Quarter-car Active Suspension Research Articles

Fully Distributed Hierarchical ET Intrusion-and Fault-Tolerant Group Control for MASs With Application to Robotic Manipulators

This paper studies group synchronization tracking problem for a class of high-order multi-agent systems (MASs) with nonidentical and unknown direction faults (NUDFs) under multiple cyber attacks (i.e., denial-of-service (DoS) attacks and false data injection attacks (FDIAs)). Be motivated by this, a fully distributed hierarchical (cyber layer and physical layer) Zeno-free event-triggered (ET) intrusion-and fault-tolerant controller is presented based on Nussbaum-type gain technique, where a positive inter-event time exists in the state-dependent asynchronous ET mechanism (ETM). The constructed virtual cyber layer realizes the interaction among different agents so as to avoid the interaction in physical processes and thus reduce the error propagation. This two layer controller greatly increase the flexibility of the controller design compared with single-layer control strategies. In addition, a novel Nussbaum function stability lemma (Lemma lem4lem4) is developed for the first time. Based on this lemma, the fully distributed adaptive controller can adjust the direction of the input to match the fault direction with the help of Nussbaum function. Finally, a robotic manipulator example demonstrates the effectiveness and merit of the proposed control scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In industrial processes, NUDFs and cyber attacks often occur in many different systems, which usually lead to performance degradation or even serious accidents. Typically, NUDFs affect the performance of chemical and industrial processes, circuits, and sensors. Meanwhile, in driverless vehicle platoon, attackers change the control signal through the wireless network, and then issue emergency braking commands, etc. Therefore, this paper designs a fully distributed hierarchical ET intrusion-and fault-tolerant scheme for high-order MASs that are usually used to model ship dynamics, robotic manipulators, and quarter-car active suspension. The control scheme gives solutions to the problem of NUDFs, multiple cyber attacks, and network bandwidth limitations at different layers, and effectively integrates the physical and cyber layers to achieve group synchronization. Meanwhile, a new event-triggered mechanism under the framework of group synchronization is developed to save communication resources. Robotic manipulator simulation studies verify the validity of the proposed scheme.

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

Control of Quarter-Car Active Suspension System Based on Optimized Fuzzy Linear Quadratic Regulator Control Method

Vehicle suspension systems, which affect driving performance and passenger comfort, are actively researched with the development of technology and the insufficient quality of passive suspension systems. This paper establishes the suspension model of a quarter of the car and active control is realized. The suspension model was created using the Lagrange–Euler method. LQR, fuzzy logic control (FLC), and fuzzy-LQR control algorithms were developed and applied to the suspension system for active control. The purpose of these controllers is to improve car handling and passenger comfort. Undesirable vibrations occur in passive suspension systems. These vibrations should be reduced using the proposed control methods and a robust system should be developed. To enhance the performance of the fuzzy logic control (FLC) and fuzzy-LQR control methods, the optimal values of the coefficients of the points where the feet of the member functions touch are calculated using the particle swarm optimization (PSO) algorithm. Then, the designed controllers were simulated in the computer environment. The success of the control performance of the applied methods concerning the passive suspension system was compared in percentages. The results are presented and evaluated graphically and numerically. Using the integral time-weighted absolute error (ITAE) criterion, the methods were compared with each other and with the studies in the literature. As a result, it was found that the proposed control method (fuzzy-LQR) is about 84.2% more successful in body motion, 90% in car acceleration, 84.5% in suspension deflection, and 86.7% in tire deflection compared to the studies in the literature. All these results show that the car’s ride comfort has been significantly improved.

Hybrid Particle Swarm Optimization Genetic LQR Controller for Active Suspension

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

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.

Design and implementation of passivity-based controller for active suspension system using port-Hamiltonian observer

The objective of this study is to design and implement an observer for quarter-car active suspension system in Port-Hamiltonian form. A novel state observer is designed for active suspension system modelled in port-Hamiltonian form to estimate the states in presence of road disturbances. The observer is designed considering suspension deflection alone as the output, which is an easily measurable output. Performance of the proposed observer is evaluated experimentally with road disturbance input mimicking a sudden bump and a continuously varying road input, and proven to be effective in minimising the error dynamics in presence of bounded unmodelled disturbances. To prove the effectiveness of the state-estimator, an Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) designed using the desired physical properties of the closed-loop system is implemented using the observer states. Experimental results of the controller implemented using the designed state observer show good improvement in the ride comfort, ride stability and suspension stroke of the active suspension system, which proves the effectiveness of the proposed port-Hamiltonian observer in terms of minimising the error dynamics.

Dynamic event-triggered practical stabilization of random suspension system based on immersion and invariance

This article investigates the practical stabilization problem of random quarter-car active suspension systems. An adaptive dynamic event-trigger strategy is proposed to stabilize the states of vehicle suspension in response to system uncertainty and controller area network resource constraints. Moreover, the model of random active suspension systems is extended to the general random robot systems; the controller is developed with the aid of a double dynamic surface filter, immersion and invariance (I&amp;I) techniques, and event-triggered mechanisms. The results show that the semi-global stability of error systems is achieved, and there are some improvements in triggering times and adaptive estimation performance under the control framework. Finally, simulation comparison results are provided to prove the advantages of the proposed scheme.

Active Suspension Control of Quarter-Car System With Experimental Validation

A reliable, efficient, and simple control is presented and validated for a quarter-car active suspension system equipped with an electro-hydraulic actuator. Unlike the existing techniques, this control does not use any function approximation, e.g., neural networks (NNs) or fuzzy-logic systems (FLSs), while the unmolded dynamics, including the hydraulic actuator behavior, can be accommodated effectively. Hence, the heavy computational costs and tedious parameter tuning phase can be remedied. Moreover, both the transient and steady-state suspension performance can be retained by incorporating prescribed performance functions (PPFs) into the control implementation. This guaranteed performance is particularly useful for guaranteeing the safe operation of suspension systems. Apart from theoretical studies, some practical considerations of control implementation and several parameter tuning guidelines are suggested. Experimental results based on a practical quarter-car active suspension test-rig demonstrate that this control can obtain a superior performance and has better computational efficiency over several other control methods.

Neural Network Adaptive Output-Feedback Optimal Control for Active Suspension Systems

The adaptive neural network (NN) output-feedback optimal control issue has been investigated for a quarter-car active electric suspension systems, where the suspension stiffness is unknown and partial state variables are unavailable for measurement. NNs are utilized to identify unknown nonlinearities, and an NN state observer is devised to estimate the unmeasurable states. For each backstepping step, via reinforcement learning (RL), a critic–actor architecture is designed to get the approximation solution of Hamilton–Jacobi–Bellman (HJB) equations and actual and virtual optimization controllers are designed, in which the input saturation constraint and road interference are considered. It is analytically proved that all controlled system signals remain bounded, while the power of the control input signal, as well as the amplitude of the vertical displacement, has been minimized. A comparative simulation is eventually given to elaborate the feasibility of the developed control algorithm.

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.

Control of Nonlinear Active Suspension System Based on Fuzzy Model Predictive Controller

Recent years, active suspension system has been widely used in automobiles to improve the road holding ability and the riding comfort. This article presents a new fuzzy model predictive control for a nonlinear quarter car active suspension system. A nonlinear dynamical model of active suspension is established, where the nonlinear dynamical characteristic of the spring and damper are considered. Based on the proposed fuzzy model predictive control method is presented to stabilize the displacement of the active suspension in the presence of different road profiles. Parameters of the model predictive and Fuzzy logic control laws are designed to estimate the (Bump and Sinusoidal) road profile input in the active suspension. At last, the reliability of the fuzzy model predictive control method is evaluated by the MATLAB simulation tool. Simulation result shows that the fuzzy model predictive control method obtained the satisfactory control performance for the active suspension system.

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.

Ant Colony Optimization Tuned Closed-Loop Optimal Control Intended for Vehicle Active Suspension System

In recent years, the suspension system in modern vehicles has played a key role both as far as driving safety and comfort is concerned. To satisfy these vehicle performance specifications, active suspension is currently studied and implemented in practice in recent decades. In contrast to passive suspensions, by introducing force into system, active suspension can alter the suspension dynamic in real-time. A design of a controller is needed for real-time tuning of the control force in an active suspension system (ASS) to fulfill the challenging control objectives of suspension system comprising road handling, ride convenience, and travel suspension. This research proposed a novel ant colony optimization (ACO) algorithm for solving multi-objective weight optimization problem of the linear quadratic regulator (LQR) for automobiles ASS. The optimization problem of ASS is to design a state-feedback controller (SFC) as a result ACO is used to find optimal LQR weights. Here both Q and R weight matrix of LQR is tuned. On a quarter-car ASS (QCASS) system, the effectiveness of ACO-tuned LQR is analytically checked with hardware in loop (HIL) analysis for an irregular road surface. Here, for experiment, ISO road D rough runway, bumpy path, and pulse-type road profile are taken into account. Experimental findings illustrate that the proposed procedure can substantially reduce the acceleration of the Car body due to irregular road profiles compared to classical tuned LQR and model predictive control (MPC). The proposed controller shows the profound impact on the efficiency of the control schemes for three different road profiles.

Analysis of Parameter Changes in Controlling the Quarter-car Active Suspension with PID Controller

Suspension is the part that connects the road surface and the car body, the car suspension is controlled by a control system to minimize car body vibrations caused by the road surface. In the operation of the car, there will be parameter changes that occur, among others, due to changes in the load of the car and tire pressure on the car and of course it affects the plant. The car suspension is controlled using the PID Controller simulated in the Simulink Matlab program and the parameters of the suspension are changed. With the change in suspension parameters, the results of control by the PID Controller can still control the suspension but there are differences in overshoot and settling time at the output

Combined Input–Output Finite-time Stability with H∞ Static Output-feedback Control Approach for Active Suspension

Combined input–output finite-time stability condition with static output-feedback H ∞ control is proposed in this work to effectively attenuate the short-duration road disturbance. The control problem is formulated based on the pre-defined condition of input–output finite-time stability with H ∞ bound along with pre-established quarter-car active suspension model. Then, a feasible static output-feedback controller is designed via variable substitution approach and linear matrix inequalities. Output-feedback control’s initial infeasibility issue is solved by state-feedback technique. The controller is specifically designed for the system which exposed with short-duration exogenous disturbances hence, this work prefers finite-time approach instead Lyapunov asymptotic stability condition. To enumerate the significance of the proposed controller numerical examples are presented and its response is effectively analyzed in distinct domains (time and frequency). The theoretical results denote that the combined input–output finite-time stability condition with static output-feedback H ∞ control can enhance the vehicle performance better when compared with passive and conventional static output-feedback control scheme. Additionally, the controller robustness is verified.

Barrier Function-Based Adaptive Sliding Mode Control for Application to Vehicle Suspensions

A barrier function-based adaptive sliding mode control (SMC) strategy is proposed for the vehicle active suspension system in this article. The barrier function-based adaptive law is applied to design the sliding mode controller, which can ensure the finite-time convergence of the suspension system. Meanwhile, the proposed adaptive law can achieve greatly chattering reduction without requiring the prior information of the upper bound of system uncertainties. Furthermore, the time-delay estimation technique is applied to design the simple and efficient model-free controller. Therefore, the proposed controller has the strong robustness against the nonlinearities and uncertainties of the active suspension system, and it is very practical in actual scenarios. In addition, considering the transient and steady-state performance of the active suspension system, a prescribed performance function is adopted to constrain the vehicle displacement with its convergence rate, maximum overshoot, and steady-state value. Finally, compared with the conventional SMC and PD control, comparative experiments of a quarter-car active suspension platform are performed to verify the effectiveness of the proposed strategy.

Design and comparisons of adaptive harmonic control for a quarter-car active suspension

Car suspensions have the job to keep the tires in contact with the road surface as much as possible, to deliver steering stability with good handling and to guarantee passenger comfort. Most modern vehicles have independent front suspension and many vehicles also have independent rear suspension. Independent suspensions are preferred instead of dependent suspensions for their better ride handling, stability, steering and comfort but they provide less overall strength and a complex design which increases the cost and maintenance expenses for such a suspension. For this reason, automotive engineers struggle to discover new suspension components or advanced control solutions. Taking a step forward in this direction, the paper presents in the beginning one of the well-known mathematical models of a quarter-car active suspension. The obtained model is then implemented in a MATLAB/Simulink simulation which compares multiple control solutions. The only feedback considered for each control algorithm is the measurement of the body acceleration. Among these investigated control algorithms is the adaptive harmonic control solution proposed by this paper. The controller generates a harmonic control signal with variable amplitude and frequency based on the body acceleration feedback. The comparison analysis shows that the proposed control solution demonstrates quite good potential, generating in some cases better results than the other control algorithms.

Reliable Control for Vehicle Active Suspension Systems Under Event-Triggered Scheme With Frequency Range Limitation

This paper is concerned with the problem of reliable finite frequency (FF) control for a cloud-aided active quarter-car vehicle suspension system subject to actuator failure. Instead of considering the entire frequency domain, we study the FF control which could restrain the external vibration input more effectively in the concerned frequency domain. In order to improve network bandwidth utilization, an adaptive hybrid event-triggered scheme is proposed for the cloud-aided quarter-car suspension framework. A fault-tolerant controller is designed with considering the communication time-delay and event-triggered mechanism. The adaptive event-triggered condition and the reliable controller are co-designed. Finally, a quarter-car active suspension model is studied to illustrate the efficient performances of the designed controller and the proposed event-triggered scheme.

Parameter-dependent actuator fault estimation for vehicle active suspension systems based on RBFNN

The actuator fault estimation (FE) problem is addressed in this study for the quarter-car active suspension system (ASS) with consideration of the sprung mass variation. Firstly, the ASS is modeled as a parameter-dependent system with actuator fault and external disturbance input. Then, a parameter-dependent FE observer is designed by using the radial basis function neural network (RBFNN) to approximate the actuator fault. In addition, the design conditions are turned into a linear matrix inequality (LMI) problem which can be easily solved with the aid of LMI toolbox. Finally, simulation and comparison results are given to show the accuracy and rapidity of the proposed FE method, as well as good adaptability against the sprung mass variation. Moreover, a simple FE-based active fault-tolerant control (AFTC) strategy is provided to further demonstrate the effectiveness and applicability of the proposed FE method.

Integral Sliding Mode Control Design for a Quarter-Car Active Suspension System

This paper utilizes the design of a robust integral sliding mode control (ISMC) for a quarter-car active suspension system. The main goal is to increase the ride comfort, whilst the road holding and rattle space remain within the safety bound. According to ISMC, the system state starts at the switch surface where the system nonlinearity, parameter changes, and road disturbances are rejected by a discontinuous control term present strongly in the suspension dynamics. This feature allows the design of a continuous controller, i.e. ideal controller during sliding motion from the first instant. Consequently, the car body is isolated from the wheel unit to perform the desired suspension requirements characteristics. The ISMC shows a high robustness control design of the suspension system, and can suppress chattering in the high-frequency band. The effectiveness of the proposed controller is performed by simulating the 2- DOF quarter car system with controlled and uncontrolled cases. The Matlab 2019a software is used to simulate the suspension models with bump road profiles as excitation disturbance.