Design of Static Output Feedback and Structured Controllers for Active Suspension with Quarter-Car Model

This paper presents a method to design active suspension controllers for a 7-Degree-of-Freedom (DOF) full-car (FC) model from controllers designed with a 2-DOF quarter-car (QC) one. A linear quadratic regulator (LQR) with 7-DOF FC model has been widely used for active suspension control. However, it is too hard to implement the LQR in real vehicles because it requires so many state variables to be precisely measured and has so many elements to be implemented in the gain matrix of the LQR. To cope with the problem, a 2-DOF QC model describing vertical motions of sprung and unsprung masses is adopted for controller design. LQR designed with the QC model has a simpler structure and much smaller number of gain elements than that designed with the FC one. In this paper, several controllers for the FC model are derived from LQR designed with the QC model. These controllers can give equivalent or better performance than that designed with the FC model in terms of ride comfort. In order to use available sensor signals instead of using full-state feedback for active suspension control, LQ static output feedback (SOF) and linear quadratic Gaussian (LQG) controllers are designed with the QC model. From these controllers, observer-based controllers for the FC model are also derived. To verify the performance of the controllers for the FC model derived from LQR and LQ SOF ones designed with the QC model, frequency domain analysis is undertaken. From the analysis, it is confirmed that the controllers for the FC model derived from LQ and LQ SOF ones designed with the QC model can give equivalent performance to those designed with the FC one in terms of ride comfort.

Controlling Chaotic Vibrations of a Quarter-Car Model Excited by Road Surface Profile using Parametric Excitation.

Chaotic Vibrations are considered for a quarter-car model excited by the road surface profile. The equation of motion is obtained in the form of a classical Duffing equation and it is modeled with deliberate introduction of parametric excitation force term to enable us manipulate the behavior of the system. The equation of motion is solved using the Method of Multiple Scales. The steady-state solutions with and without the parametric excitation force term is investigated using NDSolve MathematicaTM Code and the nonlinear dynamical system’s analysis is by a study of the Bifurcations that are observed from the analysis of the trajectories, and the calculation of the Lyapunov. In making the system more strongly nonlinear the excitation amplitude value is artificially increased to various multiples of the actual value. Results show that the system’s response can be extremely sensitive to changes in the amplitude and the that chaos is evident as the system is made more nonlinear and that with the introduction of parametric excitation force term the system’s motion becomes periodic resulting in the elimination of chaos and the reduction in amplitude of vibration.

Application of Anti-Diagonal Averaging in Response Reconstruction

Response reconstruction is used to obtain accurate replication of vehicle structural responses of field recorded measurements in a laboratory environment, a crucial step in the process of Accelerated Destructive Testing (ADA). Response Reconstruction is cast as an inverse problem whereby an input signal is inferred to generate the desired outputs of a system. By casting the problem as an inverse problem we veer away from the familiarity of symmetry in physical systems since multiple inputs may generate the same output. We differ in our approach from standard force reconstruction problems in that the optimisation goal is the recreated output of the system. This alleviates the need for highly accurate inputs. We focus on offline non-causal linear regression methods to obtain input signals. A new windowing method called AntiDiagonal Averaging (ADA) is proposed to improve the regression techniques’ performance. ADA introduces overlaps within the predicted time signal windows and averages them. The newly proposed method is tested on a numerical quarter car model and shown to accurately reproduce the system’s outputs, which outperform related Finite Impulse Response (FIR) methods. In the nonlinear configuration of the numerical quarter car, ADA achieved a recreated output Mean Fit Function Error (MFFE) score of 0.40% compared to the next best performing FIR method, which generated a score of 4.89%. Similar performance was shown for the linear case.

Vibration Control of Quarter Car Model Using Modified PID Controller

The purpose of this research is to control a quarter car suspension system and also to reduce the fluctuated movement caused by passing thevehicle over road bump using modified PID (Proportional Integral and Derivative) controller. The proposed controller deals with dual loopfeedback signals instead of single feedback signal as in the conventional PID controller. The structure of the modified PID controller wascreated by moving the proportional and derivative actions in the feedback path while remaining the integral action in the forward path. Thus,high accuracy results were obtained. Firstly, modelling and simulation of linear passive suspension system for a quarter car system wasperformed using Matlab – Simulink software. Then the linear suspension system was activated and simulated by using an active hydraulicactuator to generate the necessary force which can be regulated and controlled by the proposed controller. The performance of whole systemhas been enhanced with a modified PID controller.

Design and comparisons of adaptive harmonic control for a quarter-car active suspension

Car suspensions have the job to keep the tires in contact with the road surface as much as possible, to deliver steering stability with good handling and to guarantee passenger comfort. Most modern vehicles have independent front suspension and many vehicles also have independent rear suspension. Independent suspensions are preferred instead of dependent suspensions for their better ride handling, stability, steering and comfort but they provide less overall strength and a complex design which increases the cost and maintenance expenses for such a suspension. For this reason, automotive engineers struggle to discover new suspension components or advanced control solutions. Taking a step forward in this direction, the paper presents in the beginning one of the well-known mathematical models of a quarter-car active suspension. The obtained model is then implemented in a MATLAB/Simulink simulation which compares multiple control solutions. The only feedback considered for each control algorithm is the measurement of the body acceleration. Among these investigated control algorithms is the adaptive harmonic control solution proposed by this paper. The controller generates a harmonic control signal with variable amplitude and frequency based on the body acceleration feedback. The comparison analysis shows that the proposed control solution demonstrates quite good potential, generating in some cases better results than the other control algorithms.

Applied Mechatronics: Designing a Sliding Mode Controller for Active Suspension System

The suspension system is referred to as the set of springs, shock absorbers, and linkages that connect the car to the wheel system. The main purpose of the suspension system is to provide comfort for the passengers, which is created by reducing the effects of road bumpiness. It is worth noting that reducing the effects of such vibrations also diminishes the noise and undesirable sound as well as the effects of fatigue on mechanical parts of the vehicle. Due to the importance of the abovementioned issues, the objective of this article is to reduce such vibrations on the car by implementing an active control method on the suspension system. For this purpose, a conventional first-order sliding mode controller has been designed for stochastic control of the quarter-car model. It is noteworthy that this controller has a significant ability to overcome the stochastic effects, uncertainty, and deal with nonlinear factors. To design a controller, the governing dynamical equation of the quarter-car system has been presented by considering the nonlinear terms in the springs and shock absorber, as well as taking into account the uncertainty factors in the system and the actuator. The design process of the sliding mode controller has been presented and its stability has been investigated in terms of the Lyapunov stability. In the current research, road surface variations are considered as Gaussian white noise. The dynamical system behavior for controlled and uncontrolled situations has been simulated and the extracted results have been presented. Besides, the effects of existing uncertainty in the suspension system and actuator have been evaluated and controller robustness has been checked. Also, the obtained quantitative and qualitative compressions have been presented. Moreover, the effect of controller parameters on the basin of attraction set and its extensiveness has been assessed. The achieved results have indicated the good performance and significant robustness of the designed controller to stabilize the suspension system and mitigate the effects of road bumpiness in the presence of uncertainty and noise factors.