Numerical describing function analysis of closed-loop discrete-time reset control systems

In this paper we study the digital implementation of reset controllers on mechatronic systems, particularly focusing on their frequency-domain behaviour. We demonstrate that the frequency-domain behaviour of a closed-loop discrete-time (DT) reset control system (RCS) can be significantly different compared to a continuous-time (CT) counterpart. Furthermore, we propose a novel frequency-domain performance prediction method – based on the describing function approach – which can take these discretization effects into account. In an illustrative numerical example we show that predictions obtained with the proposed method, are more accurate compared to predictions obtained using existing methods aimed for CT RCSs. Finally, the improved prediction accuracy of the proposed method is also experimentally validated on an industrial wirebonding machine.