Adaptive IIR filtering techniques for dynamic modeling of a twin rotor system

This paper investigates the development of a parametric model to characterise pitch movement in a twin rotor multi-input multi-output system (TRMS) using adaptive infinite impulse response (IIR) models. The TRMS is a laboratory platform designed for control experiments. In certain aspects, its behaviour resembles that of a helicopter. It typifies a high-order nonlinear system with significant cross coupling between its two channels. It also simulates similar problems and challenges encountered in real systems. These include complex dynamics that lead to both parametric and dynamic uncertainty, unmeasurable states and sensor and actuator noise. In this work, adaptive IIR filtering techniques using least mean square (LMS) and recursive least square (RLS) algorithms are investigated for dynamic modelling of the system. The system is initially excited with random gaussian sequence input signal of sufficient bandwidth (0-10Hz) to ensure that all resonance modes of interest are captured. The magnitude of the input signal is selected so that it does not drive the system out of its linear operating range. Good excitation is achieved from 0-2.5 Hz, which includes all the important rigid body and flexible modes. Then, adaptive IIR filters based on equation error formulation are used for modelling the system. Three standard algorithms; namely, LMS, normalized LMS and RLS are utilized as learning algorithms to update the parameters of the filter during the modelling process. A comparative assessment of the three learning algorithms, in characterising the system, is conducted. The performance of each model is assessed in terms of output tracking, minimization of the mean-square error, stability and algorithm convergence.