The reliable performance of a complete control system depends on accurate model information being used to represent each subsystem. The identification
and modelling of multivariable systems are complex and challenging due to cross-coupling. Such a system may require multiple steps and decentralized
testing to obtain full system models effectively. In this paper, a direct identification strategy is proposed for the coupled two-input two-output
(TITO) system with measurable input–output signals. A well-known closed-loop relay test is utilized to generate a set of inputs–outputs data from a single
run. Based on the collected data, four individual fractional-order transfer functions, two for main paths and two for cross-paths, are estimated from
single-run test signals. The orthogonal series-based algebraic approach is adopted, namely the Haar wavelet operational matrix, to handle the fractional
derivatives of the signal in a simple manner. A single-step strategy yields faster identification with accurate estimation. The simulation and experimental
studies depict the efficiency and applicability of the proposed identification technique. The demonstrated results on the twin rotor multiple-input multiple-
output (MIMO) system (TRMS) clearly reveal that the presented idea works well with the highly coupled system even in the presence of measurement
noise
