Robust Gain-Scheduled Observer Design with Application to Vehicle State Estimation

Abstract

This dissertation develops an application of the state-of-the-art convex optimization algorithms to the vehicle state estimation problem. The main challenge in this field is that the time-varying uncertain parameters and nonlinearity are both contained in the vehicle dynamical models. In the automotive control systems products, the gain-scheduled control and estimation algorithms are widely used to deal with these difficult components. However, the tuning of the stable controller and observer parameters is a heuristic and time-consuming task. A vast amount of simulation and validation experiments have to be implemented to verify the performance of the algorithm. Sometimes, the trial-and-error cycle is inevitable. Therefore, an efficient gain-scheduled observer design methodology for both linear and nonlinear systems is the main topic of this dissertation.

First, the linear-parameter-varying (LPV) representation of the three degree-of-freedom (DOF) bicycle model is presented, where the longitudinal velocity and acceleration are treated as the online measurable time-varying parameters. The LPV design methodology overcomes some eminent drawbacks of the traditional gain scheduled design methods. In the LPV framework, the search of the globally convergent observer parameters are resorted to a semidefinite programming problem. It is also shown that some robust controller design methods can be applied to develop an optimal unstructured LPV observer.

Next, the LPV observer is extended to a gain-scheduled interval observer where the variation range of the uncertain cornering stiffness parameters is incorporated into the observer design. Instead of a single estimation curve for each state variable, the interval observer computes the lower and upper bounds of all the admissible values of the states in the presence of parametric uncertainty. For automotive active safety systems, this envelope provides an estimation of the worst case bounds for the critical vehicle state under uncertain road conditions.

Although the gain-scheduled interval observer directly takes the uncertain cornering stiffness parameters into consideration, the tire-road friction is a highly complex nonlinear phenomenon such that the linear observer is far from satisfactory in some extreme maneuvers. To further improve the performance of the estimation algorithm, a nonlinear observer design methodology is also developed for a class of differentiable Lipschitz continuous nonlinear systems. Since the nonlinear bicycle model also contains the time-varying parameters, the time invariant nonlinear observer is further augmented to a gain scheduled nonlinear observer.

The simulation results demonstrate the validity of the proposed gain-scheduled observer design to provide accurate and robust estimation of vehicle states, such as tire slip angles in the presence of time-varying parameters and nonlinearities.

All the vehicle state estimation algorithms proposed in this dissertation are verified by using the simulation data from CarSim, a commercial vehicle simulation software package. Additionally, all the observer design methodologies are formulated in a high-level systematic approach, which allow them to be applied to other systems.