Discrete Event Based Simulation and Control of Continuous Systems

ii This Thesis introduces the fundamentals and the theory of a new way to approximate differential equations applied to numerical integration and digital control. Replacing the classic time discretization with state quantization –an approximation approach already available in the literature – two new numerical integration methods are introduced. Due to this kind of discretization technique, the resulting simulation models are discrete event systems instead of a discrete time as in all classic numerical methods. This fact yields many practical advantages like an efficient sparsity exploitation and an important computational cost reduction in hybrid system simulation. From a theoretical point of view, it is shown that the methods can be analyzed as continuous systems with bounded perturbations and thus, stability, convergence and error bound properties are proven showing also some interesting advantages with respect to classic approaches. The application of the new first order method to the discretization of continuous controllers with the addition of an asynchronous sampling scheme allow to define a new digital control methodology in which the time discretization is ideally avoided. As a result, this new technique improves considerably the dynamic response of digital control systems, reduces the quantization effects, the computational costs and the information traffic between plant and controller. When it comes to theoretical properties, the new control scheme can ensure stability, convergence and error bound properties which can be applied to linear, non linear and time varying cases. Based on these properties, different design algorithms are also provided. i i