Nonlinear Suspension Research Articles

Observer-Based Security Control for Nonlinear Suspension Systems With Cyber-Attacks and Hybrid-Triggered Scheme

Observer-Based Security Control for Nonlinear Suspension Systems With Cyber-Attacks and Hybrid-Triggered Scheme

On the internal and boundary stabilization of a nonlinear suspension bridge system: Exponential and polynomial decay rates

On the internal and boundary stabilization of a nonlinear suspension bridge system: Exponential and polynomial decay rates

Bifurcation analysis of a rotor-bearing system with temperature-dependent viscosity

A flexible rotor supported by two journal bearings under nonlinear suspension and the lubricating oil is assumed to be temperature dependent in this study. Analytical tools were inclusive of bifurcation diagrams, dynamic trajectories, power spectra, Poincaré map, fractal dimension, and Lyapunov exponent are used to verify the dynamic characteristics of the rotor-bearing system, and abundant periodic, subharmonic, quasi-periodic, and even chaotic motions are found in this study. From the simulation results, the higher operating temperature will also cause the dynamic trajectory of the system to become non-periodic vibration. The rotor-bearing system operating in a non-periodic motion state may lead to possible broadband vibration with large amplitude and increase the possibility of fatigue or failure of the system. Such simulation analysis will help engineers avoid unnecessary trial and error when designing and applying rotor-bearing systems.

Control of a nonlinear active suspension system based on deep reinforcement learning and expert demonstrations

A well-controlled active suspension system has the potential to provide better ride comfort. Benefiting from its powerful feature extraction and nonlinear generalization capabilities, the deep reinforcement learning (DRL), such as deep deterministic policy gradient (DDPG), has shown great potential to make decisions adaptively and intelligently in the control of active suspension system. However, the DDPG is troubled by the problem of low training efficiency due to the high proportion of illegal strategies. This paper proposed a novel DDPG controller for a nonlinear uncertain active suspension system by combining DRL with expert demonstrations. Specifically, the improved training method integrated with both a pre-training mechanism based on PID expert samples and an adaptive experience replay mechanism, is put forward for the DDPG to achieve both the goals of imitating the expert and improving the training efficiency. Moreover, considering the ride comfort and the state constraints as targets, a mixed reward function is designed to guide RL agents for learning effective actions. It is shown that the proposed training methods effectively accelerate the convergence of the DDPG. Furthermore, the comparison experiments demonstrate that the proposed controller provides great vibration attenuation, and has better adaptiveness to various working conditions and parametric uncertainty.

Mathematical Modelling and PID Controller Implementation to Control Linear and Nonlinear Quarter Car Active Suspension

Mathematical Modelling and PID Controller Implementation to Control Linear and Nonlinear Quarter Car Active Suspension

Determination of optimal battery locations for ride comfort in electric automobiles using a nonlinear half-vehicle suspension model

Batarya elektrikli araçların ağırlığına katkıda bulunan en büyük kalemlerden biridir ve konumu süspansiyon sisteminin performansını doğrudan etkilemektedir. Bu makalenin amacı tekerlek içi motorlu elektrikli otomobillerde sürüş konforu açısından optimal batarya konumlarının lineer olmayan bir taşıt süspansiyon modeli kullanılarak belirlenmesidir. Analizlerde tüm yay ve amortisörlerin lineer karakteristiklerine ilaveten kübik doğrusalsızlıklarının da hesaba katıldığı yedi serbestlik dereceli bir yarım taşıt süspansiyon modeli kullanılmıştır. Modelde yay ve amortisör doğrusalsızlıklarına ek olarak tüm trigonometrik doğrusalsızlıklar da dikkate alınmıştır. Sinüzoidal formda 48 farklı yol profili ve 3 farklı ilerleme hızı ile toplamda 144 farklı sürüş senaryosu oluşturulmuş ve her bir senaryo için aracın boylamasına ekseni boyunca 36 batarya konumu test edilerek optimal olanı bulunmuştur. Optimizasyon kriteri, sürücü ve koltuğunun dikey ivmesinin kök ortalama kare değerinin minimizasyonudur. Gerçekleştirilen 5184 analiz neticesinde optimal batarya konumunun 0,2 ila 5 m arasındaki dalga boylarına sahip yol profilleri için aracın orta kısmı; 10 ila 30 m arasındaki dalga boylarına sahip yol profilleri içinse aracın arka kısmı olduğu görülmüştür.

Modelling and Dynamic Analysis of Adaptive Neuro-Fuzzy Inference System-Based Intelligent Control Suspension System for Passenger Rail Vehicles Using Magnetorheological Damper for Improving Ride Index

The ride comfort and safety of passenger rail vehicles depend on the performance of the suspension system in attenuating vibrations induced by track irregularities. This paper investigates the effectiveness of an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based semi-active controlled suspension system using a magnetorheological fluid damper in reducing nonlinear lateral vibrations of a passenger rail vehicle. A complete rail vehicle model is developed, including the carbody, front and rear bogies, and the passive suspension system’s nonlinear stiffness and damping characteristics are considered from experimental data. The passive suspension model is validated through experiments, and an ANFIS-based controller is incorporated with the secondary vertical suspension system to improve ride behavior. Three semi-active suspension strategies are considered under varying speeds and track irregularities, and their effectiveness is compared to the nonlinear passive suspension system in terms of rms acceleration, rms displacement, ride quality, and comfort. The results shows that the ANFIS-based semi-active suspension system with a magnetorheological fluid damper outperforms the passive suspension system and semi-active strategies in all tested conditions. There is a reduction in rms acceleration by approximately 11.11% to 23.64% and rms displacement by about 5.36% to 32.06%. Moreover, it significantly improves ride quality (9.20% to 31.02%) and comfort (9.96% to 31.50%). The rms acceleration and displacement are reduced, and the Sperling ride index and Percentage Reduction Index values demonstrate that the ANFIS-based semi-active suspension effectively minimizes the impact of rail irregularities and vibrations, resulting in a significant gain in ride quality and passenger comfort.

Parametric analysis of non-linear suspension system by optimal MR damper by rider model with sensor

Parametric analysis of non-linear suspension system by optimal MR damper by rider model with sensor

A Linear Variable Parameter Observer-Based Road Profile Height Estimation for Suspension Nonlinear Dynamics Improvements

The accuracy of road profile height estimation has a significant impact on suspension control quality, which in turn influences handling, stability of vehicle motion and occupants' comfort. Based on our previous published work, this article designs and proposes a novel method for road profile estimation that is based on suspension nonlinear dynamics. The proposed approach first establishes the road profile height estimation model considering a real suspension design, including nonlinear characteristics of the shock absorber, bushing stiffness and damping, actual geometry of the control arms, and positioning of absorber. Unlike the conventional sprung-unsprung mass model, the real nonlinear suspension model provides much higher output prediction accuracy as computational and experimental results demonstrated. Moreover, the established estimation method and model require only two easily measurable parameters, which are the acceleration of the sprung mass and the travel of the shock absorber. While considering nonlinearity and hysteretic characteristics of the damping force, the proposed approach is based on the estimation framework of linear parameter-varying systems and establishes a sliding mode observer for estimating the road profile height. The stability of estimation error dynamics of the observer is guaranteed by the Lyapunov stability analysis. As bench-test experiments of a hardware implementation of the suspension-wheel unit validated the computational results. The tests demonstrated that the proposed method allows for real-time estimating of the road profile height in different road conditions and electric currents of the suspension damper and is robust to uncertainty of the payload.

A Novel Robotic GWO LDI Modeling and Control for Nonlinear Systems

This works aims to develop a new and improved GWO (Grey Wolf Optimizer), the so-called Robotic GWO (RGWO). First, to improve GWO's update formula position with an optimal learning strategy, we adapt the algorithm to real mobile environments, including robots, so that tracking robots can move prey toward targets. Then, the nonlinear active suspension (AS) control system is linearized by a neural network (NN) based linear differential inclusion (LDI) using feedback and feedforward linearization. In theory, it is found that the general SM (Sliding Mode) optimal control cannot provide sudden optimal results for the active linearized suspension system, so a method is proposed to improve the shortcomings of the active linearized suspension system. By constructing an extended SM-optimal manifold function, an improved SM-optimal controller is designed, which incorporates information on the entire structure and the expected performance of the suspension. For comparison purposes, the performance of three kinds of controls: SM optimal refinement control, logic-fuzzy SM control, and PS (passive suspension), shows the proposed controller's advantages . Finally, our improved SM optimal control for nonlinear AS systems, in general, can achieve the actual nominal optimal suspension performance, as confirmed by the simulation results. The results also show that the improved SM optimal control method provides better robustness even when the operating conditions or parameters of the structure vary.

An Adaptive Controller Design for Nonlinear Active Air Suspension Systems with Uncertainties

Active air spring suspensions can improve the vehicle ride comfort and meanwhile realize the vehicle height regulation, and therefore, they have been widely used and studied. However, to achieve better ride comfort and a satisfactory vehicle body height adjustment, the active air suspension controller becomes an indispensable and significant part of the system. Since the nonlinear suspension system possesses uncertainties, it is difficult to take into account both ride comfort and height regulation. This study innovatively proposes an adaptive control algorithm to specifically address the problem of vehicle height regulation and ride comfort for nonlinear active air suspension systems with uncertainties. The accurate tracking to reference vehicle body height curves is realized, and the ride comfort is also improved. Through simulations with two scenarios, it is illustrated that the active air suspension controller owns better control effectiveness than the PID controller. Compared with the PID controller, the designed controller can track the reference vehicle body height curves faster and more accurately. The result also verifies the priority of the designed controller.

Improved Method for Calculating the Gauge of Railway Vehicles Considering the Non-Linearity of Suspension Systems

An improved method for calculating the gauge of railway vehicles is proposed in this study, which can provide more reasonable results for vehicles with nonlinear springs in the suspension system. Typical mechanics models of nonlinear springs are built and then introduced into the calculation formulas described in the Chinese Gauge Standard CJJ 96-2018. The relative displacement equations for the primary and secondary suspensions are defined, based on the calculation formulas, and an iterative algorithm based on Taylor expansion is applied to solve these nonlinear equations. By solving the equations, the relative displacements of the control points of the suspension system are obtained and the parameters for gauge calculation are updated. The updated parameters are then used to calculate the transverse and vertical displacements of the car body, bogie, unsprung components, flange, and tread, and to determine the quantity of throw of the vehicle profile. Finally, a numerical example is given to verify the feasibility, accuracy, and applicability of the method, and the results are also compared with those calculated from European Standard EN 15273. The method is applicable to a wide range of railway vehicles with nonlinear suspension systems, giving more reasonable results compared with existing calculation methods.

Neural Network Trajectory Tracking Control on Electromagnetic Suspension Systems

A new adaptive-like neural control strategy for motion reference trajectory tracking for a nonlinear electromagnetic suspension dynamic system is introduced. Artificial neural networks, differential flatness and sliding modes are strategically integrated in the presented adaptive neural network control design approach. The robustness and efficiency of the magnetic suspension control system on desired smooth position reference profile tracking can be improved in this fashion. A single levitation control parameter is tuned on-line from a neural adaptive perspective by using information of the reference trajectory tracking error signal only. The sliding mode discontinuous control action is approximated by a neural network-based adaptive continuous control function. Control design is firstly developed from theoretical modelling of the nonlinear physical system. Next, dependency on theoretical modelling of the nonlinear dynamic system is substantially reduced by integrating B-spline neural networks and sliding modes in the electromagnetic levitation control technique. On-line accurate estimation of uncertainty, unmeasured external disturbances and uncertain nonlinearities are conveniently evaded. The effective performance of the robust trajectory tracking levitation control approach is depicted for multiple simulation operating scenarios. The capability of active disturbance suppression is furthermore evidenced. The presented B-spline neural network trajectory tracking control design approach based on sliding modes and differential flatness can be extended to other controllable complex uncertain nonlinear dynamic systems where internal and external disturbances represent a relevant issue. Computer simulations and analytical results demonstrate the effective performance of the new adaptive neural control method.

Robust fuzzy fault tolerant control for nonlinear active suspension systems via adaptive hybrid triggered scheme

SummaryThis article is concerned with the problem of robust fuzzy fault tolerant control for the nonlinear active suspension system via adaptive hybrid triggered scheme. To describe the system with high nonlinearity, a Takagi‐Sugeno fuzzy approach is applied by weighting a series of linear subsystems. During the design of the controller, the actuator failure is taken into consideration. To ease the network communication pressure, a novel adaptive hybrid triggered scheme is proposed for the suspension system. By applying a Bessel‐Legendre inequality and a Jensen's inequality together, the control algorithm can be derived in the form of linear matrix inequalities with less conservatism. Finally, compared with the existing sampled‐data control and adaptive event triggered control, numerical simulations are performed to demonstrate the effectiveness and superiority of the proposed controller.

Research on dynamic characteristics of a novel triple-magnet magnetic suspension dynamic vibration absorber

A novel Triple-magnet Magnetic Suspension Dynamic Vibration Absorber is designed and modeled in this paper. The equivalent dynamic model of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber vibration reduction system is established. Meanwhile, the calculation model of the nonlinear magnetic suspension force is derived. Based on the force model, it is found that the nonlinear stiffness feature can be adjusted by changing the magnet distance of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber. Then the dynamic equations of the vibration reduction system are solved by using the Complex Variable Average method. And the correctness of the derivation procedure is verified through the Runge–Kutta method. From the numerical solutions, bifurcation phenomena occur in the system responses when the excitation amplitude is larger than a certain value. Adjusting the magnet distance and the damping coefficient of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber can delay or avoid bifurcation behaviors. When the excitation amplitude varies over a wide range, the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber with a larger magnet distance and damping coefficient shows better vibration reduction performance. This study provides a theoretical basis for the practical application of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber and new ideas for controlling the bifurcation of traditional nonlinear dynamic vibration absorbers.

Backpack with a nonlinear suspension system designed for low walking speeds

Backpack with a nonlinear suspension system designed for low walking speeds

A novel fuzzy PID controller for nonlinear active suspension system with an electro-hydraulic actuator

A novel fuzzy PID controller for nonlinear active suspension system with an electro-hydraulic actuator

Oscillations of a Channel Wall on a Nonlinear Elastic Suspension Under the Action of a Pulsating Layer of Viscous Gas in the Channel

Oscillations of a Channel Wall on a Nonlinear Elastic Suspension Under the Action of a Pulsating Layer of Viscous Gas in the Channel

A Differential Flatness-Based Model Predictive Control Strategy for a Nonlinear Quarter-Car Active Suspension System

Controlling an automotive suspension system using an actuator is a complex nonlinear problem that requires both fast and precise solutions in order to achieve optimal performance. In this work, the nonlinear model of a quarter-car active suspension is expressed in terms of a flat output and its derivatives in order to embed the nonlinearities of the system in the flat output. Afterward, a Model Predictive Controller based on the differential flatness derivation (MPC-DF) of the quarter-car is proposed in order to achieve optimal control performance in both passenger comfort and road holding without diminishing the lifespan of the wheel. This formulation results in a linear optimization problem while maintaining the nonlinear behavior of the active suspension system. Afterward, the optimization problem is solved by means of Quadratic Programming (QP), enabling real-time implementation. Simulation results are presented using a realistic road disturbance to show the effectiveness of the proposed control strategy.

Analysis of nonlinear vibration transmission through a vehicle suspension damper at low audio frequencies

Active control is an attractive solution to the problem of structure-borne interior road noise in cars. However, nonlinear suspension dynamics could limit the cancellation that can be achieved with a linear feedforward road noise control system. The hydraulic dampers in a vehicle suspension have previously been found to be a source of nonlinear vibration transmission at low audio frequencies. This paper presents experimental measurements and modelling of the front and rear suspension dampers in a test vehicle aimed at understanding the physical processes causing their nonlinear dynamics. Experiments are shown that highlight the different nonlinear effects present in the dampers, including friction and the mechanics of the piston valves. A suitable model was then selected from the literature, fitted to the measurements and validated. Analysis of the models revealed that, in the front damper, both friction and the valve mechanics contribute significantly to the damper’s nonlinear dynamics between 50–300 Hz. Friction in the rear damper is much less significant, meaning that its nonlinear dynamics are almost entirely caused by the piston valves. Although the front damper’s friction behaviour proved challenging to model, the effect of the piston valves was captured very accurately in both damper models.