A feasible and stable distributed interactive control design in energy state space

Abstract

In this paper, we formulate for the first time an interactive input-output (I-O) distributed control problem in dynamic energy state space. The primary difficulty in distributed control problem by component i is finding consistent relations between control specifications on the output of interest y <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> and shared output variables by the neighboring components z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</inf> . The basic idea in the paper is to align these seemingly inconsistent objectives by imposing generalized Tellegen’s theorem conditions in energy state-space at the component interfaces. The shared variable z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</inf> is then shown to take on a physical meaning of power and the rate of change of reactive power. Using this modeling approach, we derive sufficient general conditions to guarantee that interconnected components form a feasible system. We elucidate steps to test whether the interconnected components will converge to an equilibrium. We show that the derived I-O feedback control stabilizes and regulates the outputs of interest by exchanging information about interaction variables between the neighboring components. Finally, we illustrate the first-of-its-kind combined feed-forward and feedback control in energy space capable of following an exogenous time-varying power reference by a controllable voltage source in an RLC circuit. Notably, the system is representative of inverter control of DC microgrids.