A New Approach to the Real-Time Simulation of Control Systems with Discontinuities

Control systems consisting of a subsystem with discontinuities often cause problems in digital simulation. Real-time simulation of this type of system using conventional fix-step integration algorithms can lead to sizable errors for reasonable step sizes. This paper suggests a new approach which replaces the subsystems with a function table. The dynamic equations of the control subsystem with discontinuities are integrated off-line over a time interval which will be used as the step-size for the on-line integration of the whole contol system. This off-line integration uses a sufficiently small step size and the necessary algorithm to handle the discontinuities of the subsystem. The process is repeated for a matrix of initial conditions and inputs. In the on-line real-time simulation, table lookup and linear interpolation are used to update the subsystem with discontinuities while the rest of the control system is integrated with conventional real-time algorithms. By proper choice of the state variables for the system, the number of variables required in the multiple-variable function can be reduced. A practical example is used to demonstrate the implementation of the method. From the example it is shown that this new approach can lead to reasonable accuracy with a relatively large step size.