Gridsada Phanomchoeng

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.

Nonlinear Observer for Bounded Jacobian Systems, With Applications to Automotive Slip Angle Estimation

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 that can directly measure slip angle are too expensive for ordinary automotive applications. This technical note develops a new nonlinear observer design technique for estimation of slip angle using inexpensive sensors normally available for yaw stability control applications. The approach utilized is to use the mean value theorem to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients. A modified form of the mean value theorem for vector nonlinear systems is presented. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can also enable observer design for a large class of differentiable nonlinear systems with a globally (or locally) bounded Jacobian. The developed nonlinear observer is evaluated through experimental tests on a Volvo XC90 sport utility vehicle. Detailed experimental results show that the developed nonlinear observer can reliably estimate slip angle for a variety of test maneuvers on road surfaces with different friction coefficients.

Tire-Road Friction-Coefficient Estimation

Tire-road forces are crucial in vehicle dynamics and control because they are the only forces that a vehicle experiences from the ground. These forces significantly affect the lateral, longitudinal, yaw, and roll behavior of the vehicle. The maximum force that a tire can supply is determined by the maximum value of the tire-road friction coefficient for a given normal vertical load on the tire. For each tire, the normalized traction force p, alternatively called the coefficient of traction, is defined as VfI + F (1) where Fχ, Fψ and Fζ are the longitudinal, lateral, and normal, that is, vertical, forces acting on the tire. The objective of friction-coefficient estimation is to predict the maximum value of the normalized traction force p that each tire can provide. This value, which is called the tire-road friction coefficient μ, depends on the characteristics of the road surface. The value of μ varies between zero and one depending on the type of road surface under consideration, such as icy, snow covered, gravel, and dry asphalt.

Observer design for Lipschitz nonlinear systems using Riccati equations

This paper presents a new observer design technique for Lipschitz nonlinear systems. Necessary and sufficient conditions for existence of a stable observer gain are developed using a S-Procedure Lemma. The developed condition is expressed in terms of the existence of a solution to an Algebraic Riccati Equation in one variable. Thus, the need to solve Linear Matrix Inequalities in multiple variables is eliminated. The advantage of the developed approach is that it is significantly less conservative than other previously published results for Lipschitz systems. It yields a stable observer for larger Lipschitz constants than other techniques previously published in literature.

New Rollover Index for the Detection of Tripped and Untripped Rollovers

Accurate detection of the danger of an impending rollover is necessary in order to effectively use active vehicle rollover prevention. A real-time rollover index is an indicator used for this purpose. A traditional rollover index utilizes lateral acceleration measurements and can detect only untripped rollovers that happen due to high lateral acceleration from a sharp turn. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. Therefore, this paper develops a new rollover index that can detect both tripped and untripped rollovers. The new rollover index utilizes vertical accelerometers in addition to a lateral accelerometer and is able to predict rollover in spite of unknown external inputs acting on the system. The accuracy of the developed rollover index is evaluated through simulations with industry-standard software CARSIM and experimental tests on a one-eighth-scaled vehicle. In order to show that the scaled vehicle experiments can represent a full-sized vehicle, the Buckingham π theorem is used to show dynamic similarity. The simulation and experimental results show that the new rollover index can reliably detect both tripped and untripped rollovers.

Real-Time Estimation of Rollover Index for Tripped Rollovers With a Novel Unknown Input Nonlinear Observer

Accurate detection of the danger of an impending rollover is necessary for active vehicle rollover prevention systems. A real-time rollover index is an indicator used for this purpose. A traditional rollover index detects only untripped rollovers that happen due to high lateral acceleration from a sharp turn. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. Therefore, this paper develops a novel new rollover index that can detect both tripped and untripped rollovers. A methodology is developed for estimation of unknown inputs in a class of nonlinear systems. The methodology is based on the nonlinear observer design and dynamic model inversion to compute the unknown inputs from output measurements. The observer design utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time-varying coefficients. The observer gains are then obtained by solving linear matrix inequalities. The developed approach can enable observer design for a large class of differentiable nonlinear systems with a globally (or locally) bounded Jacobian. The developed nonlinear observer is then applied for rollover index estimation. The developed rollover index is also evaluated through simulations with an industry standard software, CARSIM, and with experimental tests on a 1/8th scaled vehicle. In order to verify that the scaled vehicle experiments can represent a full-sized vehicle, the Buckingham π theorem is used to show dynamic similarity. The simulation and experimental results show that the developed nonlinear observer can reliably estimate vehicle states, unknown normal tire forces, and rollover index for predicting both untripped and tripped rollovers.

The bounded Jacobian approach to nonlinear observer design

This paper presents a new observer design technique for a nonlinear system with a globally (or locally) bounded Jacobian. The approach utilized is to use the mean value theorem to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can enable observer design for a large class of differentiable nonlinear systems. Its advantage is that it enables easy observer design for a much wider range of operating conditions compared to linear or Lipschitz observer design methods. The use of the observer design technique is illustrated for estimation of vehicle roll angle in an automotive system involving a complex nonlinearity. The performance of the new observer is shown to be clearly superior to that of a standard Lipschitz observer.

Real-time estimation of rollover index for tripped rollovers with a novel unknown inputs nonlinear observer

In rollover prevention systems, a traditional rollover index can detect only un-tripped rollovers that happen due to high lateral acceleration from sharp turns. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. In order to develop a new rollover index that can detect both tripped and un-tripped rollovers, state estimation in the presence of unknown disturbance inputs is required. Therefore, this paper develops a methodology for estimation of unknown inputs in a class of nonlinear systems. The methodology is based on nonlinear observer design and dynamic model inversion to compute the unknown inputs from output measurements. The observer design utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can enable observer design for a large class of bounded Jacobian nonlinear systems with unknown inputs. The developed nonlinear observer is then applied for rollover index estimation. The developed rollover index is evaluated through simulations with an industry standard software, CARSIM, and with experimental tests on a 1/8th scaled vehicle. The simulation and experimental results show that the developed nonlinear observer can reliably estimate vehicle states, unknown normal tire forces, and rollover index for predicting both un-tripped and tripped rollovers.

Real-time automotive slip angle estimation with nonlinear observer

This paper utilizes a new nonlinear observer design technique for estimation of slip angle in automotive applications. Inexpensive sensors that measure yaw rate and lateral acceleration and are normally available for yaw stability control systems are used. The observer design approach utilizes the mean value theorem to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients. A modified form of the mean value theorem for vector nonlinear systems is presented. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach also can enable observer design for a large class of differentiable nonlinear systems with a globally (or locally) bounded Jacobian. The developed nonlinear observer is evaluated through experimental tests on a Volvo XC90 sport utility vehicle. Detailed experimental results show that the developed nonlinear observer can reliably estimate slip angle for a variety of test maneuvers on road surfaces with different friction coefficients.

New rollover index for detection of tripped and un-tripped rollovers

Accurate detection of the danger of an impending rollover is necessary for active vehicle rollover prevention. A real-time rollover index is an indicator used for this purpose. A traditional rollover index utilizes lateral acceleration measurements and can detect only un-tripped rollovers that happen due to high lateral acceleration from a sharp turn. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. Therefore, this paper develops a new rollover index that can detect both tripped and un-tripped rollovers. The new rollover index utilizes vertical accelerometers in addition to a lateral accelerometer and is able to predict rollover in spite of unknown external inputs acting on the system. The accuracy of the developed rollover index is evaluated with experimental tests on a 1/8th scaled vehicle. The experimental results show that the new rollover index can reliably detect both tripped and un-tripped rollovers.