In this paper we present the co-simulation of a PID class power converter
controller and an electrical circuit by means of the waveform relaxation
technique. The simulation of the controller model is characterized by a
fixed-time stepping scheme reflecting its digital implementation, whereas a
circuit simulation usually employs an adaptive time stepping scheme in order to
account for a wide range of time constants within the circuit model. In order
to maintain the characteristic of both models as well as to facilitate model
replacement, we treat them separately by means of input/output relations and
propose an application of a waveform relaxation algorithm. Furthermore, the
maximum and minimum number of iterations of the proposed algorithm are
mathematically analyzed. The concept of controller/circuit coupling is
illustrated by an example of the co-simulation of a PI power converter
controller and a model of the main dipole circuit of the Large Hadron Collider
