Quarter Car Semi-active Suspension Research Articles

Online optimal tuning of fuzzy PID controller using grey wolf optimizer for quarter car semi-active suspension system

In order to reduce vibration and increase ride comfort, this article utilizes a system of quarter-car suspension integrated with a Fuzzy PID controller. To build and improve the Fuzzy PID controller for the semi-active suspension system used in quarter cars, using a novel meta-heuristic technique known as Grey Wolf Optimizer (GWO). Here the magnetorheological damper (MR) fluid with the Fuzzy PID controller was examined to optimize using the GWO algorithm. With the GWO technique and the integral of time absolute error (IAE) as a fitness function, the three gain parameters of the Fuzzy PID controller – Kp, Ki, and Kd– have been optimally set. The suggested approach has additional advantages for the optimization of functions with three variables, including simplicity in implementation, quick convergence traits, and superior computational capabilities. This work is significant, to the best of the author’s knowledge there is no optimization method using GWO to online tune a Fuzzy PID controller for a semi-active suspension system. The optimal output parameters of the controller can be updated online in real-time by GWO. The performance of the proposed controller was examined by assessing the root mean square (RMS) values and peak-to-peak (PTP) values of body displacement and body acceleration under various road profiles. To ensure that the intelligent controller was of the highest caliber, an online test rig was constructed. Results from simulations and online experiments demonstrated that the Fuzzy GWO PID controller significantly improved ride comfort under a variety of road conditions when compared to the Fuzzy PID controller and passive suspension system.

Optimal Control Method of Semi-Active Suspension System and Processor-in-the-Loop Verification

This study presents an implementation of a proportional–integral–derivative (PID) controller utilizing particle swarm optimization (PSO) to enhance the compromise on road holding and ride comfort of a quarter car semi-active suspension system (SASS) through simulation and experimental study. The proposed controller is verified with a processor-in-the-loop (PIL) approach before real-time suspension tests. Using experimental data, the magnetorheological damper (MR) is modeled by an artificial neural network (ANN). A series of experiments are applied to the system for three distinct bump disturbances. The algorithm performance is evaluated by various key metrics, such as suspension deflection, sprung mass displacement, and sprung mass acceleration for simulation. The phase plane method is used to prove the stability of the system. The experimental results reveal that the proposed controller for the SASS significantly improves road holding and ride comfort simultaneously.

Observer-based robust gain-scheduled control for semi-active air suspension systems subject to uncertainties and external disturbance

In this paper, an observer-based robust gain-scheduled control scheme is designed for a semi-active air suspension (SAAS) system subject to uncertainties and external disturbance. Since the air spring in SAAS system is a highly nonlinear component and its stiffness relies on the spring interior pressure and displacement, an air spring model is constructed based on aerothermodynamics theory. Aiming at comprehensive and simplified expression of air spring nonlinear dynamics, the air spring model is expressed as linear-parameter-varying (LPV) form and further integrated into a quarter car semi-active air suspension model. To identify system states under the noisy condition with lower cost, a LPV-Kalman filter is proposed to estimate the states which are difficult to be measured or physically unmeasurable in the semi-active air suspension. With the proposed observer, a robust gain-scheduled controller is developed to overcome complex nonlinear dynamics, actuator uncertainties and external disturbance. To realize a better transient response, the control law is improved by constraining eigenvalues of the closed-loop system in desired linear matrix inequality (LMI) region. At last, simulations and experiments are conducted to illustrate the effectiveness of proposed control scheme in a quarter car test rig.

Reinforcement-Learning-Based Vibration Control for a Vehicle Semi-Active Suspension System via the PPO Approach

The vehicle semi-active suspension system plays an important role in improving the driving safety and ride comfort by adjusting the coefficients of the damping and spring. The main contribution of this paper is the proposal of a PPO-based vibration control strategy for a vehicle semi-active suspension system, in which the designed reward function realizes the dynamic adjustment according to the road condition changes. More specifically, for the different suspension performances caused by different road conditions, the three performances of the suspension system, body acceleration, suspension deflection, and dynamic tire load, were taken as the state space of the PPO algorithm, and the reward value was set according to the numerical results of the passive suspension, so that the corresponding damping force was selected as the action space, and the weight matrix of the reward function was dynamically adjusted according to different road conditions, so that the agent could have a better improvement effect at different speeds and road conditions. In this paper, a quarter–car semi-active suspension model was analyzed and simulated, and numerical simulations were performed using stochastic road excitation for different classes of roads, vehicle models, and continuously changing road conditions. The simulation results showed that the body acceleration was reduced by 46.93% under the continuously changing road, which proved that the control strategy could effectively improve the performance of semi-active suspension by combining the dynamic changes of the road with the reward function.

Hybrid Modelling and Sliding Mode Control of Semi-Active Suspension Systems for Both Ride Comfort and Road-Holding

Rigorous model-based design and control for intelligent vehicle suspension systems play an important role in providing better driving characteristics such as passenger comfort and road-holding capability. This paper investigates a new technique for modelling, simulation and control of semi-active suspension systems supporting both ride comfort and road-holding driving characteristics and implements the technique in accordance with the functional mock-up interface standard FMI 2.0. Firstly, we provide a control-oriented hybrid model of a quarter car semi-active suspension system. The resulting quarter car hybrid model is used to develop a sliding mode controller that supports both ride comfort and road-holding capability. Both the hybrid model and controller are then implemented conforming to the functional mock-up interface standard FMI 2.0. The aim of the FMI-based implementation is to serve as a portable test bench for control applications of vehicle suspension systems. It fully supports the exchange of the suspension system components as functional mock-up units (FMUs) among different modelling and simulation platforms, which allows re-usability and facilitates the interoperation and integration of the suspension system components with embedded software components. The concepts are validated with simulation results throughout the paper.

Performance Investigation of Integrated Model of Quarter Car Semi-Active Seat Suspension with Human Model

In this paper, an integrated model of a semi-active seat suspension with a human model over a quarter is presented. The proposed eight-degrees of freedom (8-DOF) integrated model consists of 2-DOF for the quarter car model, 2-DOF for the semi-active seat suspension and 4-DOF for the human model. A magneto-rheological (MR) damper is implemented for the seat suspension. The fuzzy logic-based self-tuning (FLST) proportional–integral–derivative (PID) controller allows to regulate the controlled force on the basis of sprung mass velocity error and its derivative as input. The controlled force is tracked by the Heaviside step function which determines the supply voltage for the MR damper. The performance of the proposed integrated model is analysed, in-terms of human head accelerations, for several road profiles and at different speeds. The performance of the semi-active seat suspension is compared with the traditional passive seat suspension to validate the effectiveness of the proposed integrated model with a semi-active seat suspension. The simulation results show that the semi-active seat suspension improves the ride comfort significantly by reducing the head acceleration effectively compared to the passive seat suspension.

Performance Investigation of H∞ Controller for Quarter Car Semi-active Suspension System Using Simulink

This paper affords the design and improvement of a semi-active suspension system for an automobile. The main idea is to increase the semi-active suspension system damping vibration of the automobile body even as crossing the bump and sine pavement on the road. This system is modelled for 1 / 4 car system after which the entire system has been simulated using Mat lab/Simulink. It is used to physically simulate the quarter vehicle system of the automobile and have a look at the time domain response to the road disturbances. H infinity controllers is used to govern the damping properties of the semi-active suspension system mechanically. The system is designed in contrast to the most of the available suspension systems using a third order hydraulic actuator. The proposed system is compared with H2 optimal controller to test the performance of the system for the control targets suspension deflection, body acceleration and body travel for the bump and sine road disturbances. The simulation result of this studies reveal the efficiency of the advanced H∞ controller for the quarter car semi-active suspension system. Keywords : Quarter Car Semi-active Suspension System, H∞ Controller, H2 optimal Controller DOI: 10.7176/CTI/9-02 Publication date: April 30 th 2020

Performance Investigation of H∞ Controller for Quarter Car Semi-active Suspension System Using Simulink

This paper affords the design and improvement of a semi-active suspension system for an automobile. The main idea is to increase the semi-active suspension system damping vibration of the automobile body even as crossing the bump and sine pavement on the road. This system is modelled for 1 / 4 car system after which the entire system has been simulated using Mat lab/Simulink. It is used to physically simulate the quarter vehicle system of the automobile and have a look at the time domain response to the road disturbances. H infinity controllers is used to govern the damping properties of the semi-active suspension system mechanically. The system is designed in contrast to the most of the available suspension systems using a third order hydraulic actuator. The proposed system is compared with H2 optimal controller to test the performance of the system for the control targets suspension deflection, body acceleration and body travel for the bump and sine road disturbances. The simulation result of this studies reveal the efficiency of the advanced H∞ controller for the quarter car semi-active suspension system. Keywords — Quarter Car Semi-active Suspension System, H∞ Controller, H2 optimal Controller DOI: 10.7176/JIEA/10-2-02 Publication date: March 31 st 2020

Differential Flatness Based LQR Control of a Magnetorheological Damper in a Quarter Car Semi-active Suspension System

Differential Flatness Based LQR Control of a Magnetorheological Damper in a Quarter Car Semi-active Suspension System

Enhancing the Closed Loop Performance of Semi-active Suspension System with I-PD Controller

This paper aims to investigate for the control quarter car semi-active suspension system using PID controller. In the study, simulation and transfer function models are constructed and used for the control of relative displacement of semi-active suspension system. The conventional PID controller is designed by using Ziegler-Nichols method and it used for the control of suspension system. The closed loop performance of PID controller is improved through reducing the derivative gain value. It shows that, the peak overshoot of closed loop responses are sluggishly reduced. The modified forms PID controller such as PI-D and I-PD controllers are furthermore used for the control of suspension system. From the results, the I-PD controller deliver better closed loop performance compared with PID and PI-D controllers. The control of suspension system using I-PD controller provide superior closed loop performance by means of minimization of peak overshoot and settling time.

Modified active disturbance rejection control for non-linear semi-active vehicle suspension with magneto-rheological damper

This paper presents a novel idea processing the complex non-linear dynamics of a magneto-rheological (MR) damper and the external road disturbance based on the linear extended state observer (LESO) technology, and further verifies its reasonability by application of linear active disturbance rejection control (LADRC) in the quarter-car non-linear semi-active suspension system. In order to optimize the body acceleration and dynamic tyre load to improve the ride comfort and road-handling ability, a modified active disturbance rejection control, the double linear active disturbance rejection control (DLADRC), is further proposed based on the idea of the hybrid skyhook–groundhook control strategy. LESO is used to estimate the total disturbance including the external road disturbance and the internal non-linear dynamic of the MR damper. For effectiveness validation of the proposed control scheme, comparison results with the existing linear quadratic regulation (LQR) control, hybrid skyhook–groundhook control and adaptive control strategies are presented for the same quarter-car semi-active suspension. It is shown from the simulation comparisons among these several control strategies that the semi-active suspension system with DLADRC has a better control performance on the ride comfort and road-handling ability corresponding to the body acceleration and dynamic tyre load.

Parametric Study on Proportional Integral Derivative Controlled Semi-Active Suspension System

This paper presents the effect of the suspension working space, body displacement, body acceleration and wheel displacement for the non-controlled suspension system (passive system) and the controlled suspension system of a quarter car model (semi-active system), and comparison between them. The quarter car passive and semi-active suspension systems are modelled using Simulink. Proportional Integral Derivative controllers are incorporated in the design scheme of semi-active models. In the experimental work, the influence of switchable damper in a suspension system is compared with the passive and semi-active suspension systems.

Influence of Fuzzy-PID Controller on Semi-Active Suspension System Performance Using Magnetorheological Damper Fuzzy Model

Semi-active suspension system is a promising device to improve performance of the suspension system by using optimal controller for magnetorheological damper. The importance of magnetorheological damper is the capability to control the semi-active suspension system by adjusting the input current exerted to the coil of wire to produce magnetic field. In this paper, a fuzzy-PID controller has been applied in a quarter car semi-active suspension system to examine the performance of the system. The whole suspension system is modelled in Simulink environment/MATLAB software in which a neuro-fuzzy model of magnetorheological damper is utilized as a mathematical model of the damper. A disturbance profile is utilized to evaluate performance of the system. Simulation results show that the proposed semi-active suspension system has successfully absorbed disturbances much better than PID controller. In addition, the accuracy of the magnetorheological damper model influences the performance of the semi-active suspension system.

LQR Control for Semi-Active Quarter Vehicle Suspension with Magnetorhehological Damper and Bouc-Wen Model

This paper discuss the problem of controlling quarter-car semi-active suspension system. Presently, the suspension system involves a magnetorheological (MR) damper with a hysteretic behavior captured through the Bouc-Wen model. This device can be integrated in the electric or hybrid electric vehicle. The control objective is to regulate well the chassis vertical position despite the road irregularities. In addition to these irregularities, the difficulty of the control problem lies in the nonlinearity of the system model and the inaccessibility to measurements of the hysteresis internal state variable. The control design is performed using the LQR theory and Lyapunov control design tools; it includes an observer providing online estimates of the hysteresis internal state. The controller is formally shown to meet the desired control objectives. This theoretical result is confirmed by several simulations. The latter illustrate the performances of the LQR method and compare them with those of the passive suspension.

Modeling, Simulation and Control of Semi Active Suspension System for Automobiles under MATLAB Simulink using PID Controller

Abstract This paper aims to investigate the performance of a quarter car semi-active suspension system using PID controller under MATLAB Simulink Model. Dynamic system used in this study is a linear system. A linear system can capture basic performances of vehicle suspension such as body displacement, body acceleration, wheel displacement, wheel deflection, suspension travels. Performance of suspension system is determined by the ride comfort and vehicle handling. It can be measured by car body displacement and wheel deflection performance. Two types of road profiles are used as input for the system. Results show that the performance of body displacement and wheel displacement can be improved by using the proposed PID controller.

A Research on Simulation for Semi-Active Suspension Control Based on Immune Algorithm

Based on two-degrees-of-freedom (2-DOFs) quarter-car semi-active suspension model, a method for semi-active suspension control is proposed based on immune algorithm. According to this algorithm, an immune controller is designed to research and simulation for semi-active suspension control. Simulation results show that the proposed algorithm is effective，and compared with the passive suspension and fuzzy logic control (FLC) algorithm, its control capability is the best. Using immune controller, the RMS of body vertical acceleration, tire loads and suspension distortion are significantly reduced, so vehicle ride performance, handling stability are effectively improved.

Design of Vehicle Semi-Active Suspension System Control Unit

This paper researches on embedded system design based on MC9s12Dp256 microcontroller for vehicle semi-active suspension. The hardware design of suspension control unit (SCU) is introduced. The integrated control strategy which integrates Skyhook and MiniMax strategies is proposed. The hardware-in-the-loop simulation (HILS) test on a two-degree-of-freedom quarter car semi-active suspension system model is carried out. The functions of SUC are verified and the performance of passive suspension and semi-active suspension is compared. The simulation results indicate that the performance of SCU achieves design requirement. In comparison with passive system, the control effect of integrated control strategy can be improved in ride comfort and drive safety.

Constrained optimal control: an application to semiactive suspension systems

This article applies three different control techniques to the design of a quarter-car semiactive suspension system. The three techniques, originally developed to solve a constrained optimal control problem, are optimal gain switching, discontinuous variable structure control and explicit model predictive control. All of them divide the state space into convex regions and assign a linear or affine state feedback controller to each region. The partition of the state space is computed off-line. During the on-line phase, the controller switches between the subcontrollers according to the current state. All the above techniques gave satisfactory results when applied to the design of semiactive suspension systems. A detailed comparison in terms of computational complexity, performance and simplicity of the design is proposed in the article.

Analysis of the explicit model predictive control for semi-active suspension

Explicit model predictive control (MPC) enhances application of MPC to areas where the fast online computation of the control signal is crucial, such as in aircraft or vehicle control. Explicit MPC controllers consist of several affine feedback gains, each of them valid over a polyhedral region of the state space. In this paper the optimal control of the quarter car semi-active suspension is studied. After a detailed theoretical introduction to the modeling, clipped LQ control and explicit MPC, the article demonstrates that there may exist regions where constrained MPC/explicit MPC has no feasible solution. To overcome this problem the use of soft constraints and combined clipped LQ/MPC methods are suggested. The paper also shows that the clipped optimal LQ solution equals to the MPC with horizon N=1 for the whole union of explicit MPC regions. We study the explicit MPC of the semi-active suspension with actual discrete time observer connected to the explicit MPC in order to increase its practical applicabili ty. The controller requires only measurement of the suspension deflection. Performance of the derived controller is evaluated through simulations where shock tests and white noise velocity disturbances are applied to a real quarter car vertical model. Comparing MPC and the clipped LQ approach, no essential improvement was detected in the control behavior.

Hybrid model predictive control application towards optimal semi-active suspension

The optimal control problem of a quarter-car semi-active suspension has been studied in the past. Considering that a quarter-car semi-active suspension can either be modelled as a linear system with state dependent constraint on control (of actuator force) input, or a bi-linear system with a control (of variable damping coefficient) saturation, the seemingly simple problem poses several interesting questions and challenges. Does the saturated version of the optimal control law derived from the corresponding un-constrained system, i.e. “clipped-optimal”, remain optimal for the constrained case as suggested in some previous publications? Or should the optimal deviate from the “clipped-optimal” as suggested in other publications? If the optimal control law of the constrained system does deviate from its unconstrained counter-part, how different are they? What is the structure of the optimal control law? Does it retain the linear state feedback form (as the unconstrained case)? In this paper, we attempt to answer some of the above questions by utilizing the recent development in model predictive control (MPC) of hybrid dynamical systems. The constrained quarter-car semi-active suspension is modelled as a switching affine system, where the switching is determined by the activation of passivity constraints, force saturation, and maximum power dissipation limits. Theoretically, over an infinite prediction horizon the MPC controller corresponds to the exact optimal controller. The performance of different finite-horizon hybrid MPC controllers is tested in simulation using mixed-integer quadratic programming. Then, for short-horizon MPC controllers, we derive the explicit optimal control law and show that the optimal control is piecewise affine in state. In the process, we show that for horizon equal to one the explicit MPC control law corresponds to clipped LQR as expected. We also compare the derived optimal control law to various semi-active control laws in the literature including the well-known “clipped-optimal”. We evaluate their corresponding performances for both a deterministic shock input case and a stochastic random disturbances case through simulations.