Quarter-vehicle Active Suspension Research Articles

Improving Vibration Performance of Electric Vehicles Based on In-Wheel Motor-Active Suspension System via Robust Finite Frequency Control

This paper presents a robust finite frequency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\infty }$ </tex-math></inline-formula> control strategy for improving vibration performance and ride comfort of electric vehicles through in-wheel motor-active suspension system(IWM-ASS). Since the human body is much sensitive to the vertical vibration of 4 -8 Hz, the main objective is dedicated to deal with the vibration challenge that matches the characteristics of the human body by applying the finite-frequency technique. Firstly, the uncertain quarter-vehicle active suspension model with dynamic damping in-wheel motor driven system is established, in which in-wheel motor is suspended as dynamic vibration absorber(DVA) to isolate the force transmitted to motor bearing in IWM-ASS. Based on the framework of generalized Kalman–Yakubovich–Popov lemma and stability theory, then the performance index of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\infty }$ </tex-math></inline-formula> norm from external disturbance to controlled output for IWM-ASS is attenuated within the concerned frequency range while other system requirements such as parameter uncertainty, suspension deflection constraint and actuator saturation are also guaranteed in controller design. The resulting robust finite frequency state feedback <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\infty }$ </tex-math></inline-formula> controller is finally designed utilizing two new theorems, and solved via a set of linear matrix inequalities. Simulations for frequency-domain and time-domain responses are implemented and compared with the entire frequency control method to evaluate the effectiveness of the proposed strategy. It can be concluded from the results that the developed control strategy can effectively attenuate the negative vibration and enhance ride comfort and road-holding ability for electric vehicles of IWM-ASS.

Pareto optimality based PID controller design for vehicle active suspension system using grasshopper optimization algorithm

In this paper, a Pareto multiobjective and grasshopper optimization algorithm (GOA) based optimum proportional–integral–derivative (P–I–D) controller design is proposed for improving the vehicle active suspension system dynamics under road disturbance conditions. The Pareto objectives considered are minimization of sprung mass suspension deflection, tyre deflection, sprung mass acceleration minimization and eigenvalue-based objective function. State space model for quarter vehicle active suspension system with P–I–D controller is developed for analyzing the stability and dynamic performance of the system. The sinusoidal-based bump road disturbances are used for testing the robustness of the proposed control technique. Simulation results have been presented to show the advantage of the proposed Pareto multiobjective and GOA-based P–I–D controller over the weighted multiobjective and genetic algorithm-based P–I–D controller in terms of stability and dynamics of the active suspension system.

A Comparative Study of Particle Swarm Optimized Control Techniques for Active Suspension System

This work presents a comparative study for performance evaluation of quarter vehicle Active Suspension System (ASS) using different control techniques. Linear and non-linear mathematical models of the systems are presented and controlled using Proportional Integral Derivative (PID), Feedback Linearization, and Fuzzy Logic Control (FLC). Particle Swarm Optimization (PSO) technique is applied to optimize the gains of the implemented controllers. A simulation process is done using MATLAB/SIMULINK and the results show that the proposed PSO-optimized PID controller has enhanced the root mean square (r.m.s) values of ride comfort, load carrying, and road holding of the linear suspension system by 26.82%, 20.95%, and 22.72% respectively compared to the linear passive suspension system. Whereas, for the nonlinear suspension system, the PSO-optimized FLC has provided better compromise of the performance criteria. The controller has improved the r.m.s values of ride comfort, load carrying, and road handling by 40.61%, 44.21%, and 27.46% respectively compared to the non-linear passive suspension system.

Anti-Saturation-Based Adaptive Sliding-Mode Control for Active Suspension Systems With Time-Varying Vertical Displacement and Speed Constraints

In this article, an adaptive sliding-mode control scheme is developed for a class of uncertain quarter vehicle active suspension systems with time-varying vertical displacement and speed constraints, in which the input saturation is considered. The integral terminal SMC is adopted to improve convergence accuracy and avoid singular problems. In addition, neural networks are used to model unknown terms in the system and the backstepping technique is taken into account to design the actual controller. To guarantee that the time-varying state constraints are not violated, the corresponding Barrier Lyapunov functions are constructed. At the same time, a continuous differentiable asymmetric saturation model is developed to improve the stability of the system. Then, the Lyapunov stability theory is used to verify that all signals of the resulting system are semi globally uniformly ultimately bounded, time-varying state constraints are not violated, and error variables can converge to the small neighborhood of 0. Finally, results of the simulation of the designed control strategy are given to further prove the effectiveness.

Modeling, analysis and PID controller implementation on suspension system for quarter vehicle model

The aim of this research is to acquire a mathematical model for the quarter vehicle model's passive and active suspension system and to build an active and passive suspension control for a quarter-vehicle model. The passive design of the suspension scheme is a compromise between vehicle handling capacity and passenger ride comfort. Passive suspension provides one of these two circumstances that conflict. Current car suspension systems use passive components only by using a coefficient of spring and damping with a fixed coefficient and two degrees of freedom. In the design and manufacture of cars, passenger comfort is a very significant parameter. The objective of the active suspension system is to enhance both the comfort of the ride and the handling of the highway by directly regulating the actuators of suspension power. In the active suspension system, the Proportional Integral Differential Controller (PID) method is applied. Various kinds of highway profiles and controllers such as P, PD, PI, and PID controllers evaluate the efficiency of the active suspension system comparing it with passive suspension scheme. This efficiency will be determined by using the MATLAB and SIMULINK to perform computer simulations.

Robust Vibration Control for Active Suspension System of In-Wheel-Motor-Driven Electric Vehicle Via μ-Synthesis Methodology

Abstract This paper proposes a robust vibration controller design for active suspension system of in-wheel-motor-driven electric vehicles (IWMD-EVs) based on unified μ-synthesis framework. First, multiple parameter uncertainties and unmodeled high-order dynamics of the suspension are analyzed and discussed. By applying the mixed uncertainties and linear fraction transformation, model perturbations are separated from the suspension system and their perturbation bounds can also be limited. Then, the uncertain quarter-vehicle active suspension model with dynamic damping in-wheel-motor-driven system is established, in which in-wheel motor is suspended as a dynamic vibration absorber. The resulting robust μ-synthesis feedback controller of generalized closed-loop active suspension system is designed with the concept of structured singular value (SSV) μ and μ-synthesis theoretics, and solved via comprehensive solution of the D–G–K iteration. The μ analysis results show that the μ-controller possesses less conservative stability and performance margins as compared to the H∞ method against system uncertainties. Furthermore, simulations of nominal and perturbed suspension systems are implemented and the corresponding frequency and time-domain responses are compared, and then simulation results confirm that the developed μ-controller is capable of attenuating the negative vibration of the active suspension system compared with H∞ controller and passive suspension.

Development of Robust Guaranteed Cost Mixed Control System for Active Suspension of In-Wheel-Drive Electric Vehicles

This paper presents a mixed H2/H∞-based robust guaranteed cost control system design of an active suspension system for in-wheel-independent-drive electric vehicles considering suspension performance requirements and parameter variation. In the active suspension system model, parameter uncertainties of active suspension are described by the bounded method, and the perturbation bounds can be also limited; then, the uncertain quarter-vehicle active suspension model where in-wheel motor is suspended as a dynamic vibration absorber is established. The robust guaranteed cost mixed H2/H∞ feedback controller of the closed-loop active suspension system is designed using Lyapunov stability theory, in which the suspension working space, dynamic tire displacement, and the active control force are taken as H∞ performance indices, the H2 norm of body acceleration is selected as the output performance index to be minimized, and then a comprehensive solution is transformed into a convex optimization problem with linear matrix inequality constraints. Simulations on random and bump road excitations are implemented to verify and evaluate the performance of the designed controller. The results show that the active suspension with developed robust mixed H2/H∞ controller can effectively achieve better ride comfort and road-holding ability compared with passive suspension and alone H∞ controller.

Modeling and controlling a quarter-vehicle active suspension model

This paper presents an application of the LQR active suspension control algorithm for a vertical planar oscillation model developed for ¼ of a vehicle. The wheel smoothness and dynamics with the road surface are two parameters to provide control signals. A simulation model is developed here based on MATLAB software to compare and evaluate the LQR active suspension model with the passive suspension. The results obtained here shows an improvement for a number of parameters when utilizing the active suspension model including fluctuating amplitude; oscillation damping time; the displacement acceleration of the active suspension body.

Design of Constrained Robust Controller for Active Suspension of In-Wheel-Drive Electric Vehicles

This paper presents a constrained robust H∞ controller design of active suspension system for in-wheel-independent-drive electric vehicles considering control constraint and parameter variation. In the active suspension system model, parameter uncertainties of sprung mass are analyzed via linear fraction transformation, and the perturbation bounds can be also limited, then the uncertain quarter-vehicle active suspension model where the in-wheel motor is suspended as a dynamic vibration absorber is built. The constrained robust H∞ feedback controller of the closed-loop active suspension system is designed using the concept of reachable sets and ellipsoids, in which the dynamic tire displacements and the suspension working spaces are constrained, and a comprehensive solution is finally derived from H∞ performance and robust stability. Simulations on frequency responses and road excitations are implemented to verify and evaluate the performance of the designed controller; results show that the active suspension with a developed H∞ controller can effectively achieve better ride comfort and road-holding ability compared with passive suspension despite the existence of control constraints and parameter variations.

Sliding mode control for uncertain active vehicle suspension systems: an event-triggered $$\varvec{\mathcal {H}}_{\infty }$$ control scheme

This paper considers the event-triggered sliding mode control problem of uncertain active vehicle suspension systems. A more comprehensive polytope approach is employed to model the uncertainties which generally exist in the sprung and unsprung masses. Moreover, the corresponding mathematical model is constructed for the quarter-vehicle active suspension system. Meanwhile, the event-triggered transmission mechanism is taken into account to schedule communication and save bandwidth. The main purpose of this paper is to develop a proper sliding mode controller which can guarantee the asymptotic stability and $$\mathcal {H}_{\infty }$$ performance for the suspension system with some constraints. By means of convex optimization technique, some sufficient conditions are derived to assure the constructed event-triggered sliding mode control law can not only ensure the corresponding sliding mode dynamics are asymptotically stable but also the predefined switching surface is reachable. Finally, the feasibility of the designed method is verified by a simulation example.

Fuzzy Adaptive Control for Nonlinear Suspension Systems Based on a Bioinspired Reference Model With Deliberately Designed Nonlinear Damping

This paper proposes a bioinspired reference model based fuzzy adaptive tracking control for active suspension systems. A general bioinspired nonlinear structure, which can present ideal nonlinear quasi-zero stiffness for vibration isolation, is adopted as tracking reference model. Fuzzy logic systems are used to approximate unknown nonlinear terms in nonlinear suspension systems. Particularly, a nonlinear damping is designed to improve damping characteristics of the bioinspired reference model. With beneficial nonlinear stiffness and improved nonlinear damping of the bioinspired reference model, the proposed fuzzy adaptive controller can effectively suppress vibration of suspension systems with less actuator force and much improved ride comfort, thus energy saving performance can be achieved. Finally, a quarter-vehicle active suspension system with considering payload uncertainties, general disturbance, and actuator saturation is provided for evaluating the validity and superiority of the bioinspired nonlinear dynamics based fuzzy adaptive control approach proposed in this paper.

Observer-based control for active suspension system with time-varying delay and uncertainty

Time-varying input delay of actuators, uncertainty of model parameters, and input and output disturbances are important issues in the research on active suspension system of vehicle. In this article, a design methodology involving state observer and observer-based dynamic output-feedback [Formula: see text] controller considering the above four factors simultaneously is put forward for active suspension system. First, the dynamics equations of active suspension system with time-varying delay are established according to its structure and principle, and its state equations, state observer, and observer-based controller considering time-varying delay, uncertainty of model parameters, and input and output disturbances are given separately. Second, the observer-based controller for quarter-vehicle active suspension system is designed in terms of the linear matrix inequality and the Lyapunov–Krasovskii functional, and the design problem of observer-based controller is converted into the solving problem of linear matrix inequalities. Finally, the gain matrix of observer and the gain matrix of controller are obtained by means of the developed controller and the model parameters of active suspension system; the MATLAB/Simulink model of this system is established; and three numerical simulation cases are given to show the effectiveness of the proposed scheme.

Minimal learning parameters-based adaptive neural control for vehicle active suspensions with input saturation

In this paper, a neural network (NN) control method is developed for nonlinear quarter vehicle active suspension systems (VASSs) which have the features of parameter uncertainties, input saturation and road disturbance, whose aim is to ensure safe driving and improve the ride comfort. The NNs are employed to approximate unkown nonlinear functions that the forming reason is uncertainties by caused varied sprung mass. When the output of actuator goes beyond its maximums, an NN control scheme combined with anti-saturation is proposed to handle this problem. Furthermore, an NN controller with the minimal learning parameters is constructed to ensure that the number of adaptive learning parameters and the burden computation are largely reduced for VASSs. Meanwhile, the control objectives of VASSs are proved based on the stability analysis. Finally, the effectiveness of designed scheme is demonstrated by an example.

An Active Vehicle Suspension Control Approach with Electromagnetic and Hydraulic Actuators

An active vibration control approach from an online estimation perspective of unavailable feedback signals for a quarter-vehicle suspension system is introduced. The application of a new signal differentiation technique for the online estimation of disturbance trajectories due to irregular road surfaces and velocity state variables is described. It is assumed that position measurements are only available for active disturbance suppression control implementation. Real-time signal differentiation is independent of detailed mathematical models of specific dynamic systems and control force generation mechanisms. Active control forces can be supplied by electromagnetic or hydraulic actuators. Analytical and simulation results prove the effective and fast dynamic performance of the online signal estimation as well as a satisfactory active disturbance attenuation on a quarter-vehicle active suspension system.

Static output feedback H∞ control for active suspension system with input delay and parameter uncertainty

This article focuses on static output feedback [Formula: see text] control for active suspension system with input delay and parameter uncertainty. The parameter uncertainty of active suspension system model, input delay of actuator, input disturbance of road, and measurement output disturbance are simultaneously introduced in active suspension system. A kind of static output feedback [Formula: see text] controller is designed, which can consider the above factors, simultaneously. First of all, the mathematical model of quarter-vehicle active suspension system and the system state equation are established. Second, the static output feedback [Formula: see text] controller is designed by employing the Lyapunov–Krasovskii functional for system state equations without or with disturbance. The design problem of static output feedback [Formula: see text] controller for closed-loop system is transformed into the solving problem of linear matrix inequality. Finally, according to the designed controller and the specific vehicle parameters, the simulation model of quarter-vehicle active suspension system is established. And the simulations of three cases, for example, without disturbance, only with input disturbance, and with input disturbance and output disturbance, are exploited to demonstrate the feasibility and effectiveness of the proposed schemes.

Finite frequency fuzzy H control for uncertain active suspension systems with sensor failure

This paper investigates the problem of finite frequency fuzzy H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for uncertain active vehicle suspension systems, in which sensor failure is taken into account. TakagiSugeno (T-S) fuzzy model is established for considered suspension systems. In order to describe the sensor fault effectively, a corresponding model is introduced. A vital performance index, H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance, is utilized to measure the drive comfort. In the framework of Kalman-Yakubovich-Popov theory, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm from external perturbation to controlled output is optimized effectively in the frequency domain of 4Hz-8 Hz to enhance ride comfort level. Meanwhile, three suspension constrained requirements, i.e., ride comfort level, manipulation stability, suspension deflection are also guaranteed. Furthermore, sufficient conditions are developed to design a fuzzy controller to guarantee the desired performance of active suspension systems. Finally, the proposed control scheme is applied to a quarter-vehicle active suspension, and simulation results are given to illustrate the effectiveness of the proposed approach.

Exponential stabilization for fuzzy sampled-data system based on a unified framework and its application

This article deals with the exponential stabilization problems of Takagi–Sugeno (T–S) fuzzy system under aperiodic sampling. The objective is to solve the H∞, L2−L∞, passive and dissipative stability and stabilization problems based on a unified performance index-extended dissipativity. Some new stability conditions consisting of both exponential stability and extended dissipativity criterion are first established. A sampling period dependent Lyapunov–Krasovskii function together with a novel efficient integral inequality, which has the advantage of reducing conservativeness, is adopted. On the basis of the stability conditions, a sampled-data controller that can not only exponentially stabilize the system but also guarantee the prescribed extended-dissipativity performance is then designed. Moreover, an exponential decay rate can be set in advance to achieve better system performance. Finally, a quarter-vehicle active suspension system with considering payload uncertainties and aperiodic sampling is provided for evaluating the validity and superiority of the extended dissipative control approach proposed in this article.

Recent Developments on Time-Delay Neural Networks

Over the past several decades, an amount of attention has been devoted to neural networks, which have wide applications in many areas, such as signal processing, pattern recognition, and combinatorial optimization. On the other hand, time delays occur in electronic implementation of analog neural networks because of the transmission of signal and the finite switching speed of amplifiers and can lead to the instability and poor performance of systems; thus neural networks with time delay have also been studied extensively because numerous interesting results have been obtained over the last decade, including stability analysis, state estimation, and passivity. In this special issue, we have accepted seven papers. The paper titled “New Pinning Synchronization of Complex Networks with Time-Varying Coupling Strength, NonDelayed and Delayed Coupling” by G. Wang et al. studies the pinning synchronization problem for a class of complex networks by a stochastic viewpoint, in which both time-varying coupling strength and nondelayed and delayed coupling are included. The paper titled “A Novel Model of Conforming Delaunay Triangulation for Sensor Network Configuration” by Y. Ma et al. proposes a new method for solvingDelaunayTriangulation problem,which is called endpoint triangle’s circumcircle model (ETCM).The paper titled “Multimodel Modeling and Predictive Control for DirectDrive Wind Turbine with Permanent Magnet Synchronous Generator” by L. Wang et al. establishes a method based on multimodel modeling and predictive control is proposed for the optimal operation of direct-drive wind turbine with permanent magnet synchronous generator. The paper titled “Independent Component Analysis Based on Information Bottleneck” by Q. Ke et al. provides the equivalence of two algorithms of independent component analysis (ICA) based on the information bottleneck (IB). In “Nonlinear Time-Delay Suspension Adaptive Neural Network Active Control” by Y. Zhu and S. Zhu, a quarter-vehicle magnetorheological active suspension nonlinear model with time delay is established, and an adaptive neural network structure for magnetorheological active suspension is presented. The paper titled “An Adaptive Regulator for Space Teleoperation System in Task Space” by C. Ge et al. studies the problem of the gravity information for bilateral teleoperation. The paper titled “Robust Stabilization of Linear Switching Systems with both Input and Communication Delays” by L. Jia and Z. Sheng considers the stabilization control of a class of linear switching systems with time delays in both the input and the communication channels.

Optimal Vibration Control for Vehicle Active Suspension Discrete‐Time Systems with Actuator Time Delay

This study researches the vibration control approach for vehicle active suspension discrete‐time systems with actuator time delay under road disturbances. First, the discrete‐time models for the quarter vehicle active suspension system with actuator time delay are presented, and road disturbances are considered as the output of an exosystem. By introducing a discrete variable transformation, the discrete‐time system with actuator time delay and the quadratic performance index are transformed into equivalent ones without the explicit appearance of time delays. Then, the problem of original vibration control with actuator time delay is transformed into the optimal vibration control for a non‐delayed system with respect to the transformed performance index. Based on the maximum principle, the feedforward and feedback optimal vibration control law is obtained from Riccati and Stein equations. The existence and uniqueness of the optimal control law is proved. A reduced‐order observer is constructed to solve the physically realizable problem of the feedforward compensator. Finally, the feasibility and effectiveness of the proposed approaches are validated by a numerical example.

Design of a genetic-algorithm-based self-tuning sliding fuzzy controller for an active suspension system

Due to the fixed damping coefficient of the passive suspension system, it is difficult to enhance ride comfort and driving quality. An active suspension system provides extra force through the actuator which allows it to effectively isolate energy from vibrations and improve passenger comfort. This paper investigates ride comfort of a quarter-vehicle active suspension system according to the ISO 2631-1 standard. Using feedback information about the sprung mass acceleration, unsprung mass acceleration, and suspension deflection, an extended Kalman filter is developed to estimate the six unknown state variables: the sprung mass displacement and velocity; unsprung mass displacement and velocity; actuating force; and spool valve displacement. In addition, the road surface irregularities are also estimated. As compared to conventional controllers, the hydraulic actuator has time-varying, uncertain, and highly non-linear characteristics; thus, this paper applies a genetic-algorithm-based self-tuning sliding fuzzy controller and feedback linearization technique to design the actuating force. Simulation results are presented that show that the proposed controller demonstrates significant improvements in the vibration suppression of the vehicle body and ride comfort compared to a linear quadratic Gaussian controller design.