Analytical expressions for relay responses of systems

Relay feedback responses are obtained from simple SISO and MIMO systems. These responses contain much information and can be modeled in time domain. Though in SISO case it has a simple structure, in MIMO case interactions among the loops makes it difficult to model. In this paper, the generalized analytical expressions for closed loop transfer functions of interacting loops (undesired responses) of 2×2 processes with FOPDT structures are derived and validated with simulated one. These analytical expressions are useful to identify unknown system parameters.