Robust Control Design of Electric Power Steering Systems

This thesis focuses on the modeling, analysis, robust stability and control performance of Electric power steering (EPS) systems as an emerging technology in the automotive industry with promising future. EPS systems offer many advantages such as ease of tuning for better steerability, modularity and environment friendliness over the more conventional hydraulic power steering technology, thus making them an attractive choice for future cars. An EPS system is a driver-assisting feedback system designed to boost the driver input torque to a desired output torque causing the steering action to be undertaken at much lower steering efforts. An electric power system is a very common human-machine interaction application. This interaction entails that the feedback control design guarantee safe operation under all conditions in the presence of inherent uncertainties in the system dynamics. Moreover, the lack of quantifiable control objectives makes the control design task unclear. Specifically, such metrics as the very subjective steering feel, comfort and safety are not readily expressible in physical quantities that could be used as the design objectives. An uncompromising requirement, however, is that the feedback control must maintain closed loop stability to ensure safe interaction between the human driver and the EPS system. The feedback control design of EPS systems employs a sector-bounded nonlinear gain known as the boost curve which sets the desired level of assist torque for a given vehicle velocity. Hence, in addition to model uncertainties and the human-arm impedance dynamics, the feedback controller has to account for the presence of the boost gain nonlinearity. Known for its unified approach to robust stability, the passivity framework offers a very general tool to handle different types of uncertainties. For this reason, control design satisfying a passivity constraint is used in this thesis to handle the uncertain driver muscle impedance dynamics as well as the boost gain nonlinearity. However, a major obstacle against passivity based control of EPS systems is that the vehicle force-impedance is not necessarily a passive environment. For this reason, a two-degree-of-freedom (2-DOF) linear controller is designed such that the first component of the controller introduces a desired phase compensation, while the second component passivates the vehicle force-impedance dynamics. This thesis involves two main optimization problems: parameter estimation of state space models with known structures and fixed-structure control design satisfying guaranteed cost H2 and Hinfinity, design objectives. These problems are solved using a new class of evolutionary algorithms known as hybrid genetic algorithms (GAs) which employ a standard GAs search along with a problem-specific optimization algorithm. This hybrid structure offers a very general algorithm to solve a large number optimization problems including non-convex problems, such as the fixed-structure control synthesis, which fail to be solved with the more conventional techniques.