Robust Control Methods with Applications to Steer-by-Wire Systems

Kurzfassung

This thesis includes mainly theoretical and methodological design contributions on robust control with applications to steer-by-wire vehicle systems. The main contributions are: 1) A complete mathematical paradigm based on singular frequencies is developed for the computation of the region in an affine parameter space where certain system properties such as stability are guaranteed. The essential advantage of the method is that non-convex regions are constructed using simple convex polyhedral slices. This approach is useful for solving the difficult problem of fixed order control. A widely spread controller of this art is PID. A software toolbox is developed for fast computation of robust stable regions in PID parameter space. 2) A two degree-of-freedom control structure for dynamic inversion and tracking tasks is introduced. The structure integrates the feedforward exact inversion and high-gain feedback principles. This structure is further extended for use in model reference control. In all cases, robust performance is provided due to the presence of the high-gain term. A mathematical framework is developed to guide the design of systems with imperfections. 3) Steer-by-wire control problems with uncertainties such as force feedback and road-wheel actuation, as well as the coupling of the two with respect to some given reference dynamics are addressed. A detailed robustness design and analysis of force feedback actuation with regard to uncertainties in the human operator bio-impedance is completed. Different steerby-wire representations (admittance, impedance, hybrid) are discussed and compared. Using the methods introduced in 1) and 2) several control structures providing model-matching and model-reference control for steer-by-wire are developed. Robustness analysis is performed in the parameter space constituted by relevant uncertain physical parameters. Therefore a method for mapping of positivity bounds of transfer function matrices in a low order parameter space is introduced.