A Novel Membership Functions Dependent Robust Control for Suspension Systems

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.

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.

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.

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.

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.

Suspension system is used to fulfil the criteria of ride comfort and road handling. In this paper, a quarter car active & semi-active suspension systems are designed using Matlab/Script software. Comparison of active & semi-active suspension systems are done using robust control theory for the control targets suspension deflection, body acceleration and body travel. H infinity controller is selected to compare the two suspensions using time domain analysis. Finally the simulation result prove the effectiveness of the active suspension system by decreasing the body acceleration & sustaining the suspension deflection and body travel outputs.

Effective control of ride quality and handling performance are challenges for active vehicle suspension systems, particularly for off-road applications. Off-road vehicles experience large suspension displacements, where the nonlinear kinematics and damping characteristics of suspension elements are significant. These nonlinearities tend to degrade the performance of active suspension systems, introducing harshness to the ride quality and reducing off-road mobility. Typical control strategies rely on linear time-invariant models of the suspension dynamics. While these models are convenient, nominally accurate, and tractable due to the abundance of linear control techniques, they neglect the nonlinearities and time-varying dynamics present in real suspension systems. One approach to improving the effectiveness of active vehicle suspension systems, while preserving the benefits of linear control techniques, is to estimate and cancel the nonlinearities using feedback linearization. In this paper, the authors demonstrate an intelligent parameter estimation approach, using structured artificial neural networks, that continually "learns" the nonlinear parameter variations of a quarter-car suspension model. This estimation algorithm becomes the foundation for an intelligent feedback linearization (IFL) controller for active vehicle suspensions. Results are presented for real-time experimental tests and field evaluations on a military HMMWV. These results clearly demonstrate the viability and effectiveness of this approach as a tool for rapid, online development of vehicle suspension models and controllers.

<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>

This paper presents the approximate optimal vibration control methodology for discrete nonlinear vehicle active suspension subject to persistent road disturbances. Based on a dynamic model of nonlinear vehicle active suspension and a linear exogenous system model of the persistent road disturbances, a nonlinear two-point boundary value (TPBV) problem is introduced. By introducing a sensitive parameter, the original TPBV problem is reformed as a series of TPBV problems without nonlinear items. A discrete approximate optimal vibration controller (DAOVC) can be obtained by solving a Riccati equation, Stein equation, and nonlinear compensation item, respectively. An iteration algorithm is designed to realize the computational realizability of DAOVC based on the control performance. It is demonstrated that the control performance of ride comfort, road holding ability, and suspension deflection under the DAOVC are much smaller than the ones under the classical feedforward and feedback optimal vibration controller (FFOVC) and open-loop vehicle suspension system.

Actuator is the key to vehicle active suspension. Based on the analyses of traditional passive suspension and active suspension system, a novel vehicle active suspension with Electro-Hydrostatic Actuator (EHA) is put forward. The system consists of two parts: spring and actuator with variable control force. The actuator is made up of hydraulic cylinder, hydraulic pump, controller and BLDCM. According to bond graph principles, bond graph model of 2 DOF passive suspensions and bond graph model of EHA active suspension are built. Moreover, fuzzy logic controller is designed and fuzzy control active suspension is simulated using MATLAB tools. The prototype and test rig of EHA active suspension are developed and bench tests are carried out. The simulation and experimental results show that fuzzy control active suspension with EHA provides better ride comfort, handling and stability than passive suspension.

Chapter 8 - Robust adaptive parameter estimation and control for vehicle active suspension systems

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.

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 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.

This work presents a comparative study for performance evaluation of quarter vehicle Active Suspension System (ASS) using different control techniques. Linear and non-linear mathematical models of the systems are presented and controlled using Proportional Integral Derivative (PID), Feedback Linearization, and Fuzzy Logic Control (FLC). Particle Swarm Optimization (PSO) technique is applied to optimize the gains of the implemented controllers. A simulation process is done using MATLAB/SIMULINK and the results show that the proposed PSO-optimized PID controller has enhanced the root mean square (r.m.s) values of ride comfort, load carrying, and road holding of the linear suspension system by 26.82%, 20.95%, and 22.72% respectively compared to the linear passive suspension system. Whereas, for the nonlinear suspension system, the PSO-optimized FLC has provided better compromise of the performance criteria. The controller has improved the r.m.s values of ride comfort, load carrying, and road handling by 40.61%, 44.21%, and 27.46% respectively compared to the non-linear passive suspension system.