Active vehicle suspension control using intelligent feedback linearization

<div class="section abstract"><div class="htmlview paragraph">The performance of suspension system has a direct impact on the riding comfort and smoothness. For the traditional suspension can not effectively alleviate the impact of road surface and the poor anti-vibration performance, The dynamics model of vehicle suspension system is established, and the control model of vehicle four-degree-of-freedom active suspension is designed with fuzzy control strategy. On this basis, a comprehensive simulation model of the control model of vehicle active suspension coupled with road excitation is established. and the ride comfort of vehicles under different types of suspension are tested through Simulink. The simulation results show that compared with the passive suspension, the reduction of vehicle acceleration and dynamic deformation of the active suspension controlled by fuzzy PID can reach 33.76% and 22.45%. and the reduction of pitch Angle speed and dynamic load of the active suspension controlled by fuzzy PID can reach 16.18% and 10.72%. Under fuzzy PID control, the amplitude of each evaluation index of active suspension in the suspension system is substantially reduced than that of the passive suspension, and the root-mean-square value decreases by about 10% on average. It can be seen that the active suspension with fuzzy PID control can improve the performance of the suspension system on the basis of ensuring the stability and rapid response of the system, and can well reduce the random vibration caused by the impact of the vehicle on the random road surface during the driving process, improve the ride comfort, smoothness and ride safety of the vehicle, and achieve a good control effect on the vehicle suspension.</div></div>

Scientific research and technological advances in recent years on car suspensions have led to an increase in their dynamic performance, improved passenger comfort and safety. The importance of the field is also given by the need for continuous increase of traffic safety factors in the context of infrastructure development and implicitly the increase of driving speed. The paper presents the classification of suspensions and methods used for modelling, simulation, and control of active vehicle suspensions. The Matlab environment was used for simulation and control design. Several control methods and comparisons between them are presented and implemented by simulation. A consistent part of the paper presents an MPC type control method applied for the control of the active suspension. Possible future developments are highlighted.

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

In this study, we investigate a robust H∞ controller for a quarter-car model of an active inerter-based suspension system under parameter uncertainties and road disturbance. Its main objective is to improve the inherent compromises between ride quality, handling performance, suspension stroke, and energy consumption. Inerters have been extensively used to suppress unwanted vibrations from various kinds of mechanical structures. The advantage of inerter is that the realized ratio of equivalent mass (inertance relative to the mass of the primary structure) is greater than its actual mass ratio, resulting in higher performance for the same effective mass. First, the dynamics and state space of the active inerter-based suspension system were achieved for the quarter-car model with parameter uncertainties. In order to attain the defined objectives, and ensure that the closed-loop system achieves the prescribed disturbance attenuation level, the Lyapunov stability function, and linear matrix inequality (LMI) techniques have been utilized to satisfy the robust H∞ criterion. Furthermore, to limit the gain of the controller, some LMIs have been added. In the case of feasibility, sufficient LMI conditions by solving a convex optimization problem afford the stabilizing gain of the robust state-feedback controller. According to numerical simulations, the active inerter-based suspension system in the presence of parameter uncertainties and external disturbance performs much better than both a passive suspension with inerter and active suspension without inerter.

the purpose of this paper is to improve the performance of a car's active suspension system (a quarter model), with two degrees of freedom , a combination of components and mechanisms ensure both passengers' comfort and driving safety, the stability and ride performance depends generally on the quality of the suspension , and this is why car manufacturers are turning to an adjustable suspension that can be adapted to any type of road surface as it controls vertical movement for car wheels. In this work we show how proportional integral differential (PID) controller tuned by using two methods, Ziegler Nichols and genetic algorithms (GA) can used to achieve a good performance of the active suspension system, The simulation results show the robustness and effectiveness of genetic algorithm (GA) in providing good ride quality and good road handling, however the presence of a time delay.

On a flat city road, the specificity of the suspension poses a challenge. Sport utility vehicles (SUVs) have less flexibility compared to regular cars, despite providing a firm grip on asphalt and concrete. Constant adjustments to the center of gravity of SUVs are necessary. Surprisingly, they are less reliable and stable in urban settings due to this characteristic. In this study, a mathematical model of the suspension system of SUVs based on the Newtonian approach is introduced and validated with data from experiments carried out by the MTS machine system on the mono-tube (oil/air) mixed damper element. The model accurately predicts the performance of this damper, commonly used in SUVs, across various operating conditions, including different frequencies. A coil spring element, serving as a passive suspension unit with this damper, is also tested experimentally under similar conditions. By integrating passive suspension elements with the active actuator, the proposed modified design reduces the power consumption needed for the actuator to function and ensures a certain level of reliability. The effectiveness and performance of the modified active suspension system in comparison to the traditional passive suspension system are assessed using three different strategies: hybrid PID-LQR, linear quadratic regulator (LQR), and proportional-integral-derivative (PID). The genetic algorithm is utilized to determine the optimal parameter values for each controller by minimizing a cost function, maximizing performance, and minimizing energy consumption. Simulation results demonstrate that the active suspension system controlled by the PID-LQR controller offers significantly improved ride comfort and vehicle stability compared to other systems. This suggests that the performance of the active suspension system is greatly enhanced by the combined application of the hybrid PID-LQR controller compared to other systems.

The performance of active suspension systems is directly related to the mechanical design and control of the system. The stable operation of the controller improves driving comfort and handling. The quarter car model is frequently used in the analysis of suspension systems due to its simple structure. In this study, Matlab Simulink software was used in the modeling, control and simulation of the quarter car active suspension model. System performance was investigated for four different road profiles with PID and fuzzy logic control methods. Two of the road profiles used are in the form of impact signals consisting of pits and bumps. The other two road profiles are random road disturbances with high frequency. The effects of active and passive suspension systems on driving comfort are compared by taking into account the control methods used. As a result of the study, it has been determined that the fuzzy logic controller gives better results in pulse signals consisting of bumps and pits, and the PID controller gives better results in high-frequency random road disturbances. In addition, with the use of fuzzy logic control method in the active suspension system, a significant decrease in the actuator force has occurred. This result is very interesting in terms of minimizing energy, reducing actuator sizes and reducing costs.

Heavy commercial vehicles have high requirements for ride smoothness due to their objective requirements. In order to study the characteristics of their suspension system, 1/4 passive suspension and 1/4 active suspension models were established, respectively. Firstly, the front axle data and road excitation model of the experimental sample vehicle are substituted into 1/4 passive suspension; the reliability of the simulation parameters is verified by comparing the vertical acceleration of the body with the data collected from the real vehicle vibration test. MATLAB Simulink platform was used to compare and analyze the performance of the passive suspension, traditional PID control active suspension, and genetic algorithm PID control active suspension with the body vertical acceleration, suspension dynamic travel, and suspension dynamic load as indexes. The simulation results show that the genetic algorithm PID active suspension system can improve the ride smoothness of heavy commercial vehicles, which lays a theoretical foundation for the subsequent bench test of active suspension of the front axle of heavy commercial vehicles to a certain extent.

This paper investigates the problem of robust sampled-data Hinfin control for active vehicle suspension systems. By using an input delay approach, the active vehicle suspension system with sampling measurements is transformed into a continuous-time system with a delay in the state. The transformed system contains possibly non-differentiable time-varying state delay. The controller design is cast into a convex optimization problem with LMI constraints. A quarter-car model with active suspension system is considered and the effectiveness of the proposed approach is illustrated by a realistic design example.

An active suspension of an intelligent electric vehicle driven by four in-wheel motors (IEV-DFIM) is a strong nonlinear system because of time-varying parameters in practice, which causes difficult controllability. For addressing this issue, the paper proposes a novel homogeneous output feedback control method. Firstly, an active suspension dynamic model which considers the time-varying sprung mass, stiffness coefficients and damping coefficients is built. Secondly, an active suspension control system is constructed based on the dynamic model whose uncertain and nonlinear terms do not meet the linear or high-order growing. Thirdly, the homogeneous output feedback method is developed to relax the growth condition imposed on the uncertain and nonlinear terms for the active suspension. Finally, the simulation and test are carried out to verify the effectiveness of the designed controller compared with the sliding mode control method and passive suspension.

In this paper, an optimal Fractional Order Proportional Integral Derivative (FOPID) controller is applied in vehicle active suspension system to improve the ride comfort and vehicle stability without consideration of the actuator. The optimal values of the five gains of FOPID controller to minimize the objective function are tuned using a Multi-Objective Genetic Algorithm (MOGA). A half vehicle suspension system is modelled mathematically as 6 degrees-of-freedom mechanical system and then simulated using Matlab/Simulink software. The performance of the active suspension with FOPID controller is compared with passive suspension system under bump road excitation to show the efficiency of the proposed controller. The simulation results show that the active suspension system using the FOPID controller can offer a significant enhancement of ride comfort and vehicle stability.

In this paper a fuzzy Sugeno rule based controller is used to manage a semi-active suspension of 1/4 vehicle model. Our semi-active suspensions have the characteristic to change the damping constant in order to reduce vertical oscillation of the vehicle, to restrain the shell vehicle acceleration and consequently to be more comfortable for passengers. On the other hand, if no control is present, the suspension works in passive mode, i.e. without damping parameters changing. The inputs of our fuzzy controller, three in total, are the dynamic wheel load described by five membership functions, its derivative and the vertical acceleration both described by three membership functions. By comparing the performances of the suspension with and without control, the Sugeno based model controller results in a more comfortable and safe system.

A 7-DOF half-car dynamic model which includes the cab mounting system and seat suspension system was established to study the performance of active seat suspension. The optimal control method was applied to design the active control system. Two dynamic simulation models of the passive seat suspension and the active seat suspension were set up by Matlab/Simulink, and the performance of the passive and active seat system was simulated in the time and frequency domain. The simulation results show that the active seat suspension can greatly improve the vehicle seat performance and the study has supplied the academic reference in the applications of the active seat suspension.

This paper presents a method for improving the performance of a vehicle suspension system using an adaptive fuzzy dual PID controller optimized with a genetic algorithm. The fuzzy dual PID controller utilizes fuzzy logic to adapt to changing conditions and improve control, while the genetic algorithm optimizes the controller parameters to further enhance performance. The study uses velocity and position PID controllers because velocity PID controls acceleration well and position PID controls position well, and the incorporation of an adaptive fuzzy combination of two controllers ensures optimal performance of the suspension system under all operating conditions. To avoid the issue of suspension distance narrowing and to prevent instability in the controller, the low‐pass filtered displacement response of unsprung mass is utilized as the reference for the position PID controller. Quantitatively, according to the ISO‐8608 road entry for the goal function, the dual PID achieved a 53.35% improvement over the passive state, 6.57% better than dual PD, 33.06% over the Velocity PID, and 32.93% over the Position PID. These significant, quantifiable results confirm that the proposed adaptive fuzzy dual PID structure offers a robust and highly effective solution for advancing active vehicle suspension control technology.

The primary aim of a vehicle's suspension system is to isolate the vehicle's main body from road irregularities, thus improving passenger comfort and ensuring optimal handling stability. This research discusses a stabilizing fuzzy control design for active vehicle suspension systems. The nonlinear model of the active suspension is then represented using a Takagi-Sugeno (TS) fuzzy model. The control approach uses a TS fuzzy controller utilizing an observer to estimate the state while reducing road disturbances. The closed-loop stability requirements of the vehicle utilizing the fuzzy controller and observer are expressed as a Linear Matrix Inequalities (LMI) problem, which can be effectively resolved through convex optimization methods. In this paper, we study the stability of the nonlinear automotive active suspension system with two degrees of freedom represented by a TS fuzzy model, where we will present the stabilization conditions by state feedback via the PDC (Parallel Distributed Compensation) control law and in the last section we introduced the TS fuzzy observer for the case of non-measurable premise variables.