focus on ride comfort based on ISO 2631-1 standards. The study demonstrates a maximum reduction of approximately 74% achieved by the optimized HB3C-LQR controllers.

Active suspension and steering system control of emergency rescue vehicle based on sliding mode dual robust coordination control

Active suspension and steering system control of emergency rescue vehicle based on sliding mode dual robust coordination control

Active suspension control strategy for vehicles based on road surface recognition

Active suspension control strategy for vehicles based on road surface recognition

Adaptive nonlinear damping control of active secondary suspension for hunting stability of high-speed trains

This study employs an active secondary suspension with adaptive nonlinear damping to enhance the hunting stability of high-speed trains. Adjusting passive suspension parameters to optimize ride comfort and hunting stability simultaneously in varied extreme operational conditions poses a significant challenge for high-speed trains. This research integrates high-order displacement-dependent nonlinear damping into the secondary lateral suspension, drawing on insights from field test data. We analyze three typical hunting motion bifurcations: carbody hunting and both subcritical and supercritical bifurcations of bogie hunting. Theoretical analysis demonstrates that (a) the adaptive nonlinear damping narrows the unstable speed range and reduces the amplitude of the limit cycle in carbody hunting, (b) while it does not increase the critical speed for supercritical bogie hunting bifurcation, it substantially reduces the amplitude of the limit cycle, and (c) it increases the nonlinear critical speed for subcritical bogie hunting bifurcation, with the potential to alter the bifurcation from subcritical to supercritical, which holds considerable practical significance. Implementing such nonlinear damping directly through passive structure is challenging. Therefore, in view of this underactuated control problem, the constraint-following control is applied in the active suspension system to inherit the benefits of adaptive nonlinear damping. The simulation results show that the proposed active suspension system can effectively suppress the abnormal vibration caused by hunting motions.

Design of Static Output Feedback Suspension Controllers for Ride Comfort Improvement and Motion Sickness Reduction

This paper presents a method to design a static output feedback active suspension controller for ride comfort improvement and motion sickness reduction in a real vehicle system. Full-state feedback controller has shown good performance for active suspension control. However, it requires a lot of states to be measured, which is very difficult in real vehicles. To avoid this problem, a static output feedback (SOF) controller is adopted in this paper. This controller requires only three sensor outputs, vertical velocity, roll and pitch rates, which are relatively easy to measure in real vehicles. Three types of SOF controller are proposed and optimized with linear quadratic optimal control and the simulation optimization method. Two of these controllers have only three gains to be tuned, which are much smaller than those of full-state feedback. To validate the performance of the proposed SOF controllers, a simulation is carried out on a vehicle simulation package. From the results, the proposed SOF controllers are quite good at improving ride comfort and reducing motion sickness.

Nonlinear adaptive fault-tolerant control for full-car active suspension with velocity measurement errors and full-state constraints

This work concentrates on the vibration suppression problem for full-car active suspension in the presence of multiple actuator faults, velocity measurement errors, full-state constraints and external disturbances, simultaneously. Herein, a novel nonlinear fault-tolerant control (FTC) strategy is developed by the aid of the online estimation of fault parameters, and it can accommodate multiple actuator faults without the information obtained from costly fault detection and isolation mechanism. Then, the violation of full-state constraints can be prevented by introducing the log-type barrier Lyapunov function (BLF) into the adaptive backstepping method, and the problems related to velocity measurement errors of car body and external disturbances are handled under the robust control framework, so the complexity caused by state constraints, actuator faults and velocity measurement errors can thus be taken into consideration. The stability analysis is subsequently conducted with the assistance of Lyapunov theory, the boundness of all signals is confirmed, and the non-violation of the displacement and velocity constraints for car body motions is guaranteed. In the end, the performance of the proposed controller is evaluated under sinusoidal and random road surfaces. Importantly, the simulation results are presented to indicate the validity and advantages of the developed approach despite the existence of multiple actuator faults, velocity measurement errors and external disturbances.

Pitch motion suppression of electric vehicle active suspensions based on multibody dynamics

Active suspension control strategies are proposed to suppress pitch motion and address the issue of motion sickness among electric vehicle passengers. In this work, we investigate the performance of the linear quadratic regulator (LQR), variable universe fuzzy control, adaptive-network-based fuzzy inference system (ANFIS), and fuzzy PID control under continuous acceleration and deceleration and bumpy road conditions. First, a 14-degrees-of-freedom (DOF) dynamics model of an electric vehicle is developed based on a semirecursive multibody dynamics method, which was originally proposed by Javier García de Jalón. The vehicle dynamics simulation is performed to accurately model the vehicle states and responses. Second, the LQR, variable universe fuzzy control, ANFIS, and Fuzzy PID control algorithms are tailored via vehicle states, including pitch, rate, and acceleration. Their performances are investigated and compared in detail. Finally, the robustness of the proposed control strategies is further discussed based on various speed bump parameters and initial velocities. The results indicate that the proposed control strategies are capable of suppressing the pitch motion of electric vehicles, enhancing the riding comfort under diverse operating conditions, thereby reducing the likelihood of motion sickness among passengers of electric vehicles.

Design of Active Suspension Controller for Ride Comfort Enhancement and Motion Sickness Mitigation

This paper presents a method for designing an active suspension controller for ride comfort enhancement and motion sickness mitigation. For this, it is necessary to design an active suspension controller, which aims to reduce the vertical acceleration and pitch rate of a sprung mass in a vehicle. A half-car vehicle model was selected. For the controller design, a static output feedback (SOF) control was selected instead of a full-state feedback control because it is hard to measure all state variables in real vehicles. With the available signals, three types of SOF controller were proposed. To determine the gains of the SOF controllers, a linear quadratic optimal control methodology and a simulation-based optimization method were adopted. To validate the proposed method, a simulation was carried out using vehicle simulation software. The simulation results show that the proposed method is quite effective for ride comfort enhancement and motion sickness mitigation.

Model Predictive Control for Speed-Dependent Active Suspension System with Road Preview Information.

This paper proposes a model predictive control (MPC) scheme based on linear parameter variation to enhance the damping control of speed-dependent active suspensions. The controller is developed by introducing a speed-dependent term, specifically front- and rear-wheel time delays, to the half-car model using the Padé approximation. Subsequently, the model is augmented with time-varying parameter dependence. An adaptive Kalman filter based on variance matching is employed to estimate system states affected by imprecise sensor measurement noise. Finally, a set of explicit control laws incorporating road preview information and available vehicle speed are determined offline using multi-parameter linear programming (mp-LP), simplifying online implementation to searching for optimal solutions in a lookup table. Simulation results demonstrate a significant improvement in active suspension control under changing vehicle speeds compared to passive control.