Rajesh Rajamani

Observers for Lipschitz nonlinear systems

This paper presents some fundamental insights into observer design for the class of Lipschitz nonlinear systems. The stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix. The correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented. These conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix. The eigenvalues have to be located sufficiently far out into the left half-plane, and the eigenvectors also have to be sufficiently well-conditioned for ensuring asymptotic stability. Based on these results, a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability.

Existence and design of observers for nonlinear systems: Relation to distance to unobservability

This paper presents a systematic design methodology and some fundamental insights into observer design for the class of Lipschitz nonlinear systems. The existence of an asymptotically stable observer is shown to be guaranteed when the distance to unobservability is larger than the Lipschitz constant of the nonlinear system. An analytical solution for the observer is provided in this case. A methodology for the use of a coordinate transformation is then developed so as to reduce the Lipschitz constant and increase the distance to unobservability in the new coordinates. The methodology is directly applicable to the important class of feedback linearizable systems. The developed theory is used successfully in the design of an observer for a flexible joint robotic system.

Development and Experimental Evaluation of a Slip Angle Estimator for Vehicle Stability Control

Real-time knowledge of the slip angle in a vehicle is useful in many active vehicle safety applications, including yaw stability control, rollover prevention, and lane departure avoidance. Sensors to measure slip angle, including two-antenna GPS systems and optical sensors, are too expensive for ordinary automotive applications. This paper develops a real-time algorithm for estimation of slip angle using inexpensive sensors normally available for yaw stability control applications. The algorithm utilizes a combination of model-based estimation and kinematics-based estimation. Compared with previously published results on slip angle estimation, this present paper compensates for the presence of road bank angle and variations in tire-road characteristics. The developed algorithm is evaluated through experimental tests on a Volvo XC90 sport utility vehicle. Detailed experimental results show that the developed system can reliably estimate slip angle for a variety of test maneuvers.

Model Predictive Multi-Objective Vehicular Adaptive Cruise Control

This paper presents a novel vehicular adaptive cruise control (ACC) system that can comprehensively address issues of tracking capability, fuel economy and driver desired response. A hierarchical control architecture is utilized in which a lower controller compensates for nonlinear vehicle dynamics and enables tracking of desired acceleration. The upper controller is synthesized under the framework of model predictive control (MPC) theory. A quadratic cost function is developed that considers the contradictions between minimal tracking error, low fuel consumption and accordance with driver dynamic car-following characteristics while driver longitudinal ride comfort, driver permissible tracking range and rear-end safety are formulated as linear constraints. Employing a constraint softening method to avoid computing infeasibility, an optimal control law is numerically calculated using a quadratic programming algorithm. Detailed simulations with a heavy duty truck show that the developed ACC system provides significant benefits in terms of fuel economy and tracking capability while at the same time also satisfying driver desired car following characteristics.

Algorithms for Real-Time Estimation of Individual Wheel Tire-Road Friction Coefficients

It is well recognized in the automotive research community that knowledge of the real-time tire-road friction coefficient can be extremely valuable for active safety applications, including traction control, yaw stability control and rollover prevention. Previous research results in literature have focused on the estimation of average tire-road friction coefficient for the entire vehicle. This paper explores the development of algorithms for reliable estimation of independent friction coefficients at each individual wheel of the vehicle. Three different observers are developed for the estimation of slip ratios and longitudinal tire forces, based on the types of sensors available. After estimation of slip ratio and tire force, the friction coefficient is identified using a recursive least-squares parameter identification formulation. The observers include one that utilizes engine torque, brake torque, and GPS measurements, one that utilizes torque measurements and an accelerometer and one that utilizes GPS measurements and an accelerometer. The developed algorithms are first evaluated in simulation and then evaluated experimentally on a Volvo XC90 sport utility vehicle. Experimental results demonstrate the feasibility of estimating friction coefficients at the individual wheels reliably and quickly. The sensitivities of the observers to changes in vehicle parameters are evaluated and comparisons of robustness of the observers are provided.

Adaptive observers for active automotive suspensions: theory and experiment

An adaptive observer is developed for a class of nonlinear systems. Conditions for convergence of state and parameter estimates are presented. The developed theory is used for observer-based parameter identification in the active suspension system of an automobile. A realistic model of the suspension system incorporating the dynamics of the hydraulic actuator is used. The observer is used to adapt on dry friction which is usually present in significant magnitudes in hydraulic actuators. The observer can also be used to adapt on spring stiffnesses, viscous damping and hydraulic bulk modulus. A special adaptive observer is proposed for identification of the sprung mass of the automobile. Since the sprung mass depends on the number of passengers and the load on the automobile, it needs to be regularly updated. The adaptive observers use measurements from two accelerometers and an LVDT. They yield good experimental performance when implemented on a half-car suspension test rig. >

AN EXPERIMENTAL COMPARATIVE STUDY OF AUTONOMOUS AND CO-OPERATIVE VEHICLE-FOLLOWER CONTROL SYSTEMS

Abstract This paper is a comparative study of the performance of constant-time-gap autonomous control systems and co-operative longitudinal control systems that use inter-vehicle communication. Analytical results show that the minimum time gap that can be achieved in autonomous control is limited by the bandwidth of the internal dynamics of the vehicle. Experimental results from typical sensors and actuators are used to show that in practice it is very difficult to achieve a time gap less than 1 s with autonomous vehicle following. This translates to an inter-vehicle spacing of 30 m at highway speeds and a theoretical maximum traffic flow of about 3000 vehicles per hour. The quality of radar range and range rate measurements pose limitations on the spacing accuracy and ride quality that can be achieved in autonomous control. Dramatic improvements in the trade-off between ride quality and spacing accuracy can be obtained merely by replacing radar range rate in the autonomous control algorithm with the difference between the measured velocities of the two cars (a rudimentary form of co-operation). As a baseline comparison, the experimental performance of fully co-operative control is presented. An inter-vehicle spacing of 6.5 m is maintained in a platoon of 8 co-operative vehicles with an excellent ride quality and an accuracy of ±20 cm. Extending this to a 10-vehicle platoon makes it possible to achieve theoretical maximum traffic flows of about 6400 vehicles per hour. Another issue of importance addressed in the paper is the need to accommodate malfunctions in radar (ranging sensor) measurements. Measurement errors can occur due to hardware malfunctions as well as due to road curves, grades and the highway environment in the case of large inter-vehicle spacing. The ability of a co-operative control system to monitor the health of the radar and correct for such errors and malfunctions is demonstrated experimentally.

Flexible solid-state paper based carbon nanotube supercapacitor

This paper presents a flexible solid-state supercapacitor of high energy density. The electrodes of the supercapacitor are made of porous and absorbent cotton paper coated with single-wall carbon nanotubes. To ensure all solid-state configuration, a solid-state polymer-based electrolyte (poly (vinyl alcohol)/phosphoric acid) is used. The as-fabricated supercapacitor can be charged to over 3 V. It has high specific capacitance and high energy density of 115.8301 F/g carbon and 48.8587 Wh/kg carbon. Its performance is comparable to that of commercial supercapacitors, which need to utilize liquid electrolytes. Flexible solid-state supercapacitors offer several significant advantages for use in hybrid electric vehicles.

Friction estimation on highway vehicles using longitudinal measurements

This paper develops a real-time tire-road friction coefficient measurement system that can reliably distinguish between different road surface friction levels and quickly detect abrupt changes in friction coefficient. The measurement system relies on the use of differential GPS and utilizes a nonlinear longitudinal tire force model. Compared to previously published results in literature, the advantage of the system developed in this paper is that it is applicable during both vehicle acceleration and braking and works reliably for a wide range of slip ratios, including high slip conditions. The system can be utilized on front/rear-wheel drive as well as all-wheel drive vehicles. Extensive results are presented from experimental results conducted on various surfaces with a winter maintenance vehicle called the SAFEPLOW. The experimental results show that the system performs reliably and quickly in estimating friction coefficient on different road surfaces during various vehicle maneuvers. The developed friction measurement system has many applications in vehicle safety systems such as ABS, skid control and collision avoidance systems and is also useful for winter maintenance vehicles in which knowledge of the friction coefficient can be used to determine the amount and type of deicing chemicals to be applied to a winter roadway.

Model predictive control of transitional maneuvers for adaptive cruise control vehicles

In this paper, model predictive control (MPC) is used to compute the spacing-control laws for transitional maneuvers (TMs) of vehicles equipped with adaptive cruise control (ACC) systems. A TM is required, for example, to establish a steady-state following distance behind a newly encountered vehicle traveling with a slower velocity. These spacing-control laws are computed by formulating the objective of a TM as an optimal control problem (OCP). The steady-state following distance, collision avoidance, and acceleration limits of the ACC vehicle are incorporated into the OCP as constraints. The spacing-control laws are then obtained by solving this constrained OCP by using a receding-horizon approach, where the acceleration command computed at each sampling instant is a function of the current measurements of range and range rate. A baseline scenario requiring a TM is used to evaluate and compare the performance of the MPC algorithm and the standard constant time gap (CTG) algorithm. The simulation results show that the ACC vehicle is able to perform the TM of the baseline scenario using the MPC spacing-control laws, whereas the ACC vehicle is unable to perform this TM using the CTG spacing-control laws. The success of the MPC spacing-control laws is shown to depend on whether collision avoidance and the acceleration limits of the ACC vehicle are explicitly incorporated into the formulation of the control algorithm.