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Dynamic game theory brings together different features that are keys to many situations in control design: optimization behavior, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely, the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degree of freedom (DOF) vehicle handling performance model is put into discrete form to develop the game equations of motion.

A graphical user interface (GUI) toolbox called Vehicle System Simulator (VSS) is developed in MATLAB to ease the use of this vehicle model and hopefully encourage its widespread application in the future. This toolbox uses the inherent MATLAB discrete-time solvers and is mainly based on Level-2 s-function design. This paper describes its built-in vehicle dynamics model based on multibody dynamics approach and nonlinear tire models, and traction/braking control systems including Cruise Control and Differential Braking systems. The built-in dynamics model is validated against CarSim 8 and the simulation results prove its accuracy. This paper illustrates the application of this new MATLAB toolbox called Vehicle System Simulator and discusses its development process, limitations, and future improvements.

Vehicle stability is maintained by proper interactions between the driver and vehicle stability control system. While driver describes the desired target path by commanding steering angle and acceleration/deceleration rates, vehicle stability controller tends to stabilize higher dynamics of the vehicle by correcting longitudinal, lateral, and roll accelerations. In this paper, a finite-horizon optimal solution to vehicle stability control is introduced in the presence of driver's dynamical decision making structure. The proposed concept is inspired by Nash strategy for exactly known systems with more than two players, in which driver, commanding steering wheel angle, and vehicle stability controller, applying compensated yaw moment through differential braking strategy, are defined as the dynamic players of the 2-player differential linear quadratic game.

This work pertains to laboratory testing of truck cab suspensions for the purpose of improving in-cab ride quality. It describes the testing procedure of a complete truck cab suspension while still being mounted on the vehicle. It allows for testing with minimal amount of resources, limited to two mobile actuators and minimal modifications to the stock vehicle. The actuators can be attached to any axle through a set of modified brake drums and excite the drive axle in a vertical plane. The excitation signal sent to the actuators can be in phase for a heave type motion or out of phase for a roll motion. The chassis shock absorbers are replaced with rigid links to prevent the actuator input from becoming filtered by the primary suspension. This allows the input to reach the cab suspension more directly and the cab to be excited across a broader range of frequencies.

This study pertains to motion control algorithms using statistical calculations based on relative displacement measurements, in particular where the rattle space is strictly limited by fixed end-stops and a load leveling system that allows for roll to go undetected by the sensors. One such application is the cab suspension of semi trucks that use widely-spaced springs and dampers and a load leveling system that is placed between the suspensions, near the center line of the cab. In such systems it is possible for the suspension on the two sides of the vehicle to settle at different ride heights due to uneven loading or the crown of the road. This paper will compare the use of two moving average signals (one positive and one negative) to the use of one root mean square (RMS) signal, all calculated based on the relative displacement measurement.

In this paper a yaw stability control algorithm along with an emergency roll control strategy have been developed. The yaw stability controller and emergency roll controller were both developed using linear two degree-of-freedom vehicle models. The yaw stability controller is based on Lyapunov stability criteria and uses vehicle lateral acceleration and yaw rate measurements to calculate the corrective yaw moment required to stabilize the vehicle yaw motion. The corrective yaw moment is then applied by means of a differential braking strategy in which one wheel is selected to be braked with appropriate brake torque applied. The emergency roll control strategy is based on a rollover coefficient related to vehicle static stability factor. The emergency roll control strategy utilizes vehicle lateral acceleration measurements to calculate the roll coefficient. If the roll coefficient exceeds some predetermined threshold value the emergency roll control strategy will deploy.

A detailed study of the effects of shim stack assemblies on performance of hydraulic mono-tube vehicle shock absorbers is presented. Currently, shim stacks are modeled as blow-off valves in hydraulic models of shock absorbers. Using this simplification, important material and geometrical properties of shim stacks cannot be studied and their effects cannot be understood on overall damper performance. In this paper, shim stack deflection is investigated and a mathematical model is presented for shim stack deflection. This model is then incorporated into the mathematical model of a hydraulic damper and various properties of shim stack and their effects on damper characteristics are studied. Energy and variational methods were used to develop the mathematical model of the shim stack. The mathematical model also takes into account the sliding effects of the shims on each other when the shim stack is deflected.

Inerters have become a hot topic in recent years, especially in vehicle, train, and building suspension systems. The performance of a passive inerter and a semi-active inerter was analyzed and compared with each other and it showed that the semi-active inerter has much better performance than the passive inerter, especially with the Hybrid control method. Eight different layouts of suspensions were analyzed with a quarter car model in this paper. The adaptation of dimensionless parameters was considered for a semi-active suspension and the semi-active inerters. The performance of the semi-active inerter suspensions with different layouts was compared with a semi-active suspension with a conventional parallel spring-damper arrangement. It shows a semi-active suspension, with more simple configuration and lower cost, has similar or better compromise between ride and handling than a semi-active inerter with the Hybrid control.

The performance of five different skyhook control methods is studied experimentally, using a quarter-car rig. The control methods that are analyzed include: skyhook control, groundhook control, hybrid control, displacement skyhook, and relative displacement skyhook. Upon evaluating the performance of each method in frequency domain for various control conditions, they are compared with each other as well as with passive damping. The results indicate that no one control method outperforms other control methods at both the sprung and unsprung mass natural frequencies. Each method can perform better than the other control methods in some respect. Hybrid control, however, comes close to providing the best compromise between different dynamic demands on a primary suspension. The results indicate that hybrid control can offer benefits to both the sprung and unsprung mass with control gain settings that provide equal contributions from skyhook control and groundhook control.

Skyhook control has been used extensively for semiactive dampers for a variety of applications, most widely for passenger vehicle suspensions. This paper provides an experimental evaluation of how well skyhook control works for improving roll stability of a passenger vehicle. After discussing the formulation for various semiactive control methods that have been suggested in the past for vehicle suspensions, the paper includes the implementation of a semiactive system with magneto-rheological (MR) dampers on a sport utility vehicle. The vehicle is used for a series of road tests that includes lane change maneuvers, with different types of suspensions. The suspensions that are tested include the stock suspension, the uncontrolled MR dampers, skyhook control, and a new semiactive control method called “SIA skyhook.” The SIA Skyhook augments the conventional skyhook control with steering input, in order to account for the suspension requirements during a lateral maneuver.

This paper studies the effect of different longitudinal load conditions, roundabout cross-sectional geometry, and different semi-truck pneumatic suspension systems on roll stability in roundabouts, which have become more and more popular in urban settings. Roundabouts are commonly designed in their size and form to accommodate articulated heavy vehicles (AHVs) by evaluating such affects as off-tracking. However, the effect of the roadway geometry in roundabouts on the roll dynamics of semi-tractors and trailers are equally important, along with their entry and exit configuration. , Because the effect of the roundabout on the dynamics of trucks is further removed from the immediate issues considered by roadway planner, at times they are not given as much consideration as other roadway design factors.

Magneto-rheological fluid squeeze mode investigations at CVeSS have shown that MR fluids show large force capabilities in squeeze mode. A novel MR squeeze mount was designed and built at CVeSS, and a dynamic mathematical model was developed, which considered the inertial effect and was validated by the test data. A variant engine mount that will be used for isolating vibration, based on the MR squeeze mode is proposed in the paper. The mathematical governing equations of the mount are derived to account for its operation with MR squeeze mode. The design method of a robust H✓ controller is addressed for the squeeze mount subject to parameter uncertainties in the damping and stiffness. The controller parameter can be derived from the solution of bilinear matrix inequalities (BMIs). The displacement transmissibility is constrained to be no more than 1.05 with this robust H✓ controller. The MR squeeze mount has a very large range of force used to isolate the vibration.

Dynamic “Game Theory” brings together different features that are keys to many situations in control design: optimization behavior, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In previous studies, it was shown that vehicle stability can be represented by a cooperative dynamic/difference game such that its two agents (players), namely, the driver and the vehicle stability controller (VSC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the VSC command is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degree of freedom (DOF) vehicle handling performance model is put into discrete form to develop the game equations of motion. This study focus on the uncertainty in the inputs, and more specifically, the driver's steering input.

This paper provides a simulation analysis of a novel interconnected roll stability control (RSC) system for improving the roll stability of semitrucks with double trailers. Different from conventional RSC systems where each trailer’s RSC module operates independently, the studied interconnected RSC system allows the two trailers’ RSC systems to communicate with each other. As such, if one trailer’s RSC activates, the other one is also activated to assist in further scrubbing speed or intervening sooner. Simulations are performed using a multi-body vehicle dynamics model that is developed in TruckSim® and coupled with the RSC model established in Simulink®. The dynamic model is validated using track test data. The simulation results for a ramp steer maneuver (RSM) and sine-with-dwell (SWD) maneuver indicate that the proposed RSC system reduces lateral acceleration and rollover index for both trailers, decreasing the likelihood of wheel tip-up and vehicle rollover.

This paper presents the results of a study on the effect of truck configurations on the roll stability of commercial trucks in roundabouts that are commonly used in urban settings with increasing frequency. The special geometric layout of roundabouts can increase the risk of rollover in high-CG vehicles, even at low speeds. Relatively few in-depth studies have been conducted on rollover stability of commercial trucks in roundabouts. This study uses a commercially available software, TruckSim®, to perform simulations on four truck configurations, including a single-unit truck, a WB-67 semi-truck, the combination of a tractor with double 28-ft trailers, and the combination of a tractor with double 40-ft trailers. A single-lane and multilane roundabout are modeled, both with a truck apron. Three travel movements through the roundabouts are considered, including right turn, through-movement, and left turn.