A Phase-Shaping Approach to the Control of Parametric Systems and Its Application

The robust performance design of parametric systems is a long-standing unsolved problem, even though its analysis has seen significant success. Most existing design methods usually treat the parameter uncertainty as other types, such as norm-bounded uncertainty, and apply the corresponding approach. However, such treatment inevitably broadens the range of uncertainty and brings about design conservatism consequentially. To overcome such difficulty and establish a less conservative performance design method for parametric systems, this article looks back at the passivity theory and put forward a phase-shaping approach. This approach is composed of a generalized Popov transformation and a phase-shaping method for the nominal system. The key idea is to transform an uncertain but positive parameter into a positive real function while shaping the phase of the nominal system via a meta-heuristic method. This design freedom of phase shaping makes it possible to achieve a higher performance. Furthermore, this method is applied to the control design of drivetrain system: a test bed for automobile drivetrains. Its superiority is validated experimentally on an industrial setup.