Fuzzy and adaptive fuzzy control for the automobiles’ active suspension system

Two typical criteria for good vehicle suspension performance are their ability to provide good road handling and increased passenger comfort. The main disturbance affecting these two criteria is terrain irregularities. Active suspension control systems reduce these undesirable effects by isolating car body motion from vibrations at the wheels. This paper describes fuzzy and adaptive fuzzy control (AFC) schemes for the automobile active suspension system (ASS). The design objective is to provide smooth vertical motion so as to achieve the road holding and riding comfort over a wide range of road profiles. The efficacy of the proposed control schemes is demonstrated via simulations. With respect to the optimal linear quadratic regulator (LQR), it is shown that superior results have been achieved by the AFC.     

Enhancing grey prediction fuzzy controller for active suspension systems

A grey prediction fuzzy controller (GPFC) was proposed to control an active suspension system and evaluate its control performance. The GPFC employed the grey prediction algorithm to predict the position output error of the sprung mass and the error change as input variables of the traditional fuzzy controller (TFC) in controlling the suspension system to suppress the vibration and the acceleration amplitudes of the sprung mass for improving the ride comfort of the TFC used; however, the TFC or GPFC was employed to control the suspension system, resulting in a large tire deflection so that the road-holding ability in the vehicle becomes worse than with the original passive control strategy. To overcome the problem, this work developed an enhancing grey prediction fuzzy controller (EGPFC) that not only had the original GPFC property but also introduced the tire dynamic effect into the controller design, also using the grey prediction algorithm to predict the next tire deflection error and the error change as input variables of another TFC, to control the suspension system for enhancing the road-holding capability of the vehicle. The EGPFC has better control performances in suppressing the vibration and the acceleration amplitudes of the sprung mass to improve the ride quality and in reducing the tire deflection to enhance the road-holding ability of the vehicle, than both TFC and GPFC, as confirmed by experimental results.     

An Original Feedback Control with a Reversible Electromechanical Actuator Used as an Active Isolation System for a Seat Suspension. Part I: Theoretical Study

This paper provides an overview of a theoretical study of an active seat suspension. The principal objective of this study is to improve ride passenger comfort by reducing transmitted seat acceleration. The seat is represented by a non-linear two degree of freedom model. The system is linearized for small perturbations around the equilibrium. To control the dynamic of the seat suspension, an original feedback control command with a reversible electromechanical actuator is achieved. The synthesis of the regulator is realized on the linearized model of the seat suspension and the root locus method is employed. Stability and robustness characteristics have been studied. Numerical simulations in time and frequency domain show the interests of the regulator and its capability to isolate seat passenger.     

Impact of inerter nonlinearities on vehicle suspension control

This paper discusses the nonlinear properties of inerters and their impact on vehicle suspension control. The inerter was recently introduced as an ideal mechanical two-terminal element, which is a substitute for the mass element, where the applied force is proportional to the relative acceleration across the terminals. Until now, ideal inerters have been applied to vehicle, motorcycle and train suspension systems, in which significant performance improvement was achieved. However, due to the mechanical construction, some nonlinear properties of the existing mechanical models of inerters are noted. This paper investigates the inerter nonlinearities, including friction, backlash and the elastic effect, and their influence on vehicle suspension performance. A testing platform is also built to verify the nonlinear properties of the inerter model.     

Roll- and pitch-plane-coupled hydro-pneumatic suspension. Part 2: dynamic response analyses

In the first part of this study, the potential performance benefits of fluidically coupled passive suspensions were demonstrated through analyses of suspension properties, design flexibility and feasibility. In this second part of the study, the dynamic responses of a vehicle equipped with different configurations of fluidically coupled hydro-pneumatic suspension systems are investigated for more comprehensive assessments of the coupled suspension concepts. A generalised 14 degree-of-freedom nonlinear vehicle model is developed and validated to evaluate vehicle ride and handling dynamic responses and suspension anti-roll and anti-pitch characteristics under various road excitations and steering/braking manoeuvres. The dynamic responses of the vehicle model with the coupled suspension are compared with those of the unconnected suspensions to demonstrate the performance potential of the fluidic couplings. The dynamic responses together with the suspension properties suggest that the full-vehicle-coupled hydro-pneumatic suspension could offer considerable potential in realising enhanced ride and handling performance, as well as improved anti-roll and anti-pitch properties in a very flexible and energy-saving manner.     

Non-stationary random vibration analysis of three-dimensional train–bridge systems

The quarter car model has been used extensively to study the benefits of active, semi-active and passive suspensions. Despite the evident simplicity of the model, the insights obtained from this model have been found to have counterparts in half- and full-car suspension models. Among the most interesting results of the analysis of the quarter car are the relationships among certain transfer function and invariant points in the frequency response functions. These results are of great interest for the application of linear control techniques to the design of active suspensions and the optimisation of linearised passive suspensions. This paper attempts to show why some of the limitations implied by the model are less absolute than they at first seem.     

Virtual test rig to improve the design and optimisation process of the vehicle steering and suspension systems

A virtual test rig is presented using a three-dimensional model of the elasto-kinematic behaviour of a vehicle. A general approach is put forward to determine the three-dimensional position of the body and the main parameters which influence the handling of the vehicle. For the design process, the variable input data are the longitudinal and lateral acceleration and the curve radius, which are defined by the user as a design goal. For the optimisation process, once the vehicle has been built, the variable input data are the travel of the four struts and the steering wheel angle, which is obtained through monitoring the vehicle. The virtual test rig has been applied to a standard vehicle and the validity of the results has been proven.     

Multi-objective control of a full-car model using linear-matrix-inequalities and fixed-order optimisation

This paper studies multi-objective control of a full-vehicle suspension excited by random road disturbances. The control problem is first formulated as a mixed ?₂/?_∞ synthesis problem and an output-feedback solution is obtained by using linear-matrix-inequalities. Next, the multi-objective control problem is re-formulated as a non-convex and non-smooth optimisation problem with controller order restricted to be less than the vehicle model order. For a range of orders, controllers are synthesised by using the HIFOO toolbox. The efficacy of the presented procedures are demonstrated by several design examples.     

Total dynamic response of a PSS vehicle negotiating asymmetric road excitations

A planar suspension system (PSS) is a novel automobile suspension system in which an individual spring–damper strut is implemented in both the vertical and longitudinal directions, respectively. The wheels in a vehicle with such a suspension system can move back and forth relative to the chassis. When a PSS vehicle experiences asymmetric road excitations, the relative longitudinal motion of wheels with respect to the chassis in two sides of the same axle are not identical, and thus the two wheels at one axle will not be aligned in the same axis. The total dynamic responses, including those of the bounce, pitch and the roll of the PSS vehicle, to the asymmetric road excitation may exhibit different characteristics from those of a conventional vehicle. This paper presents an investigation into the comprehensive dynamic behaviour of a vehicle with the PSS, in such a road condition, on both the straight and curved roads. The study was carried out using an 18 DOF full-car model incorporating a radial-spring tyre–ground contact model and a 2D tyre–ground dynamic friction model. Results demonstrate that the total dynamic behaviour of a PSS vehicle is generally comparable with that of the conventional vehicle, while PSS exhibits significant improvement in absorbing the impact forces along the longitudinal direction when compared to the conventional suspension system. The PSS vehicle is found to be more stable than the conventional vehicle in terms of the directional performance against the disturbance of the road potholes on a straight line manoeuvre, while exhibiting a very similar handling performance on a curved line.     

Non-fragile multi-objective static output feedback control of vehicle active suspension with time-delay

This paper presents an approach to design a delay-dependent non-fragile H_∞/L₂–L_∞ static output feedback (SOF) controller for active suspension with input time-delay. The control problem of quarter-car active suspension with actuator time-delay is formulated to a H_∞/L₂–L_∞ control problem. By employing a delay-dependent Lyapunov function, new existence conditions of delay-dependent non-fragile SOF H_∞ controller and L₂–L_∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities (BMIs). Then, a procedure based on linear matrix inequality optimisation and a hybrid algorithm of the particle swarm optimisation and differential evolution is used to solve an optimisation problem with BMI constraints. Design and simulation results of non-fragile H_∞/L₂–L_∞ controller for active suspension show that the designed controller not only can achieve the optimal performance and stability of the closed-loop system in spite of the existence of the actuator time-delay, but also has significantly improved the non-fragility characteristics over controller perturbations.