Arie Verhoeven

Automatic Control for Adaptive Time Stepping in Circuit Simulation: Numerical Mathematics Applied to Electronics Arie Verhoeven

DAE-solvers are used to find the numerical solution of the transient analysis of electrical circuits. For onestep methods, the local truncation error only depends on the last stepsize, but for multistep methods, this error is also depends on previous stepsizes in a nonlinear way. Adaptive stepsize control and order control can be used to control these truncation errors. In connection with the articles of prof. S¨oderlind, the possibilities of a control-theoretic approach are investigated. For onestep methods, the stepsize control process can be viewed as a digital linear control system for the logarithms of the errors and steps. From a control-theoretic point of view, the goal is to keep the error close to a reference level with use of the stepsizes as input. If the stepsize control process is correctly modelled, a finite order digital linear controller can be designed. From the results, it appears that it is possible to design linear controllers that achieve better properties than the commonly used deadbeat- controllers.