Random Road Input Research Articles

Comparison of Air Spring Actuator and Electro-Hydraulic Actuator in Automotive Suspension System

The present article introduces an approach that combines modelling and simulation of air spring actuator and electro-hydraulic actuator for comparison in automotive suspension system. Both hydraulic and air spring actuators are controlling the vehicle body by developing a desired force between sprung mass and unsprung mass using fuzzy logic controller. The vehicle body along with the wheel system is modelled as a two degree of freedom quarter car model. The actuator performance is investigated using the quarter car suspension model under single road bump with severe peak amplitude excitations and random road input. From the results of simulation, it can be concluded that air spring actuator gave better performance than electro-hydraulic actuator in all conditions under vertical body deflection.

State Dependent Riccati Equation Control of an Active Hydro-Pneumatic Suspension System

In this study, a nonlinear active Hydro-Pneumatic (HP) suspension system is modelled. The HP suspension system model is then incorporated into the quarter car model and a nonlinear controller for the vehicle system is developed. A linear structured model with state dependent matrices of the nonlinear quarter car model is derived for use in controller design. A nonlinear control method, State Dependent Riccati Equation control (SDRE) is used to attenuate sprung mass acceleration, suspension deflection, and tire deflection. The performance of the controller is examined in both frequency and time domains. Active HP suspension system is simulated with sinusoidal inputs at discrete amplitudes and frequencies, and the approximate frequency response functions are obtained. The active HP suspension system is simulated with random road inputs and the root mean square values of the responses are used to evaluate the performance of the controller. The results show that the active suspension successfully and simultaneously decreases the sprung mass acceleration, suspension deflection, and tire deflection around body bounce frequency and thus improved ride comfort and road holding are obtained.

Research on Vehicle Dynamics Random Response to Uneven Road

An 8-dof vehicle vibration model with four-wheeled random road inputs was established. The frequency-domain method was applied to researching the random response of linear vehicle dynamic system. The results show that the frequency error calculated by the 8-dof model is small, but the amplitude is slightly large. Hence, it has referential value to use a simple model to estimate the peak frequency of a practical system. The model of vehicle dynamics as well as the method and program of the calculation of its vibration can predict the ride comfort and safety of the vehicle, and can also provide the scientific basis of researching the stability of vehicle and its influential factors.

Study of Active Suspension Based on Fuzzy Neural Network Control

Based on the established full-car active suspension model, fuzzy control theory was combined with neural network control, the fuzzy neural network control system of vehicle active suspension was designed, simulation and analysis of random road input and sine wave input were carried on. The results show that, by comparison with the traditional suspension system, the peak and standard deviation of vehicle mass vertical acceleration decreased by 55.38% and 59.04%, the peak of vehicle mass vertical acceleration decreased by 49.96% when vehicle go through the sine wave at the speed of 5m/s, the ride comfort was improved obviously.

Design of active and energy-regenerative controllers for DC-motor-based suspension

In this paper, active and energy-regenerative controllers are designed for the DC-motor-based suspension, which is able to operate in two modes: active control for ride comfort promotion and energy-regenerative control for energy harvesting. In order to achieve these two modes, the main/torque-tracking loop control structure is presented in this paper. Then by simplifying torque-tracking loop, working areas of the DC-motor actuator are analyzed. As for main loop controller design, H∞ robust control is investigated for the active suspension based on a full-car suspension model. The restricted H∞ controller, which is the combination of proposed H∞ controller and a restriction strategy that confines the motor to the working areas of energy regeneration, is employed as the main controller to realize energy regeneration. Simulations are carried out with random uneven road inputs and the results demonstrate that better ride comfort can be achieved by proposed active suspension and energy-regenerative (ER) suspension compared with passive counterpart. Moreover, effects of uncertainties are also investigated under several cases, indicating good robustness of designed suspension systems. Meanwhile, capacity of energy regeneration is also ensured by the ER suspension.

Active suspension robust control based on main/torque-tracking loop structure

This paper presents a robust control method for a direct current (DC)-motor-based active suspension based on main/torque-tracking loop structure. The control structure is divided into two loops. The main loop deals with parametric uncertainties for a full-car suspension model and calculates the demand torque of DC-motors for active control. Several uncertain parameters are taken into consideration and a mixed-μ robust controller is proposed for the main loop. The torque-tracking loop employs the control of a three-phase motor by using hysteresis current control to track the demand torque calculated by the main loop. Simulations are carried out with random road input and bump input. The results demonstrate that the DC-motor-based active suspension with the designed controller can greatly improve vehicle ride comfort in comparison with the corresponding passive one.

Control and Evaluation of Slow‐Active Suspensions with Preview for a Full Car

An optimal control design method based on the use of the correlation between the front and rear wheel inputs (wheelbase preview) is introduced and then applied to the optimum design of a slow‐active suspension system. The suspension consists of a limited bandwidth actuator in series with a passive spring, the combination being in parallel with a passive damper. A three‐dimensional seven degrees of freedom car riding model subjected to four correlated random road inputs is considered. The performance potential of the limited bandwidth system with wheelbase preview in comparison with the nonpreview (uncorrelated inputs) case is investigated.

Energy flow analysis and hybrid controller design for non-linear electromagnetic suspension

In this paper, a mathematical model for the developed electromagnetic suspension actuator is established based on measured parameters and test data. A main/inner-loop control strategy is proposed for its active control and the inner loop undertakes the control of a three-phase motor by applying a hysteresis current control method to track the calculated signal by the main loop. With the simplification of the inner-loop control system, the achievable range of control current and energy flow states of the actuator are analysed. Then, owing to the non-linear damping characteristic of the actuator, a hybrid system model which involves real and integer variables is built up for the main loop and optimal control to improve vehicle ride comfort is carried out based on a model predictive control method. Simulations are carried out with bump impulse and random uneven road inputs and the results demonstrate that the electromagnetic suspension with the designed hybrid controller can improve vehicle ride comfort compared with a corresponding passive suspension while energy is consumed from the battery.

Predictive controller design for electromagnetic suspension based on mixed logical dynamical model

In this paper, a mathematical model for the developed electromagnetic suspension actuator is established using measured parameters and test data. A main/inner-loop control structure is proposed for its active control where the inner loop undertakes the control of a three-phase motor and applies hysteresis current control method to track the calculated signal by the main loop. With the simplification of the inner-loop control system, an achievable range of control current is acquired. Then, due to the nonlinear damping characteristic of the actuator, a mixed logical dynamical model is built up for the vehicle system and the optimal control to improve vehicle ride comfort is carried out based on the model predictive control method. Simulations are carried out using random uneven road inputs and the results demonstrate that the electromagnetic suspension with the proposed controller can provide better vehicle ride comfort compared with a corresponding passive suspension.

Random displacement and acceleration responses of vehicles with uncertainty

Dynamic displacement and acceleration responses of cars with uncertain parameters under random road input excitations are investigated by using a quarter-car model. Based on the theory of random vibration, the vehicle’s random displacement and acceleration responses are developed in time domain and frequency domain. The sprung mass, unsprung mass, suspension damping, suspension and tire stiffness are considered as random variables. The mean value, standard deviation and variation coefficient of the vehicle’s natural frequencies and mode shapes are obtained by using the Monte-Carlo simulation method. The computational expressions for the numerical characteristics of the root mean square value of vehicle’s random displacement and acceleration responses in the frequency domain are developed by means of the random variable’s functional moment method and algebra synthesis method. The influences of the uncertainty of the vehicle’s parameters on the vehicle’s random responses are investigated in detail using a practical example, and some useful conclusions are obtained.

A stochastic quarter-car model for dynamic analysis of vehicles with uncertain parameters

A quarter-car model is used to investigate the vibration response of cars with uncertainty under random road input excitations in this paper. The sprung mass, unsprung mass, suspension damping, suspension stiffness, and tyre stiffness are considered as random variables. The road irregularity is considered a Gaussian random process and modelled by means of a simple exponential power spectral density. The power spectral density, mean value, standard deviation, and variation coefficient of the vehicle's natural frequencies and mode shapes are obtained by using the Monte Carlo simulation method. The computational expressions for the numerical characteristics of the mean square value of the vehicle's random response in the frequency domain are developed by means of the random variable's functional moment method. The influences of the randomness of the vehicle's parameters on the vehicle's dynamic response are investigated in detail using a practical example, and some useful conclusions are obtained.

Pitch plane analysis of a twin-gas-chamber strut suspension

A twin-gas-chamber hydropneumatic suspension strut concept is proposed to achieve enhanced bounce and pitch ride, and pitch attitude control. The response characteristics of the twin-gas-chamber strut suspension are compared with those of a single-gas-chamber strut suspension to demonstrate not only superior performance potentials but also the added design flexibility offered by the twin-gas-chamber struts. The relative responses of both strut suspensions are evaluated through analysis of a pitch plane vehicle model, subject to straight-line braking inputs and excitations arising from randomly distributed road elevations. A generalized formulation for the strut forces is presented to derive the bounce and pitch rates of the proposed strut suspensions. The results reveal that the twin-gas-chamber strut suspension exhibits a slightly lower pitch stiffness in the vicinity of design ride height, but progressively hardening effects with increasing pitch deflections. Moreover, the twin-gas-chamber strut suspension exhibits considerably fewer hardening—softening effects in suspension rate compared with the suspension involving the single-gas-chamber struts. The results attained from the parametric studies are also discussed to demonstrate superior design flexibility of the twin-gas-chamber struts for tuning of the suspension bounce and pitch stiffness properties. The dynamic responses of the vehicle model with different suspensions are assessed subject to random road roughness excitations as well as braking torque inputs. The results demonstrate that the twin-gas-chamber strut suspension offers considerable potential for enhancing bounce and pitch ride, pitch attitude control, and suspension travel responses under braking, while the influence on the ride and road-holding responses under random road inputs is insignificant. The results also suggest that a relatively soft front suspension design could provide further enhancement of pitch ride and pitch deflection responses under random road roughness excitations.

Dynamic analysis of vehicles with uncertainty

The probabilistic and interval dynamic analysis of cars with uncertain parameters under random road input excitations by using a two-degree-of-freedom car model are presented in this paper. In the probabilistic analytical model, the vehicle parameters, including the sprung mass, unsprung mass, suspension damping, suspension, and tyre stiffness, are considered as random variables. The mean value, standard deviation, and variation coefficient of the vehicle's natural frequencies and mode shapes are obtained by using the Monte Carlo simulation method. Then, the computational expressions for the numerical characteristics of the mean square value of the vehicle's random response in the frequency domain are developed by means of the random variable's functional moment method. Considering the vehicle parameters as interval variables, the lower bound, upper bound, and interval change ratio value of the vehicle's random responses are obtained by means of the interval operations. The influences of the uncertainty of the vehicle parameters on the vehicle's natural frequencies, mode shapes, and dynamic responses are investigated in detail using a practical example. The comparison of the vehicle's dynamic characteristics using the probabilistic and interval analysis are also demonstrated.

Integrated control of automobile steering and suspension system based on disturbance suppression

A vehicle nonlinear lateral and vertical dynamics model is built under crosswind disturbance. With the L2-gain method of disturbance suppression, the nonlinear H_∞output feedback controller is designed for electrical power steering (EPS) and active suspension system (ASS) with considerations of random road input and strong crosswind disturbance. Simula- tions for driver-vehicle-road closed-loop system are carried out by using Matlab soft'ware. The results show that the designed controller can suppress the disturbances effectively and improve handling stability, handiness and ride characteristics of a vehicle.

Spectral Decomposition Methods for the Computation of RMS Values in an Active Suspension

The theory of the spectral decomposition of a matrix with distinct eigenvalues is reviewed briefly and then applied to the closed-loop system matrix of a quarter-car active suspension with preview. RMS values of the state variables and the control force are derived for an integrated white noise type random road input with the assumption of an optimised control system. The explicit formulæ obtained are easily computed numerically using MATLAB with accurate results at all speeds.

Multidisciplinary design optimization of mechatronic vehicles with active suspensions

A multidisciplinary optimization method is applied to the design of mechatronic vehicles with active suspensions. The method is implemented in a GA-A’GEM-MATLAB simulation environment in such a way that the linear mechanical vehicle model is designed in a multibody dynamics software package, i.e. A’GEM, the controllers and estimators are constructed using linear quadratic Gaussian (LQG) method, and Kalman filter algorithm in Matlab, then the combined mechanical and control model is optimized simultaneously using a genetic algorithm (GA). The design variables include passive parameters and control parameters. In the numerical optimizations, both random and deterministic road inputs and both perfect measurement of full state variables and estimated limited state variables are considered. Optimization results show that the active suspension systems based on the multidisciplinary optimization method have better overall performance than those derived using conventional design methods with the LQG algorithm.

ADAPTIVE CONTROL OF AN ACTIVE SUSPENSION FOR NONLINEAR TIME VARYING VEHICLE PLANT

This paper presents a new adaptive control approach to general multi-degrees-of-freedom suspension models. The control concept diverts from the widely applied optimal control to adaptive control. The basic idea involves obtaining optimal performance of any nonlinear time varying suspension model by adaptively following a predefined reference model. Optimal performance is achieved by an adaptive control law, which involves feed forward, feedback and auxiliary controller parameters. Model reference adaptive control is used to derive adaptation laws for the controller. The proposed control scheme is computationally fast and does not require a priori knowledge of complex nonlinear dynamic variations and time varying parameters of the model. Simulation results for a two-degree of freedom nonlinear suspension model subjected to random asphalt road input are presented. The time and frequency domain results indicate good performance of adaptive controller even for large dynamic variations of model.

Handling Safety Simulation of Driver-Vehicle Closed-Loop System with Evolutionary Random Road Input

The response simulation is studied and the handling safety is evaluated using finer integration method for driver-vehicle closed-loop system with stationary random road input. This algorithm is not only precise, but can also shorten the evaluation period of handling safety and reduce the tremendous cost for real vehicle testing. The response simulation and the vehicle handling safety evaluation are also studied for the closed-loop system with evolutionary random road input. The study can more truly simulate vehicle handling quality for including the varying of vehicle velocity with time.

An Experimental Investigation of Preview Control

There is mounting theoretical evidence to suggest that preview control can be of substantial benefit to a semi-active suspension for random road inputs. In this paper, the benefits of wheel-base preview control are measured experimentally, using a prototype semi-active damper in a half-car ‘Hardware-in-the-loop’ (HiL) rig with a planar two-axle heavy vehicle model. The benefits of preview control using the prototype semi-active damper are found to be less than theoretically possible, due to the phase lag between the demanded and achieved damping force. It is shown that the performance of the prototype damper can be improved significantly by having a theoretical simulation running ahead of the HiL vehicle. The theoretical simulation is used to predict the demanded damper force for the HiL vehicle, and thereby compensate for the phase lag in the prototype damper.

Physically Realisable Feedback Controls for a Fully Active Preview Suspension Applied to a Half-Car Model

SUMMARY An optimal preview type active suspension with feedback control based on easily measured relative displacements, velocities and accelerations is proposed. Measurements relative to the road, except by the preview sensor, are not required and the front and rear spring rates are quite arbitrary. Also, state estimators or observers are unnecessary and as a practical alternative the body accelerometers may be replaced by load cells. The effects of preview on the performance, for a theoretical step type road input and an analogous random road input, are described. The definition of the optimum preview function, and its consequent effects on performance, receives attention and an example is given.