Semi-Active Suspension Suboptimal Control Using Dynamic Programming of a Quarter Car Suspension System

2016 ◽  
Author(s):  
John Dye ◽  
Nathan BuchMueller ◽  
Hamid Lankarani
Keyword(s):  
Cost Function ◽  
Vehicle Dynamics ◽  
Ride Comfort ◽  
Active Suspension ◽  
Suboptimal Control ◽  
Damping Coefficient ◽  
Handling Characteristics ◽  
Car Suspension ◽  
Quarter Car ◽  
The Cost

Many modern vehicle control systems utilize automatic braking and torque control to enhance driver inputs for improved stability and deceleration performance of passenger cars. A semi-active suspension approach may allow changes to the suspension characteristics under various conditions or driver inputs during vehicle operation. Suspensions are increasingly using semi active components to enhance handling characteristics by electronically adjusting vehicle dynamics. The active style of adjustment includes modifying suspension parameters directly such as electronic damping rates. The type of controller is important to react or adjust dynamically to the nonlinear nature of suspension systems. An optimal controller is introduced in attempt to improve ride comfort or road handling capability by manipulating the damping coefficient for a given trajectory. A suboptimal approach is given by utilizing a type of receding horizon control. The cost function, as used by Savaresi, contains a bias parameter to shift focus between road holding and passenger comfort. A dynamic quarter car suspension model is presented for simulation of nonlinear vehicle dynamics. During simulation at a given time step, various control inputs are simulated for finite steps into the future. The control input that minimizes the cost function is selected and the simulation time is allowed to advance with that input. The model is simulated using parameters for a typical passenger car and a 100 millisecond update rate from the suboptimal controller. A road profile with a bump is simulated and its transients are analyzed. The suboptimal controller is compared to its purely mechanical realization with a fixed damping coefficient. It is shown when manipulating the cost function ride comfort is desired chassis accelerations are minimized and when maximum road holding is desired tire deflection is minimized.

Analysis of MR Damper for Quarter and Half Car Suspension Systems of a Roadway Vehicle

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
D.V.A.R. Sastry ◽  
K.V. Ramana ◽  
N.M. Rao ◽  
P. Pruthvi ◽  
D.U.V. Santhosh
Keyword(s):  
Ride Comfort ◽  
Silicone Oil ◽  
Active Vibration Control ◽  
Mr Damper ◽  
Active Suspension ◽  
Suspension System ◽  
Magnetorheological Damper ◽  
Car Suspension ◽  
Quarter Car ◽  
Spencer Model

Magnetorheological (MR) dampers are evolving as one of the most promising devices for semi-active vibration control of various dynamic systems. In this paper, the suspension system of a car using MR damper is analysed for 2DOF quarter car and 4DOF half car models and then compared with corresponding suspension system using passive damper for ride comfort and handling. Magnetorheological damper is fabricated using a MR fluid of Carbonyl iron powder and Silicone oil added with additive. Experiments are conducted to establish the behaviour of the MR damper and are used to validate Spencer model for MR damper. Further, using the validated Spencer model of MR damper, the quarter car and half car models of Vehicle Suspension system are simulated by implementing a semi-active suspension system for analysing the resulting displacement and acceleration in the car body. The ride comfort and vehicle handling performance of each specific vehicle model with passive suspension system are compared with corresponding semi-active suspension system. The simulation and analysis are carried out using MATLAB/SIMULINK.

Improvement on Ride Comfort of Quarter-Car Active Suspension System Using Linear Quadratic Regulator

2018 ◽  
pp. 431-441
Author(s):  
Sharifah Munawwarah Syed Mohd Putra ◽  
Fitri Yakub ◽  
Mohamed Sukri Mat Ali ◽  
Noor Fawazi Mohd Noor Rudin ◽  
Zainudin A. Rasid ◽  
...  
Keyword(s):  
Ride Comfort ◽  
Linear Quadratic Regulator ◽  
Active Suspension ◽  
Suspension System ◽  
Linear Quadratic ◽  
Quarter Car

A quarter-car suspension model for dynamic evaluations of an in-wheel electric vehicle

2017 ◽  
Vol 232 (9) ◽  
pp. 1139-1148 ◽  
Author(s):  
Ambarish Kulkarni ◽  
Sagheer A Ranjha ◽  
Ajay Kapoor
Keyword(s):  
Ride Comfort ◽  
Combustion Engine ◽  
Permanent Magnet Motor ◽  
Plot Analysis ◽  
Car Suspension ◽  
Switch Reluctance Motor ◽  
Suspension Dynamics ◽  
Quarter Car ◽  
Derived Design ◽  
Suspension Model

Electric vehicles (EVs) are an alternative architecture in the automotive industry that provide reduced emissions. This research has developed a switch reluctance motor (SRM) in-wheel drivetrain for an EV. SRM drivetrains are cheaper and do not use rare earth elements unlike a permanent magnet motor (PMM). Conversely, the in-wheel SRM has a drawback of an increased mass on the suspension when compared with an equivalent power output PMM drivetrain. This situation results in an increased mass at the wheels; hence, a suspension analysis is required. This paper discusses the suspension dynamics evaluated using a quarter-car simulation of an in-wheel SRM EV and compares it to the internal combustion engine (ICE) vehicle. The simulation used step loads derived design scenarios, namely (1) sprung, (2) unsprung and (3) driver’s seat. Further Bode plot analysis techniques were used to determine the ride comfort range for the developed EV.

scholarly journals Experimentally validated dynamic results of a relaxation-type quarter car suspension with an adjustable damper

2017 ◽  
Vol 36 (2) ◽  
pp. 148-159 ◽  
Author(s):  
AN Thite ◽  
F Coleman ◽  
M Doody ◽  
N Fisher
Keyword(s):  
Shock Absorber ◽  
Ride Comfort ◽  
Damping Ratio ◽  
Closed Form Solution ◽  
Nonlinear Function ◽  
Frequency Domain Analysis ◽  
Form Solution ◽  
Damping Coefficient ◽  
Design Stage ◽  
Quarter Car

Models of varying degree of sophistication are used in vehicle dynamic studies. For ride comfort, Kelvin–Voigt arrangement is preferred and for impact harshness analysis, a relaxation-type suspension model, Zener or Maxwell type is used. The nonconsideration of relaxation-type models in ride comfort studies can result in significant errors for frequencies below ∼30 Hz. The object of the paper is to show the influence of the series stiffness on the effective suspension damping both experimentally and numerically. A frequency domain analysis of two-degree of freedom Zener quarter car model is performed to find the complex relation between effective damping coefficient and the limiting value of damping ratio for a given series stiffness. The nonlinear relation between shock absorber damping and the natural frequencies is clearly illustrated. A novel four-post rig set-up is used to validate the results by measuring transmissibilities, giving damping ratios for varying shock absorber settings. A closed form solution, based on a simplified partial model, of optimal damping coefficient, which is a nonlinear function of stiffnesses, shows good agreement with numerical simulations of the complete system. The nonlinearities in shock absorbers also influence the outcome. These findings can be a great value at early design stage.

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

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8231
Author(s):  
Manbok Park ◽  
Seongjin Yim
Keyword(s):  
Output Feedback ◽  
Ride Comfort ◽  
Linear Quadratic Regulator ◽  
Active Suspension ◽  
Static Output Feedback ◽  
State Variables ◽  
Linear Quadratic ◽  
Suspension Control ◽  
Quarter Car ◽  
Static Output

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.

System Identification and Optimal Control of Half-Car Active Suspension System Using a Single Noisy IMU With Position Uncertainty

2017 ◽  
Author(s):  
Tamer Attia ◽  
Kevin Kochersberger ◽  
John Bird ◽  
Steve C. Southward
Keyword(s):  
System Identification ◽  
Channel Model ◽  
Ride Comfort ◽  
Active Suspension ◽  
Measurement Unit ◽  
Linear Quadratic ◽  
Position Uncertainty ◽  
Inertial Measurement ◽  
Handling Characteristics ◽  
Frequency Domain Methods

An active suspension based on Linear Quadratic Gaussian (LQG) optimal controller is an effective system for enhancing the ride comfort and handling characteristics of a vehicle. LQG requires a good plant model for success, and this may be difficult to extract using a single inertial measurement device in the presence of noise. This paper presents a method for estimating the vehicle states by measuring both the vehicle bounce and pitch accelerations using an Inertial Measurement Unit (IMU) with position uncertainty relative to the sprung mass center of gravity. Frequency domain methods are used for System Identification (SysId). The state estimation is based on channel-by-channel model estimation using uncorrelated random excitation which is applied to the front wheels, rear wheels, front actuator, and rear actuator. An anti-aliasing filter eliminates false response harmonics and a Kalman filter is used to estimate the current states of the actual plant and the LQR block for the full-states-feedback controller. The controllers and observer are implemented in simulation using a four degree-of-freedom half car linear model.

Application of Semi-Active Inerter in Semi-Active Suspensions Via Force Tracking

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Michael Z. Q. Chen ◽  
Yinlong Hu ◽  
Chanying Li ◽  
Guanrong Chen
Keyword(s):  
Active Control ◽  
Ride Comfort ◽  
Controller Design ◽  
Active Suspension ◽  
Damping Coefficient ◽  
Control Law ◽  
Control Force ◽  
Car Model ◽  
Force Tracking ◽  
Active Damper

This paper investigates the application of semi-active inerter in semi-active suspension. A semi-active inerter is defined as an inerter whose inertance can be adjusted within a finite bandwidth by online control actions. A force-tracking approach to designing semi-active suspension with a semi-active inerter and a semi-active damper is proposed in this paper. Two parts are required in the force-tracking strategy: a target active control law and a proper algorithm to adjust the inertance and the damping coefficient online to track the target active control law. The target active control law is derived based on the state-derivative feedback control methodology in the “reciprocal state-space” (RSS) framework, which has the advantage that it is straightforward to use the acceleration information in the controller design. The algorithm to adjust the inertance and the damping coefficient is to saturate the active control force between the maximal and the minimal achievable suspension forces of the semi-active suspension. Both a quarter-car model and a full-car model are considered in this paper. Simulation results demonstrate that the semi-active suspension with a semi-active inerter and a semi-active damper can track the target active control force much better than the conventional semi-active suspension (which only contains a semi-active damper) does. As a consequence, the overall performance in ride comfort, suspension deflection, and road holding is improved, which effectively demonstrates the necessity and the benefit of introducing semi-active inerter in vehicle suspension.

scholarly journals Optimal Control of an 8-DOF Vehicle Active Suspension System Using Kalman Observer

2008 ◽  
Vol 15 (5) ◽  
pp. 493-503 ◽  
Author(s):  
S. Hossein Sadati ◽  
Salar Malekzadeh ◽  
Masood Ghasemi
Keyword(s):  
Optimal Control ◽  
Ride Comfort ◽  
Active Suspension ◽  
Suspension System ◽  
The Body ◽  
Control Approach ◽  
Seat Suspension ◽  
Handling Characteristics ◽  
Road Profile ◽  
Passive Suspension System

In this paper, an 8-DOF model including driver seat dynamics, subjected to random road disturbances is used in order to investigate the advantage of active over conventional passive suspension system. Force actuators are mounted parallel to the body suspensions and the driver seat suspension. An optimal control approach is taken in the active suspension used in the vehicle. The performance index for the optimal control design is a quantification of both ride comfort and road handling. To simulate the real road profile condition, stochastic inputs are applied. Due to practical limitations, not all the states of the system required for the state-feedback controller are measurable, and hence must be estimated with an observer. In this paper, to have the best estimation, an optimal Kalman observer is used. The simulation results indicate that an optimal observer-based controller causes both excellent ride comfort and road handling characteristics.

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