A computational model of time for stiff hybrid systems applied to control synthesis

Abstract

Computation has quickly become of paramount importance in the design of engineered systems, both to support their features as well as their design. Tool support for high-level modeling formalisms has endowed design specifications with executable semantics. Such specifications typically include not only discrete-time and discrete-event behavior, but also continuous-time behavior that is stiff from a numerical integration perspective. The resulting stiff hybrid dynamic systems necessitate variable-step solvers to simulate the continuous-time behavior as well as solver algorithms for the simulation of discrete-time and discrete-event behavior. The combined solvers rely on complex computer code which makes it difficult to directly solve design tasks with the executable specifications. To further leverage the executable specifications in design, this work aims to formalize the semantics of stiff hybrid dynamic systems at a declarative level by removing implementation detail and only retaining ‘what’ the computer code does and not ‘how’ it does it. A stream-based approach is adopted to formalize variable-step solver semantics and to establish a computational model of time that supports discrete-time and discrete-event behavior. The corresponding declarative formalization is amenable to computational methods and it is shown how model checking can automatically generate, or synthesize, a feedforward control strategy for a stiff hybrid dynamic system. Specifically, a stamper in a surface mount device is controlled to maintain a low acceleration of the stamped component for a prescribed minimum duration of time.