Equation-based modelling and simulation of hybrid systems

Equation-based modelling of hybrid systems has to consider dynamical systems consisting of components with continuous and/or discrete behavior. The paper focuses on such systems under special consideration of systems with variable model structure. Some ideas are presented how a simulation of continuous and discrete phenomena can be handled correctly. The main process is a continuing alternation between continuous and discrete simulation phases, where in the discrete phase the changeover can be performed to a new model structure which is valid during the next continuous phase. The paper addresses the problem of finding a new valid model structure as a process within the discrete phase. This new valid model structure has to be found under consideration of the time history of the model's variables within the preceding continuous phase. To this end, the usage of the Linear Complementarity Problem (LCP) is proposed. After a definition of hybrid systems and the term model structure, different types of events - with and without influence on the model structure - are listed and properties of complementarity are presented. To find the correct switchover from continuous to discrete phase, so-called indicator functions are used. Contrariwise, to find the correct switchover from discrete to continuous phase, the LCP is applied. Some simulation results for an electromechanical system are presented shortly.