Topics in Automotive Rollover Prevention: Robust and Adaptive Switching Strategies for Estimation and Control

The main focus in this thesis is the analysis of alternative approaches for estimation and control of automotive vehicles based on sound theoretical principles. Of particular importance is the problem rollover prevention, which is an important problem plaguing vehicles with a high center of gravity (CG). Vehicle rollover is, statistically, the most dangerous accident type, and it is difficult to prevent it due to the time varying nature of the problem. Therefore, a major objective of the thesis is to develop the necessary theoretical and practical tools for the estimation and control of rollover based on robust and adaptive techniques that are stable with respect to parameter variations. Given this background, we first consider an implementation of the multiple model switching and tuning (MMST) algorithm for estimating the unknown parameters of automotive vehicles relevant to the roll and the lateral dynamics including the position of CG. This results in high performance estimation of the CG as well as other time varying parameters, which can be used in tuning of the active safety controllers in real time. We then look into automotive rollover prevention control based on a robust stable control design methodology. As part of this we introduce a dynamic version of the load transfer ratio (LTR) as a rollover detection criterion and then design robust controllers that take into account uncertainty in the CG position. As the next step we refine the controllers by integrating them with the multiple model switched CG position estimation algorithm. This results in adaptive controllers with higher performance than the robust counterparts. In the second half of the thesis we analyze extensions of certain theoretical results with important implications for switched systems. First we obtain a non-Lyapunov stability result for a certain class of linear discrete time switched systems. Based on this result, we suggest switched controller synthesis procedures for two roll dynamics enhancement control applications. One control design approach is related to modifying the dynamical response characteristics of the automotive vehicle while guaranteeing the switching stability under parametric variations. The other control synthesis method aims to obtain transient free reference tracking of vehicle roll dynamics subject to parametric switching. In a later discussion, we consider a particular decentralized control design procedure based on vector Lyapunov functions for simultaneous, and structurally robust model reference tracking of both the lateral and the roll dynamics of automotive vehicles. We show that this controller design approach guarantees the closed loop stability subject to certain types of structural uncertainty. Finally, assuming a purely theoretical pitch, and motivated by the problems considered during the course of the thesis, we give new stability results on common Lyapunov solution (CLS) existence for two classes of switching linear systems; one is concerned with switching pair of systems in companion form and with interval uncertainty, and the other is concerned with switching pair of companion matrices with general inertia. For both problems we give easily verifiable spectral conditions that are sufficient for the CLS existence. For proving the second result we also obtain a certain generalization of the classical Kalman-Yacubovic-Popov lemma for matrices with general inertia

A methodology for the design of robust rollover prevention controllers for automotive vehicles: Part 1-Differential Braking

In this paper we apply recent results from robust control to the problem of rollover prevention in automotive vehicles. Specifically, we exploit the results of Pancake, Corless and Brockman, which provide controllers to robustly guarantee that the peak values of the performance outputs of an uncertain system do not exceed certain values. We introduce a new measure of performance for rollover prevention, the Load Transfer Ratio LTRd , and design differential-braking based rollover controllers to keep the value of this quantity below a certain level; we also obtain controllers which yield robustness to variations in vehicle speed. We present numerical simulations to demonstrate the efficacy of our controllers

Adaptive Rollover Prevention for Automotive Vehicles with Differential Braking

In this paper we present an adaptive controller implementation based on the multiple models, switching, and tuning (MMST) paradigm for preventing untripped rollover in automotive vehicles. Our approach relies on differential-braking to keep the value of the Load Transfer Ratio (LTR) below a threshold. We first employ multiple models to infer the unknown center of gravity height and the suspension parameters of the vehicle, which are subsequently used to switch to the corresponding rollover controller. The proposed multicontroller switched scheme is shown via numerical simulations to result in better performance than its fixed robust counterpart

A methodology for the design of robust rollover prevention controllers for automotive vehicles: Part 2-Active steering

In this paper we apply recent results from robust control to the problem of rollover prevention in automotive vehicles. Specifically, we exploit the results of Pancake, Corless and Brockman, which provide controllers to robustly guarantee that the peak magnitudes of the performance outputs of an uncertain system do not exceed certain values.We use the dynamic Load Transfer Ratio LTRd as a performance output for rollover prevention, and design active-steering based rollover controllers to keep the magnitude of this quantity below a certain level, while we use control input u as an additional performance output to limit the maximum amount of control effort. We present numerical simulations to demonstrate the efficacy of our controllers

On the Kalman-Yakubovich-Popov lemma and common Lyapunov solutions for matrices with regular inertia

In this paper we extend the classical Lefschetz version of the Kalman-Yacubovich-Popov (KYP) lemma to the case of matrices with general regular inertia. We then use this result to derive an easily verifiable spectral condition for a pair of matrices with the same regular inertia to have a common Lyapunov solution (CLS), extending a recent result on CLS existence for pairs of Hurwitz matrices

General Inertia and Circle Criterion

In this paper we extend the well known Kalman-Yacubovic-Popov (KYP) lemma to the case of matrices with general regular inertia. We show that the version of the lemma that was derived for the case of pairs of stable matrices whose rank difference is one, extends to the more general case of matrices with regular inertia and in companion form. We then use this result to derive an easily verifiable spectral condition for a pair of matrices with the same regular inertia to have a common Lyapunov solution (CLS), extending a recent result on CLS existence for pairs of Hurwitz matrices that can be considered as a time-domain interpretation of the famous circle criterion

A global attractivity result for a class of switching discrete-time systems

In this paper we present the global attractivity properties of a class of discrete-time switching systems of the form x(k+1)=Aix(k), Ai A , {A1, ...,Am}, where each constituent matrices Ai Rnn are Schur stable. We show that for a special subset of such switching systems the origin is globally attractive, and it is possible to prove this without requiring the existence of a common quadratic Lyapunov function (CQLF)

On the quadratic stability of switched interval systems: Preliminary results

In this paper we present some preliminary results on the quadratic stability of switched systems with uncertain parameters. We show that the quadratic stability of a class of switched uncertain systems may be readily verified using simple algebraic conditions. Examples are presented to demonstrate the efficacy of our techniques

Realtime Multiple-Model Estimation of Center of Gravity Position in Automotive Vehicles

In this paper we present a methodology based on multiple models and switching for realtime estimation of center of gravity (CG) position in automotive vehicles. The method utilizes well-known simple linear vehicle models for lateral and roll dynamics and assumes the availability of standard stock automotive sensors. We illustrate the technique with numerical simulations as well as with measured sensor data from an SUV vehicle. We also compare our estimation results with traditional linear-least squares estimators to show the efficacy of our technique. Finally, we give a simple application example for implementing the idea in automotive vehicles as a switch for rollover controller activation

Some results on quadratic stability of switched systems with interval uncertainty

In this paper we present some results on the quadratic stability of switched systems with uncertain parameters. We show that the quadratic stability of a class of switched uncertain systems may be readily veried using simple algebraic conditions