Search Results (37)

The automotive suspension must perform competently to support comfort and safety when driving. Traditionally, car suspension control tuning is performed through trial and error or with classical techniques that cannot guarantee optimal performance under varying road conditions. The study aims at designing a Linear Quadratic Regulator-based Bacterial Memetic Algorithm (LQR-BMA) for suspension systems of automobiles. BMA combines the bacterial foraging optimization algorithm (BFOA) and the memetic algorithm (MA) to enhance the effectiveness of its search process. An LQR control system adjusts the suspension’s behavior by determining the optimal feedback gains using BMA. The control objective is to significantly reduce the random vibration and oscillation of both the vehicle and the suspension system while driving, thereby making the ride smoother and enhancing road handling. The BMA adopts control parameters that support biological attraction, reproduction, and elimination-dispersal processes to accelerate the search and enhance the program’s stability. By using an algorithm, it explores several parts of space and improves its value to determine the optimal setting for the control gains. MATLAB 2024b software is used to run simulations with a randomly generated road profile that has a power spectral density (PSD) value obtained using the Fast Fourier Transform (FFT) method. The results of the LQR-BMA are compared with those of the optimized LQR based on the genetic algorithm (LQR-GA) and the Virus Evolutionary Genetic Algorithm (LQR-VEGA) to substantiate the potency of the proposed model. The outcomes reveal that the LQR-BMA effectuates efficient and highly stable control system performance compared to the LQR-GA and LQR-VEGA methods. From the results, the BMA-optimized model achieves reductions of 77.78%, 60.96%, 70.37%, and 73.81% in the sprung mass displacement, unsprung mass displacement, sprung mass velocity, and unsprung mass velocity responses, respectively, compared to the GA-optimized model. Moreover, the BMA-optimized model achieved a −59.57%, 38.76%, 94.67%, and 95.49% reduction in the sprung mass displacement, unsprung mass displacement, sprung mass velocity, and unsprung mass velocity responses, respectively, compared to the VEGA-optimized model. Full article

Wave-based control (WBC) offers a relatively novel approach to the challenge of controlling flexible mechanisms by treating the interaction between actuator and system as the launch and absorption of mechanical waves. WBC is a robust approach but has been unexplored in active suspension systems to date. This study adapts WBC to a quarter-car suspension model. Having embedded an actuator as the active element of a car suspension, a novel but simple ‘force impedance’ adaptation of WBC is introduced and implemented for effective vibration control. Testing with various input signals (pulse, sinusoidal, and random profile) highlights the active system’s significant ride comfort and rapid vibration suppression with zero steady-state error. Compared to two other models—one employing an ideal skyhook strategy and the other a passive suspension—the active system utilizing WBC outperforms across many criteria. The active controller achieves over 38% superior ride comfort compared to the skyhook model for a pulse road input. This is accomplished while adhering to WBC principles: relying solely on actuator-interface measurements, simplicity, cost-effectiveness, with no need for detailed system models, extensive sensors, or deep system knowledge. Full article

This study examines the smoothness of an intelligent chassis for electric vehicles, analyzes the chassis structure and configuration, and considers the impacts of the primary energy subsystem, electric drive subsystem, and auxiliary control subsystem on smoothness. The influence of suspension parameters on smoothness is examined, highlighting the significance of elastic element stiffness and the shock absorber damping ratio. Dynamic models of quarter- and half-car suspension systems, as well as a comprehensive nine-degree-of-freedom vehicle model, are developed to examine the vibration characteristics under varying road conditions. The chassis suspension dynamic model is developed, simulated, and analyzed using ADAMS/View software 2024. The suspension damping value is optimized with the ADAMS/PostProcessor tool, revealing that smoothness can be enhanced by judiciously decreasing the damping value. The article discusses the human body’s reaction to vibration and assessment metrics, referencing worldwide standards to establish a foundation for evaluation. The study offers theoretical backing for the design and optimization of an intelligent chassis, hence advancing the technological development of electric vehicles. Full article

This study investigates the effect of active control on a quarter-vehicle suspension system. The car suspension system was modeled using the Lagrange–Euler method. The linear quadratic Gaussian (LQG) and fuzzy linear quadratic Gaussian (FLQG) control methods were designed and used for active control to increase vehicle handling and passenger comfort, with the aim of reducing or eliminating vibrations by performing active control of passive suspension systems using these methods. The optimum values of the coefficients of the points where the membership functions of the LQG and Fuzzy LQG methods touch were obtained using the grey wolf optimization (GWO) algorithm. The success of the control performance rate of the applied methods was compared based on the passive suspension system. In addition, the obtained results were compared with each other and with other studies using the integral time-weighted absolute error (ITAE) performance criterion. The proposed control method yielded significant improvements in vehicle parameters compared with the passive suspension system. Vehicle body movement, vehicle acceleration, suspension deflection, and tire deflection improved by approximately 88.2%, 91.5%, 88%, and 89.4%, respectively. Thus, vehicle driving comfort was significantly enhanced based on the proposed system. Full article

In this paper, a semi-active and fully active suspension system using a PID controller were designed and tuned in MATLAB/Simulink to achieve simultaneous optimisation of comfort and road holding ability. This was performed in order to quantify and observe the trends of both the semi-active and active suspension, which can then influence the choice of controlled suspension systems used for different applications. The response of the controlled suspensions was compared to a traditional passive setup in terms of the sprung mass displacement and acceleration, tyre deflection, and suspension working space for three different road profile inputs. It was found that across all road profiles, the usage of a semi-active or fully active suspension system offered notable improvements over a passive suspension in terms of comfort and road-holding ability. Specifically, the rms sprung mass displacement was reduced by a maximum of 44% and 56% over the passive suspension when using the semi-active and fully active suspension, respectively. Notably, in terms of sprung mass acceleration, the semi-active suspension offered better performance with a 65% reduction in the passive rms sprung mass acceleration compared to a 40% reduction for the fully active suspension. The tyre deflection of the passive suspension was also reduced by a maximum of 6% when using either the semi-active or fully active suspension. Furthermore, both the semi-active and fully active suspensions increased the suspension working space by 17% and 9%, respectively, over the passive suspension system, which represents a decreased level of performance. In summary, the choice between a semi-active or fully active suspension should be carefully considered based on the level of ride comfort and handling performance that is needed and the suspension working space that is available in the particular application. However, the results of this paper show that the performance gap between the semi-active and fully active suspension is quite small, and the semi-active suspension is mostly able to match and sometimes outperform the fully active suspension n in certain metrics. When considering other factors, such as weight, power requirements, and complexity, the semi-active suspension represents a better choice over the fully active suspension, in the author’s opinion. As such, future work will look at utilising more robust control methods and tuning procedures that may further improve the performance of the semi-active suspension. Full article

This paper introduces a novel adaptive control method for suspension vehicle systems in response to road disturbances. The considered model is based on an active symmetry quarter car (SQC) fractional order suspension system (FOSS). The word symmetry in SQC refers to the symmetry of the suspension system in the front tires or the rear tires of the car. The active suspension controller is generally driven by an external force like a hydraulic or pneumatic actuator. The external force of the actuator is determined using fractional dynamic sliding mode control (FDSMC) to counteract road disturbances and eliminate the chattering caused by sliding mode control (SMC). In FDSMC, a fractional integral acts as a low-pass filter before the system actuator to remove high-frequency chattering, necessitating an additional state for FDSMC implementation assuming all FOSS state variables are available but the parameters are unknown and uncertain. Hence, an adaptive procedure is proposed to estimate these parameters. To enhance closed-loop system performance, an adaptive proportional-integral (PI) procedure is also employed, resulting in the FDSMC-PI approach. A comparison is made between two SQC suspension system models, the fractional order suspension system (FOSS) and the integer order suspension system (IOSS). The IOSS controller is based on dynamic sliding mode control (DSMC) and a PI procedure (DSMC-PI). The results show that FDSMC outperforms DSMC. Full article

The technical condition of the shock absorbers used in automotive suspension systems is important with respect to vehicle occupants’ comfort and traffic safety. Therefore, much effort has been made for many years to find diagnostic methods that would be more effective. There is a preference for those methods where the shock absorbers do not have to be dismounted from the vehicle. Among those being in use, the ‘forced vibration methods’ have earned the widest acceptance. One of them is the solution where the angle of phase shift between the vertical displacement of the vibration plate and the tyre–plate interaction force is measured. The authors decided to assess this method’s usability by comparing simulation results with the results of experiments run on a prototype diagnostic test stand. They used two ‘quarter-car’ simulation models (linear and non-linear) and experimentally tested suspension systems of two medium-class cars. In the first stage, computations were made in the frequency domain for the linear model with two degrees of freedom, followed by simulations in the time domain, where an analogous but strongly non-linear model was used. In the latter model, the actual characteristic curves (determined during the laboratory measurements) of shock absorber damping, tyre and suspension elasticity, sliding friction in the suspension system, and tyre bouncing were taken into account. The authors have presented the computation results in the form of curves representing the phase angle as a function of the relative damping in the suspension system under test for the two medium-class cars. The suspensions of the cars had similar inertia properties but different characteristics of the spring and damping forces. The cars also differed from each other in the observed and measured level of the friction forces (twice bigger). The computation results obtained for the linear and non-linear model and the experiment results show a similar qualitative nature. In quantitative terms, however, they differ significantly from each other. The role of non-linearities is important. Nevertheless, the results show monotonicity and noticeable sensitivity to changes in the technical condition of the shock absorbers, which is an essential and desirable feature in diagnostics. Full article

This paper addresses the trade-off between ride comfort and road-holding capability of a quarter-car semi-active suspension system, collaborated by an active aerodynamic surface (AAS), using an optimal control policy. The semi-active suspension system is more practical to implement due to its low energy consumption than the active suspension system while significantly improving ride comfort. First, a model of the two-DOF quarter-car semi-active suspension in the presence of an active airfoil with two weighting sets based on ride comfort and road-holding preferences is presented. Then, a comprehensive comparative study of the improved target performance indices with various suspension systems is performed to evaluate the proposed suspension performance. Time-domain and frequency-domain analyses are conducted in MATLAB^® (R2024a). From the time-domain analysis, the total performance measure is enhanced by about 50% and 35 to 45%, respectively, compared to passive and active suspension systems. The results demonstrate that a semi-active suspension system with an active aerodynamic control surface simultaneously improves the conflicting target parameters of passenger comfort and road holding. Utilizing the aerodynamic effect, the proposed system enhances the vehicle’s dynamic stability and passenger comfort compared to other suspension systems. Full article

This study presents an effective control strategy for improving the dynamic performance index of a two degrees-of-freedom (DOF) quarter-car model equipped with an active suspension system that collaborates with an active aerodynamic surface, using optimal control theory. The model takes several road excitations as input and applies an optimal control law to improve the ride comfort and road-holding capability, which are otherwise in conflict. MATLAB^® (R2024a) simulations are carried out to evaluate the time and frequency domain characteristics of the quarter-car active suspension system. Individual performance indices in the presence of an active aerodynamic surface are calculated based on mean squared values for different sets of weighting factors and compared with those of passive and active suspension systems. From the viewpoint of total performance, the overall results show that the proposed control strategy enhances the performance index by approximately 70–80% compared to the active suspension system. Full article

This paper explores the modeling and simulation of an innovative double-damper suspension system, evaluating its effectiveness through different test scenarios. The double damper integrates two individual dampers into a unified assembly. The modeling process involves representing the damper as two distinct dampers and a body block, accounting for the additional degree of freedom introduced by combining the two dampers. Simulink/MATLAB is employed for modeling the pressure, discharge, and force equations of the damper. A simplified quarter-car model is designed to conduct simulations for different road profiles, evaluating the efficacy of this double-damper model. The reduced-order modeling approach, suitable for complex systems like dampers, is utilized. Dedicated mathematical models are utilized to examine both single- and double-damper configurations, with the resulting non-linear equations solved using Newton’s iterative method. The equations derived for the single damper provide the basis for modeling the double-damper system. In this model, two separate dampers, each possessing similar properties, are simulated and considered to be rigidly linked at their connection point. Consequently, it is assumed that a portion of the force and velocity experienced by the lower damper is transmitted to the upper damper, and vice versa. Simulation results demonstrate that the innovative double-damper design outperforms a single passive damper in attenuating the oscillations of both the sprung and unsprung masses. Moreover, this innovative concept offers increased adaptability to balance between ride comfort and road holding, a feature previously limited to passive suspension systems. Full article

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. Full article

Limiting the suspension stroke in vehicles holds critical and conceivable benefits. It is crucial for the safety, stability, ride comfort, and overall performance of the vehicle. Furthermore, it improves the reliability of suspension components and maintains consistent handling during regular and rough driving conditions. Hence, the design of a safety-critical controller to limit the suspension stroke for active suspension systems is of high importance. In this study, we employed a quarter-car model that incorporates a suspension spring with cubic nonlinearity. The proposed safety-critical controller is the control Lyapunov function–control barrier function–quadratic programming (CLF-CBF-QP). Initially, we designed the reference controller as a linear quadratic regulator (LQR) controller based on the linearized quarter-car model. The reference state-feedback LQR controller simplified the design of the control Lyapunov function. Consequently, from the nonlinear model, we construct a simple control Lyapunov function that relies only on the sprung mass velocity to have a relative degree of one. The CLF intends to improve the performance by considering the nonlinearity and via online optimization. We then formulate the control barrier function to restrict the suspension stroke from breaching its limits. To assess the effectiveness of the proposed controller, we present two challenging road inputs for the nonlinear quarter-car model when employing CLF-CBF-QP and LQR controllers. The CLF-CBF-QP findings surpassed the LQR controller in terms of safety and performance. This study highlights the immense potential of CLF-CBF-QP for suspension systems, improving the time-domain performance, limiting the suspension stroke, and guaranteeing safety. Full article

Suspension systems are critical parts of modern cars. In this study, a radial basis function neural networks-based adaptive PID optimal method is presented for vehicle suspension systems. To avoid the shortcoming that the parameters of PID control are determined by experience in the traditional method, to avoid the local optimality problem and the slow rate of convergence in the modern intelligence method, radial basis function neural networks are applied in this paper. First, a quarter-car suspension is presented. Then, the radial basis function neural networks are employed to obtain the parameters of proportional, integral, and derivate components that are used in PID control. The simulation is conducted later. Next, a comparison of the progress between uncontrolled suspension, the radial basis function-based PID control, the $H_{\infty }$ control method, and the FPM control method is presented. According to the simulation results, the proposed control method performs better than the others. This contrast reveals the superior characteristics of the suggested control strategy. Full article

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. Full article

The concept of controlling vehicle comfort is a common problem that is faced in most under- and postgraduate courses in Engineering Schools. The aim of this study is to provide a simplified approach for the feedback control design and simulation of active suspension systems, which are applied in vehicles. Firstly, the mathematical model of an active suspension system (a quarter model of a car) which consists of a passive spring, a passive damper and an actuator is provided. In this study, we chose to design and compare the following controllers: (a) conventional P, PI and PID controllers that were tuned through two conventional methodologies (Ziegler–Nichols and Tyreus–Luyben); (b) an optimal PID controller that was tuned with a genetic algorithm (GA) optimization framework in terms of the minimization of certain performance criteria and (c) an internal model controller (IMC) based on the process transfer function. The controllers’ performance was assessed in a series of realistic scenarios that included set-point tracking with and without disturbances. In all cases, the IMC controller and the optimal PID showed superior performance. On the other hand, the P and PI controllers showed a rather insufficient behavior that involved persistent errors, overshoots and eventually, uncomfortable ride oscillations. Clearly, a step-by-step approach such as this, that includes modeling, control design and simulation scenarios can be applied to numerous other engineering examples, which we envisage to lead more students into the area of automatic control. Full article