Quarter-car Suspension Research Articles

Design and evaluation of self-tuning optimal control for vibration suppression of magnetorheological semi-active suspension

The objective of this paper is to enhance the vibration damping capabilities of magnetorheological (MR) semi-active suspension by utilizing a self-tuning LQG control method. Firstly, to determine the mechanical model of MR damper using the hyperbolic tangent model, mechanical experiments were performed with a damping force test machine under various input excitations. Experimental and simulation data were compared to confirm the accuracy of the mechanical model for MR damper. The MR damper is then incorporated into the vehicle’s semi-active suspension system to create a quarter-car suspension model. In order to tackle the problems associated with low control accuracy and poor dynamic adjustment in traditional LQG controllers where the weighting matrix coefficients are difficult to determine, a self-tuning LQG controller based on gravity search algorithm (GSA-LQG) was designed. Finally, the designed controller performance was evaluated by the simulation and experimental results obtained from the random and sinusoidal excitation roads. Experimental data reveal that when subjected to GSA-LQG control, the suspension control performance is considerably enhanced compared to the passive control, PID control and conventional LQG control suspension. Based on these outcome, it can be concluded that the proposed algorithm is effective and the experimental platform is feasible.

Adaptive Control for Suspension System of In-Wheel Motor Vehicle with Magnetorheological Damper

This study proposes two adaptive controllers and applies them to the vibration control of an in-wheel motor vehicle’s (electric vehicle) suspension system, in which a semi-active magnetorheological (MR) damper is installed as an actuator. As a suspension model, a nonlinear quarter car is used, providing greater practical feasibility than linear models. In the synthesis of the controller design, the values of the sprung mass, damping coefficient and suspension stiffness are treated as bounded uncertainties. To take into account the uncertainties, both direct and indirect adaptive sliding mode controllers are designed, in which the principal control parameters for the adaptation law are updated using the auto-tune method. To reflect the practical implementation of the proposed controller, only two accelerometers are used, and the rest of the state values are estimated using a Kalman observer. The designed controller is applied to a quarter car suspension model of an in-wheel motor vehicle featuring an MR damper, followed by a performance evaluation considering factors such as ride comfort and road holding. It is demonstrated in this comparative work that the proposed adaptive controllers show superior control performance to the conventional proportional–integral–derivative (PID) controller by reducing the vibration magnitude by 50% and 70% for the first and second modes, respectively. In addition, it is identified that the second mode (wheel mode) of the in-wheel motor vehicle is more sensitive than the first body mode depending on the mass ratio between the sprung and unsprung mass.

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.

The riding comfort improvement by the paralleled semi-active magnetorheological damper and passive inertance suspension from the power perspective

Extensive research demonstrates that a semi-active damper in combination with inerter-based suspension could improve the ride comfort and road-holding performance of vehicles. However, the inherent dynamics of a semi-active damper is always neglected. The underlying mechanism of the controller with inerter in different frequency ranges is not well understood. Accordingly, this paper investigated the quarter-car suspension consisting of the paralleled nonlinear hysteretic semi-active magnetorheological (MR) damper and a passive inerter. To study the influence of different strategies, the clipped optimum controlled- (COC) and the mixed skyhook power-driven damper (SKYPDD) controlled- MR damper with the inerter are both adopted and denoted as COCI and SKYPDI, respectively. The optimal inertance is selected to minimize the sprung acceleration. Since there lacks quantitative method to analyze the working mechanism of semi-active controllers, an innovative power-based criterion was proposed in this paper. The trajectory of the control force and the sprung mass velocity determines the equivalent damping ratio added to the sprung mass and the input power it receives from the unsprung mass. The sprung mass vibration is reduced by decreasing the input power or increasing the damping ratio. Under harmonic excitation, the additional inertance decreases the power input to the sprung mass in the low-frequency range and isolates the sprung mass from the forced vibration at the unsprung resonance. Under the broadband stochastic excitation, SKYPDI and COCI can effectively decrease the input power spectrum and increase the damping ratio spectrum in the dominant sprung mass resonance. A parametric study on varying stiffness ratio demonstrates the semi-active strategy takes effects mainly in the high-stiffness-ratio range where the additional inertance more evidently enhances the damping ratio, especially for COCI. In summary, this paper proposes the power-based criterion for analyzing the working mechanism of semi-active strategies in ride comfort improvement.

Equations of Motion of Mechanical Systems with Switchable Constraints

The article deals with a numerical and analytical approach to solving the equations of motion, which enables to treat the considered problems with the change of system structure or number of degrees of freedom without interrupting the numerical integration process. The described methodology allows effectively incorporate switchable constraints in the systems in accordance with their flexible structures. The crucial idea is based on the formulation of the resulting differentialalgebraic equations into a saddle point system, where the switchable constraints are represented by a sign matrix with variable rank. In connection with this property, a pseudoinversion is applied to eliminate algebraic variables and transform the problem to the first order system of ordinary differential equations. Moreover, the time independent case leads to linear autonomous systems with non-diagonalizable matrices, as is proved. The relevant numerical scheme is based on Runge-Kutta methods, that correspond to the power series of the resulting matrix exponential for time independent problems. The methodology presented is illustrated on the idealized two-mass oscillator with a switchable constraint. The numerical experiments performed range from initial stages, through simple transient cases to damped intentional control. The advanced applications can be found in robotics, active and controlled systems, and in the simulations of complex systems in biology and related areas. Moreover, the methodology can also be applied in the simulation of transport systems, especially in relation to vehicle technology, a quarter car suspension system, a vibration control mechanism, a torsion system with a clutch, and machine balancing and storage should to be highlighted.

Distributed Lebesgue Approximation Model for Distributed Continuous-Time Nonlinear Systems.

Approximation models play a crucial role in model-based methods, as they enhance both accuracy and computational efficiency. This article studies distributed and asynchronous discretized models to approach continuous-time nonlinear systems. The considered continuous-time system consists of some distributed but physically coupled nonlinear subsystems that exchange information. We propose two Lebesgue approximation models (LAMs): 1) the unconditionally triggered LAM (CT-LAM) and 2) the CT-LAM. In both approaches, a specific LAM approximates an individual subsystem. The iteration of each LAM is triggered by either itself or its neighbors. The collection of different LAMs executing asynchronously together form the approximation of the overall distributed continuous-time system. The aperiodic nature of LAMs allows for a reduction in the number of iterations in the approximation process, particularly when the system has slow dynamics. The difference between the unconditionally and CT-LAMs is that the latter checks an "importance" condition, further reducing the computational effort in individual LAMs. Furthermore, the proposed LAMs are analyzed by constructing a distributed event-triggered system which is proved to have the same state trajectories as the LAMs with linear interpolation. Through this specific event-triggered system, we derive conditions on the quantization sizes in LAMs to ensure asymptotic stability of the LAMs, boundedness of the state errors, and prevention of Zeno behavior. Finally, simulations are carried out on a quarter-car suspension system to show the advantage and efficiency of the proposed approaches.

Experimentation and Damping Performance Analysis of a MR Damper for Resonance Control in a Quarter Car Suspension System

Experimentation and Damping Performance Analysis of a MR Damper for Resonance Control in a Quarter Car Suspension System

Optimal Tuning of a LQR Controlled Active Quarter Car System Using Global Best Inertia Weight Modified Particle Swarm Optimization Algorithm

A key factor in the design of a car is the comfort and safety of its passengers. The quarter-car suspension system is a feature of the car that ensures load-carrying capacity as well as comfort and safety. It comprises links, springs, and shock absorbers (dampers). Due to its significance, several research has been conducted, to increase its road handling and holding capability while trying to keep its cost moderate. To enhance customer comfort and load carrying, the road holding capacity of an active quarter car suspension was improved/controlled in this study, using the Global Best Inertia Weight Modified Particle Swarm Optimization Algorithm. The observation of the closed loop and open loop systems after designing and simulating on MATLAB reveals a significant improvement in the closed loop system's road holding ability compared to the open loop, in that, when the system was subjected to pothole, the deflection of sprung mass reached steady state in 37.37 seconds as opposed to 7000 seconds for the open loop.

Using statistical linearization to optimize a class of semi-active on-off control in a general state space system

This paper uses statistical linearization to analyze a state space system controlled by a class of semi-active on-off control. The control input is proportional to a feedback state, while the coefficient of proportionality is switched based on the sign of the product of feedback state and a control state. The explicit simultaneous equations are derived to obtain the system's statistics. The usefulness of the approach is demonstrated through 4 examples. In the example of vibration isolation system, the analytical best performance of skyhook control is found. In the example of mass damper system, the analytical best performance of groundhook control is presented. In the example of quarter-car suspension system, the skyhook-groundhook control is optimized. At last, in the example of 4-mass system, the clipped-linear-quadratic-regulator control is demonstrated.

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.

Optimization of Quarter Car Suspension Dynamics Using Power Spectral Density of Irregular Road Profile

Optimization of Quarter Car Suspension Dynamics Using Power Spectral Density of Irregular Road Profile

Lnertia Weight-free Particle Swarm Optimization in Optimal Control Design for Vehicle Active Suspension Systems

Vehicle active suspension systems play an important role in ride comfort and driving safety. This study considers the problem of an efficient control scheme design for vehicle active suspension systems. The active suspension systems aim to get more comfortable riding and good handling for random road disturbances. The purpose of this work is to reduce the driver’s entire body acceleration and thereby improve ride comfort. The inertial weight-free particle swarm optimization (PSO) method is utilized to obtain weighting matrices of the optimal control namely linear quadratic regulator (LQR) for the active suspension systems. The designed state-feedback controller is applied to the quarter-car suspension system under different road profiles. Simulation results of the inertia weight-free PSO-tuned LQR are compared with the results of the classical-tuned controller and standard PSO-tuned LQR controller to show the effectiveness.

Multi-objective optimization and experimental investigation of quarter car suspension system

Multi-objective optimization and experimental investigation of quarter car suspension system

Simulation Study of Semi-active Suspension Fuzzy Adaptive PID Control System

This work develops a mathematical model of a quarter car suspension system with two degrees of freedom and suggests a fuzzy adaptive PID controller by assessing the drawbacks of conventional control methods. The three PID parameters are automatically modified by fuzzy control, and the PID parameters are adjusted in real time. The Matlab/Simulink platform is used to create the relevant simulation model. The simulation results demonstrate the superiority of the fuzzy adaptive PID control system suggested in this study by demonstrating a reduction in the Sprung Mass Acceleration by 17.85%, the Suspension Working Space by 14.42%, and the Dynamic Tyre Load by 9.48%.

Model of a Quarter Car Suspension with a Damper Containing Magnetorheological Fluid and with Damaged Parts Controlled by Backstepping Method

The work focuses on the minimization of the body deflection from its equilibrium position after a deflection by force applied to the wheel with the task of simulating obstacles encountered by the wheel. The model presents a quarter of the car’s suspension with a nonlinear spring and a damper with magnetorheological fluid, by which the damping of the suspension is modified. The system was created in harmony with Lyapunov’s stability. The model was designed using Matlab-Simulink. The model was designed for testing many different damaged parts of the suspension, for example, a spring or a damper. In further attempts, the model was tested for numerous damaged parts, and the sequence of events was different. The model was tested for different characteristics of springs and dampers and variable method deflection wheel from its equilibrium position such as force and displacement. This work discusses the detection of damage to the suspension along with the possibility of adapting the MR damper control system to avoid reducing the comfort and safety of the vehicle.

The Influence of Friction Force and Hysteresis on the Dynamic Responses of Passive Quarter-Car Suspension with Linear and Non-Linear Damper Static Characteristics

Abstract Vehicle passive suspensions consist of two major elements generating force – spring and passive damper. Both possess non-linear characteristics, which are quite often taken into account in simulations; however, the friction forces inside the hydraulic damper and the damping force’s hysteresis are usually left out. The researchers in this paper present the results of examination of the influence of using complex damper models – with friction and hysteresis; and with linear and non-linear static characteristics – on the chosen dynamic responses of a suspension system for excitations in the typical exploitation frequency range. The results from the simulation tests of the simplified and advanced versions of the damper model – different transfer functions and their relation to the reference model’s transfer functions – are compared. The main conclusion is that friction and hysteresis add extra force to the already existing damping force, acting similar to damping increase for the base static characteristics. But this increase is not linear – it is bigger for smaller frequencies than for higher frequencies. The research shows the importance of including non-linear characteristics and proposed modules in modelling passive dampers.

Linear Quadratic Optimal Control with the Finite State for Suspension System

The control algorithm could greatly help the suspension system improve the comprehensive performance of the vehicle. Existing control methods need to obtain the intermediate states, which are difficult to obtain directly or accurately when estimated by filters or observers. Thus, this paper proposed a new practical finite state LQR control method to deal with this problem. By combining with the output state of the finite sensor of the vehicle suspension system and weakening the unknown state as the goal, an optimization model is established with the design variables as the LQR weight coefficients. Then, the direct relationship between the current control input and the finite sensor output is obtained, and the finite state LQR control is realized. Taking the quarter-car suspension model as an example, the corresponding noise is added considering sensor accuracy, and the control performance of the four control methods is studied considering the uncertainties of suspension system parameters. In addition, the acceleration of sprung mass and the dynamic travel coefficient of suspension have been separately calculated by methods of finite state LQR control, LQR control, and PID control. The results show that there is not much difference between them under shock excitation or random excitation. However, the finite state LQR control method has the best comprehensive control performance in that its dynamic tire load coefficient is better than other methods; it could take into account the suspension work stroke coefficient, dynamic tire load coefficient, and sprung mass’ acceleration of the vehicle suspension system at the same time. In order to realize the optimal control effect with limited sensor arrangement, the finite state LQR control method only needs to obtain the current sensor output and the current control input, without estimating the unknown intermediate state. By this means, the proposed control method greatly simplifies the design of the control system and has great advantages on practical value.

Analysis and Study Indicators for Quarter Car Model with Two Air Suspension System

Modeling and simulation of non-linear quarter-car suspension system for two air spring models (traditional and dynamic new air spring) are contrasted in terms of (RMS) sprung mass acceleration, dynamic load coefficient, the vertical displacement, they are compared. Two and three (DOF) of the mathematical quarter models are implemented in MATLAB/Simulink platform. The Ride Comfort (RC), Dynamic Load Coefficient (DLC) and Road Handling (RH) responses are evaluated as objective functions respectively considering a vehicle speed at 72 km/h and road ISO Class B. The obtained results indicate that the vertical displacement, the (RMS) of the sprung mass acceleration, and dynamic load coefficient values with the new air model system decrease by 10.7 %, 30.6 %, and 13.49 % respectively, in comparison to a tradition suspension system, this one gives more comfort and effortless handling.

Influence of bushing flexibility and its constitutive behavior on the performance of suspension system

We study the effect of strut top mount bushing flexibility and its constitutive law on the ride comfort performance of a quarter car suspension model. A fractional Kelvin–Voigt model has been employed to capture the viscoelastic behavior of the top mount bushings. To study the effectiveness of the suspension system, we have considered sinusoidal and standard (motion over bumps) road inputs. For the sinusoidal input, the frequency response function for both the traditional and fractional Kelvin–Voigt models has been obtained using the harmonic balance method. However, we have resorted to numerical simulations for the standard base inputs for which a reduced-order system of ODEs has approximated the fractional derivative term. Convergence of the reduced system of ODEs is established by comparing the numerical results for sinusoidal forcing with those obtained analytically. We find that the bushing modeled as a traditional Kelvin–Voigt element increases the response amplitude in the resonance zone, while for higher frequencies, the response reduces. Hence, the inclusion of bushing flexibility is equivalent to decreasing the damping in the suspension. These observations also remain valid for the fractional Kelvin–Voigt model, but the effect is less pronounced than in the traditional model. Ride comfort for standard road profile is studied in terms of performance indices which suggests that a fractional Kelvin–Voigt bushing improves the ride comfort. Accordingly, bushing flexibility with an appropriate constitutive law should be accounted in the design of a suspension system for ride comfort. • Effect of strut top mount bushing (STMB) flexibility on ride comfort is studied. • Fractional Kelvin–Voigt model is employed for the viscoelastic behavior of the STMB. • Studied the suspension system response on sinusoidal and standard road inputs. • Ride comfort has been studied in terms of transmissibility and performance indices. • We find that STMB flexibility improves ride comfort especially during transient loads.

Multi-objective H2/H∞ control of uncertain active suspension systems with interval time-varying delay

The vehicle active suspension has been widely used as it could effectively improve the vehicle ride comfort. To solve the issues of actuator uncertainty and time delay existing in the active suspension system, a multi-objective non-fragile [Formula: see text] control algorithm is proposed in this work. First, to effectively describe the vehicle suspension dynamics, a quarter-car suspension model is constructed first in this study. Second, aiming at improving the ride quality and guarantee the hard constraints of the suspension system, a multi-objective H2/ H∞ performance index is proposed. Subsequently, the issues of external disturbances, actuator uncertainty and delay are considered in the design process of the suspension controller. Then, a multi-objective non-fragile control algorithm is proposed based on an effective Lyapunov functional. The control gain can be obtained by solving a convex optimization problem in terms of linear matrix inequalities. Finally, numerical simulations are implemented on MATLAB/Simulink platform to show the robustness and superiority of the proposed controller. Experiments are implemented on a quarter-car test rig to validate the practical performance of the designed controller.