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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.

Race teams frequently use tools like shock dynamometers (dynos) to characterize the complex behavior of shock absorbers after they are built and before they are put on the race car for testing to make sure they perform as expected. One way to make use of this shock dyno data is to use it to create a model to predict shock absorber performance over a wide range of inputs. These shock models can then be integrated into vehicle simulations to predict how the vehicle will respond to different shock selections, and aid the race engineer to narrow down possible shock setups before track testing. This paper develops an intuitive nonlinear dynamic shock absorber model that can be quickly fit to experimental data and implemented in simulation studies. Unlike other existing dynamic race shock models, it does not suffer from the complexity of modeling complex physical behavior, or the inefficiencies of unstructured black-box modeling.

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.

This paper presents a parametric study of two semiactive adaptive control algorithms through simulation: the non-model based skyhook control, and the newly developed model-based nonlinear adaptive vibration control. This study includes discussion of suspension model setup, dynamic analysis approach, and controller tuning. The simulation setup is from a heavy-duty truck seat suspension with a magneto-rheological (MR) damper. The dynamic analysis is performed in the time domain using sine sweep excitations without the need to linearize such a nonlinear semiactive system that is studied here. Through simulation, the effectiveness of both control algorithms is demonstrated for vibration isolation. The computation flops of the simulation in the SIMULINK environment are compared, and the adaptability is studied with respect to plant variations and different excitation profiles, both of which come across typically for vehicle suspension systems.

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.

A comprehensive comparison between an air-inflated seat cushion designed for truck seats and a commonly used foam cushion is provided, using a single-axis test rig designed for seat dynamic testing. Different types of tests were conducted in order to evaluate various aspects of each type of cushion; in terms of their response to narrowband (single frequency) dynamics, broadband input of the type that is commonly used in the trucking industry for testing seats, and a step input for assessing the damping characteristics of each cushion. The tests were conducted over a twelve-hour period—in four-hour intervals—measuring the changes that occur at the seat cushion over time and assessing how these changes can affect the metrics that are used for evaluating the cushions. The tests indicated a greater stiffening of the foam cushion over time, as compared with the air-inflated cushion that showed almost no change in stiffness when exposed to a static weight for twelve hours.

Two alternative methods are presented for studying the comfort, and possibly fatigue, effects of vehicle seats, in particular truck seats that include a seat suspension. The methods, named “aPcrms” and “SPD%” for the purpose of this study, are based on analyzing the pressure profile at the seat cushion/human body interface in a manner that accounts for the contact area, pressure distribution, and change in contact pressure. The alternative methods are compared with methods suggested in the past for vehicle seats, using a laboratory test rig and a truck seat with a conventional foam cushion and an air-inflated seat cushion. The results show that the proposed methods better highlight the human comfort differences between the two cushion types, and provide objective measures that better correlate with subjective measures from a separate field study on the same types of seats.

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 study reports the subjective results from a project investigating the effectiveness of several newly proposed metrics to compare fatigue performance between two distinct truck seat cushions, specifically standard foam versus air-inflated cushions. We also highlight some of the fundamental differences between air-inflated and foam seat cushion based on driver's perceptions. Road tests were performed using existing commercial trucks in the daily operations of Averitt Express. A retrofit air-inflated seat cushion was installed in the fleet's trucks, and the drivers were allowed to adjust to the seats over approximately one week. After this adjustment period, twelve drivers rode on both the air-inflated seat cushion and their original foam seat cushion during their regularly scheduled routes. Surveys were collected throughout the test sessions and the truck seats were fitted with instrumentation to capture physical measurements of seat pressure distribution.

This study provides an experimental account of the effect of panhard rod suspensions on heavy truck ride, as evaluated by the B-post vertical and fore-aft accelerations. After describing the test setup, the paper will describe the details of two rear cab suspensions that are commonly used in North American trucks. Cab suspensions with dampers or similar elements that are used to provide lateral forces at the rear of the cab (called “baseline” cab suspension for the purpose of this study) and those that use a lateral link with a torsion spring at one end-commonly called “panhard rod”-are the two classes of rear cab suspensions that are considered in this study. The tests are performed on a class 8 truck that is setup in the laboratory for the purpose of providing good test repeatability and conducting an accurate design of experiment. The test results, which are analyzed in frequency domain, are compared for the two cab suspensions.

Using a simulation model, this study intends to provide a preliminary evaluation of whether semiactive dampers are beneficial to improving ride and handling in class 8 trucks. One of the great challenges in designing a truck suspension system is maintaining a good balance between vehicle ride and handling. The suspension components are often designed with great care for handling, while maintaining good comfort. For Class 8 trucks, the vehicle comfort is also greatly affected by the cab and seat suspensions. Dampers for passive suspensions are tuned “optimally,” using various metrics that the ride engineer may consider, for the condition in which the truck operates most frequently. In recent years, the popularity of semiactive dampers in passenger vehicles has prompted the possibility of considering them for class 8 trucks. In this study, the vehicle safety versus ride comfort trade-off is studied for a certain class of suspensions with semiactive fuzzy control.

The close proximity of seat suspensions to human body presents several challenges in terms of the perception of the suspension forces by the vehicle operator. This is particularly true of the suspensions with time-varying forces, such as semiactive seat suspensions. The major challenge in such suspensions is changing the suspension force from one state to under, without causing excessive amounts of dynamic jerk. This paper looks into the cause of dynamic jerk in semiactive suspensions with skyhook control, and presents two alternative implementations of skyhook control, called “no-jerk skyhook,” and “skyhook function,” for the purpose of this study. An analysis of the relationship between absolute velocity of the sprung mass and the relative velocity across the suspension is used to show the damping force discontinuities that result from skyhook control.

This study reports the objective results from a project investigating the effectiveness of several newly proposed metrics to compare fatigue performance between two distinct truck seat cushions, specifically standard foam versus air-inflated cushions. The subjective results from this project have shown the drivers in our study prefer the air-inflated seat cushion over their normal foam cushion, and that air-inflated seat cushions provide advantages in terms of comfort, support, and fatigue [1]. This study aims to further explore the differences between these two different seat cushions by highlighting the differences in objective pressure distribution measurements. Road tests were performed using existing commercial trucks in the daily operations of Averitt Express. A retrofit air-inflated seat cushion was installed in the fleet's trucks, and the drivers were allowed to adjust to the seats over approximately one week.

The effect of primary suspensions (shock absorbers) on the body and axle motion of heavy trucks is investigated. A simulation program is used to show how damper tuning of conventional passive dampers and “skyhook” semiactive dampers effect ride, as measured by body acceleration, and axle motion, as measured by tire acceleration and tire deflection. Special attention is made to the coupling and interaction between the body and the axle motion. It is shown that passive and semiactive dampers have a different effect on the axle and body dynamics.

One popular complement to track testing that successful race teams use to better understand their vehicle's behavior is dynamic shaker rig testing. Compared to track testing, rig testing is more repeatable, costs less, and can be conducted around the clock. While rig testing certainly is an attractive option, an extensive number of tests may be required to find the best setup. To make better use of rig test time, more efficient testing methods are needed. One method to expedite rig testing is to use rig test data to generate a model of the experiment and then applying the model to identify potential gains for further rig study. This study develops the method at the quarter-car scale, using data from a quarter-car rig with a Penske 7300 shock absorber. The method is first validated using data generated from a known quarter-car model to assure the method can reproduce the original model behavior.

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.