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

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.

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.

A viewpoint on observability and observer design for nonlinear systems.- Model-based observers for tire/road contact friction prediction.- Observer design for nonlinear oscillatory systems.- Transformation to state affine system and observer design.- On existence of extended observers for nonlinear discrete-time systems.- Stability analysis and observer design for nonlinear diffusion processes.- Nonlinear passive observer design for ships with adaptive wave filtering.- Nonlinear observer design for integration of DGPS and INS.- Variants of nonlinear normal form observer design.- Separation results for semiglobal stabilization of nonlinear systems via measurement feedback.- Observer-controller design for global tracking of nonholonomic systems.- A separation principle for a class of euler-lagrange systems.- High-gain observers in nonlinear feedback control.- Output-Feedback Control of stochastic nonlinear systems.- Output feedback control of food-chain systems.- Output feedback tracking control for ships.- Dynamic UCO controllers and semiglobal stabilization of uncertain nonminimum phase systems by output feedback.- Fault detection observer for a class of nonlinear systems.- Nonlinear observer for signal and parameter fault detection in ship propulsion control.- Nonlinear observers for fault detection and isolation.- Application of nonlinear observers to fault detection and isolation.- Innovation generation for bilinear systems with unknown inputs.- Synchronization through extended kalman filtering.- Nonlinear discrete-time observers for synchronization problems.- Chaos synchronization.

In order to develop a rollover prevention system, it is essential to have a reliable index that properly indicates real-time rollover danger during vehicle maneuvers. The existing rollover indices are mainly for un-tripped rollovers and have limitations in detecting tripped rollovers. This study introduces a general rollover index (GRI) for the detection of rollover in both tripped and un-tripped cases and also on flat and sloped roads. Based on the lateral load transfer ratio, the proposed index is analytically derived in terms of measurable vehicle parameters and state variables. The general rollover index considers both lateral and vertical road inputs and thus can indicate tripped rollovers in the instance of curbs, soft soil or bumps. Sensitivity analysis for the proposed index is also provided to evaluate the effects of different vehicle parameters and different state variables on tripped and un-tripped rollovers. The introduced index can be used not only for the development of active rollover prevention systems, but also for rollover analysis and design of vehicles. The performance of the introduced general rollover index is validated through simulations using a high-fidelity CarSim model for a SUV.

In the present work, nonlinear observer design using differential mean value (DMV) theorem is extended to the design of nonlinear unknown input observer. To address the unknown input, famous approach of decoupling the unknown input has been used. Here, by the use of differential mean value theorem, the problem of designing unknown input observer evolves as stabilization of linear parameter varying system. On the basis of Lyapunov approach, linear matrix inequality (LMI) conditions for the existence of such observer are derived. For nonlinear systems, large value of Lipschitz constant may render LMI infeasible. DMV theorem may address the issue by replacing Lipschitz constants with more refined constants of lesser magnitude. DMV theorem-based approach is shown to be less conservative compared to Lipschitz constant. The proposed approach is shown to be effective for both continuous and discrete time systems. For discrete time systems, unknown input recovery scheme is also presented. Extensive simulations are shown in the end for continuous time chaotic Chen system, discrete Lorenz chaotic system and flexible joint robot link system, to highlight the efficacy of proposed strategy.

This paper presents a novel mass-center-position (MCP) metric for vehicle rollover propensity detection. MCP is first determined by estimating the positions of the center of mass of one sprung mass and two unsprung masses with two switchable roll motion models, before and after tire lift-off. The roll motion information without saturation can then be provided through MCP continuously. Moreover, to detect completed rollover statues for both tripped and untripped rollovers, the criteria are derived from d’Alembert principle and moment balance conditions based on MCP. In addition to tire lift-off, three new rollover statues, rollover threshold, rollover occurrence, and vehicle jumping into air can be all identified by the proposed criteria. Compared with an existing rollover index, lateral load transfer ratio, the fishhook maneuver simulation results in CarSim® for an E-class SUV show that MCP metric can successfully predict the vehicle impending rollover without saturation for untripped rollovers. Tripped rollovers caused by a triangle road bump are also successfully detected in the simulation. Thus, MCP metric can be successfully applied for rollover propensity prediction.

Rollover index is an essential metric to detect vehicle rollover propensity, which is used to warn a driver or trigger an active rollover prevention system to perform corrective action. To give continuous and completed rollover information, this paper presents a novel rollover index based on a mass-center-position (MCP) metric. The MCP is first determined by estimating the positions of the center of mass of the vehicle, which consists of one sprung mass and two unsprung masses with two switchable roll motion models, before and after tire liftoff. The roll motion information can then be provided through the MCP continuously without saturation for both tripped and untripped rollovers. Moreover, to describe the completed rollover status, different criteria are derived from D'Alembert's principle and the moment balance conditions based on the MCP. In addition to tire liftoff, three new rollover statuses, “rollover threshold,” “rollover,” and vehicle jumping “in the air,” can be all identified by the proposed criteria. Furthermore, the sensitivity analysis is conducted on some key parameters, such as the sprung/unsprung masses and the height of the center of gravity, to validate the robustness of the proposed detection method. Compared with an existing representative rollover index, lateral load transfer ratio, the fishhook maneuver simulation results in CarSim for an electric vehicle show that the MCP metric can successfully predict vehicle impending rollover status continuously and completely for both untripped and tripped rollovers.

In this paper, the problem of designing a nonlinear unknown input observer (NIUO) for a general class of nonlinear systems in the presence of disturbances is addressed. This approach combined two criteria : the modified H∞ criterion and mean value theorem. The first criterion allows to solve the problem of unknown input observer design in the presence of disturbances. While the second is used to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients. A sufficient conditions for the existence of the unknown input observer is derived. The observer gains are obtained by solving the linear matrix inequality (LMI). The advantage of the proposed method is that no a priori assumption on the unknown input is required and also can be employed with a wider class of nonlinear systems. Performances of the proposed approach are shown through the application to a diesel engine model.

We consider the problem of estimating the state and unknown input for a large class of nonlinear systems subject to unknown exogenous inputs. The exogenous inputs themselves are modeled as being generated by a nonlinear system subject to unknown inputs. The nonlinearities considered in this work are characterized by multiplier matrices that include many commonly encountered nonlinearities. We obtain a linear matrix inequality (LMI), that, if feasible, provides the gains for an observer which results in certified $L$ 2 performance of the error dynamics associated with the observer. We also present conditions which guarantee that the $L$ 2 norm of the error can be made arbitrarily small and investigate conditions for feasibility of the proposed LMIs.

In present work, reduced order unknown input observer is designed for a class of discrete time nonlinear systems. In reduced order observer design, state estimates are developed only for those states which are not directly measured at the output. To proceed with the design, system dynamics is split into two sets, dynamics of the measured state variables and unknown state variables. Then discrete observer is designed for the second set i.e. unmeasured state variables. Unknown input part of the system dynamics is tackled using famous decoupling approach, because of which the state estimation error dynamics becomes independent of the unknown input. Equivalent representation for the nonlinear vector function is achieved using Differential Mean Value (DMV) theorem which is likely to give less conservative results in comparison to Lipschitz constant based approach. Application of DMV theorem leads the error dynamical system to evolve as Linear Parameter Varying (LPV) system, which is then analyzed using convexity principle. Finally, the Linear Matrix Inequality (LMI) condition is achieved which is solved for feasibility to obtain observer design matrices. Reconstruction of unknown input is also discussed, which has application in secure communication. To justify the proposed theoretical results, simulation results are presented for chaotic Lorenz system which is a member of addressed class of nonlinear systems.

A general class of MIMO non-linear systems with unknown inputs is considered with a view to observer synthesis. The particularity of this class of systems lies in the fact that the expression of the outputs depends on the unknown inputs. Different situations are considered, and in each case, a non-linear observer, synthesised under appropriate hypotheses, is proposed to jointly estimate all state variables together with the unknown inputs. Simulation results are given in order to highlight the performances of the proposed observers.

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A generalized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> observers design is proposed for linear systems with unknown inputs. It generalizes the existing results concerning the proportional observer (PO) design and the proportional integral observer (PIO) design. The approach is based on the solutions of the algebraic constraints obtained from the unbiasedness conditions of the estimation error. The observer design is obtained from the solutions of linear matrix inequalities (LMIs). A numerical example is given to illustrate our approach.

This article addresses the problem of state and unknown inputs (UIs) estimation for nonlinear systems with arbitrary relative degree with respect to the UIs. For this purpose, a novel nonlinear unknown input observer (UIO) is proposed, which is able to decouple the UIs by using the derivatives of the output signal. The error dynamics is attained by an exact handling and a factorization of its gradient to obtain a local polytopic representation suitable for input‐affine nonlinear systems. For that representation, a novel design condition based on convex optimization and linear matrix inequalities is proposed to exponentially stabilize the estimation error and to guarantee the validity of the proposed nonlinear UIO. Numerical simulations indicate the effectiveness of the proposed approach for different classes of nonlinear systems, for which the UIs could be totally decoupled from the state estimation.