Conic-sector-based analysis and control synthesis for linear parameter varying systems
For control engineers designing LPV systems, this provides a less conservative stability analysis and synthesis method by allowing temporary operation outside conic regions.
The paper extends the conic sector theorem to LPV systems that violate conicity for certain parameter values, enabling stability analysis and controller design that allow brief operation in nonconic regions. This reduces conservatism compared to traditional designs, demonstrated by stabilizing a power grid with high renewable penetration while minimizing transmission losses.
We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We show that such LPV systems can be defined to be conic in an average sense if the parameter trajectories are restricted so that the system operates with such values of the parameter sufficiently rarely. We then show that such an average definition of conicity is useful in analyzing the stability of the system when it is connected in feedback with a conic system with appropriate conic properties. This can be regarded as an extension of the classical conic sector theorem. Based on this modified conic sector theorem, we design conic controllers that allow the closed-loop system to operate in nonconic parameter regions for brief periods of time. Due to this extra degree of freedom, these controllers lead to less conservative performance than traditional designs, in which the controller parameters are chosen based on the largest cone that the plant dynamics are contained in. We demonstrate the effectiveness of the proposed design in stabilizing a power grid with very high penetration of renewable energy while minimizing power transmission losses.