Quarter-car Active Suspension Research Articles

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.

A Neural Network Sliding Controller for Active Vehicle Suspension

The hydraulic active suspension systems have certain nonlinear and time-varying behaviors. It is difficult to establish an appropriate dynamic model for model-based controller design. Here a novel neural network based sliding mode control is proposed by combining the advantages of the adaptive, radial basis function neural network and sliding mode control strategies to release the model information requirement. It has on-line learning ability for handling the system time-varying and nonlinear uncertainty behaviors by adjusting the neural network weightings and/or radial basis function parameters. It is implemented on a quarter-car hydraulic active suspension system. The experimental results show that this intelligent control approach effectively suppresses the oscillation amplitude of sprung mass in response to road surface disturbances.

RMS Values for Force, Stroke and Deflection in a Quarter-car Model Active Suspension with Preview

Summary In the case of a quarter-car vehicle model incorporating an active suspension, the addition of preview to the system necessitates finding new techniques for the direct computation of rms values for control force, suspension stroke and tyre deflection on a random road. Here we obtain these rms values from the performance index components as derived analytically by means of matrix operations requiring the solution of Lyapunov equations and the use of similarity transformations. Some numerical examples and MATLAB programs are included.

A Simplified Robust Circle Criterion Using the Sensitivity-Based Quantitative Feedback Theory Formulation

The circle criterion provides a sufficient condition for global asymptotic stability for a specific class of nonlinear systems, those consisting of the feedback interconnection of a single-input, single-output linear dynamic system and a static, sector-hounded nonlinearity. Previous authors (Wang et al, 1990) have noted the similarity between the graphical circle criterion and design bounds in the complex plane stemming from the Quantitative Feedback Theory (QFT) design methodology. The QFT formulation has specific advantages from the standpoint of controller synthesis. However, the aforementioned approach requires that plant uncertainty sets (i.e., “templates”) be manipulated in the complex plane. Recently, a modified formulation for the QFT linear robust performance and robust stability problem has been put forward in terms of sensitivity function bounds. This formulation admits a parametric inequality which is quadratic in the open loop transfer function magnitude, resulting in a computational simplification over the template-based approach. In addition, the methodology admits mixed parametric and nonparametric plant models. The disk inequality which results represents a much closer analog of the circle criterion, requiring only scaling and a real axis shift. This observation is developed in this paper, and the methodology is demonstrated in this paper via feedback design and parametric analysis of a quarter-car active suspension model with a sector nonlinearity.

A tunable fuzzy logic controller for vehicle-active suspension systems

A novel fuzzy-logic-based control for vehicle-active suspension is suggested. The vehicle vibration and disturbance are reduced considerably with a fuzzy logic controller, to enhance comfort in riding faced with uncertain road terrains. A quarter-car active suspension system is controlled to reduce the vertical acceleration to a level of, that of, a hypothetical reference model. A new look-up table for the rule base of the fuzzy logic controller has been developed. The parameters, like, the spread, flex and centre of the bell-shaped membership functions associated with the different linguistic variables are fine tuned by trial and error method to get the suspension acceleration and deflection on par with that of the model. Simulation studies clearly demonstrate the effectiveness of the fuzzy logic controller for active suspension systems. The performance of the fuzzy logic controller under variations in the suspension component characteristics are also studied and was found to give reasonably good responses.

Application of Nonlinear Control Theory to Electronically Controlled Suspensions

SUMMARY This paper illustrates the use of nonlinear control theory for designing electro-hydraulic active suspensions. A nonlinear, “sliding” control law is developed and compared with the linear control of a quarter-car active suspension system acting under the effects of coulomb friction. A comparison will also be made with a passive quarter-car suspension system. Simulation and experimental results show that nonlinear control performs better than PID control and improves the ride quality compared to a passive suspension.

Robust Linear-Optimal Control Laws for Active Suspension Systems

The stability robustness of linear-optimal control laws for quarter-car active suspension systems is evaluated using stochastic robustness analysis. Simultaneous parameters variations and neglected actuator and sensor dynamics are considered for LQ active suspension systems and for a single-measurement LQG system to determine the effects of uncertainty on system stability. The results indicate that neglected actuator and sensor dynamics have a small effect on stability robustness, while parameter uncertainty, particularly that of the “sprung mass” is of great concern. The effectiveness of Loop Transfer Recovery on active suspension systems with both parameter uncertainty and higher-order uncertainty is discerned. The analysis shows that when Loop Transfer Recovery is applied arbitrarily to uncertain systems, both estimator performance and system robustness can decrease. Nevertheless, it is concluded that the impact of the robustness recovery method is determined by stochastic stability robustness analysis, and the recovery design parameter that provides sufficient robustness with minimal performance degradation is readily identified. The effect of LQ design parameters on robustness also is considered. The paper presents robustness analysis and synthesis methods for a quarter-car model that can be applied to higher-order active suspension systems.

The Influence of Tire Damping in Quarter Car Active Suspension Models

Setting tire damping to zero when modeling automotive active suspension systems compels the misleading conclusions that, at the wheelhop frequency, no matter what forces are exerted between sprung and unsprung masses, their motion are uncoupled, and the vertical acceleration of the sprung mass will be unaffected. Alternatively, taking tire damping to be small but nonzero, the motions of the sprung and unsprung masses are coupled at all frequencies, and control forces can be used to reduce the sprung mass vertical acceleration at the wheelhop frequency. The effect of introducing tire damping can be quite large. In the case of a force law chosen to enhance ride along a straight smooth road, where road holding is not a major concern, setting the tire damping ratio to 0.02 reduces rms body acceleration by 30 percent.