This paper concerns with the non-linear system having multiple-inputs multiple-outputs (MIMO). The plant mainly comprises: bench-top helicopter, tail and main rotor of a helicopter system. The dynamics are presented with control methodologies where a conventional strategy proves the instability of the system while the deadbeat and sliding mode control with linear matrix inequality regulates the future estimates. There have been disturbances like presence of unwanted ripples in the output of the non-linear systems (in case of stability also after 100[Formula: see text]s) and in the tracking of states accurately by updating the minimization error regularly. These problems originate mainly from the rotor section and are visited carefully by studying the dynamics of the blade, whereas, the design of filter makes the solution more appealing. The adaptive filter is capable of handling the frequency spectra of noise (reducing noise by 10[Formula: see text]dB), Euler angle deviations and travel angle accurately. Also, the stability analysis does not confirm the behavior in the case of bounded and a varying range of initial angular velocity. Hence, the problem of fluctuations is overcome by deadbeat and SMC-LMI approach which not only improved the ripples but also allowed the final response of the future states to be more exact and noiseless. As the previous research involved in position tracking (either translational or rotational) of these MIMO systems was concerned with software tools like MATLAB. This paper justifies its validation tested experimentally on OPAL RT hardware. The key findings involve the comparison of frequency spectra, the Euler deviation plot compared to CSL Helicopter and the three set-point variations providing accuracy in results in four modes — desired, actual, with controller-without filter and with controller-with filter. The use of adaptive filter with controllers have encouraged the suppression of noisy waveforms in the bench-top system very smoothly. The details regarding hardware setup are also discussed.

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There has always been an increasing interest in the space related activities. The research on aerospace vehicles have become popular due to the problems and complexity of the systems involved. The main challenge lies in keeping a balance when in motion and hence tracking plays a key role here. The satellite system discussed in this paper is described for the problem arising due to presence of disturbances (colored and white noise). This model is evinced by the augmentation of discrete Kalman filter, a powerful tool for controlling the noisy estimates. Whereas, the regulation of the state dynamics (Euler angles and velocity) is achieved with the adaptive law which focuses on guaranteeing stability of adaptive control scheme using a good choice of Lyapunov argument. The presence of Gaussian White noise is also mentioned where a comparison resembles stability for almost, mean square, third moment and mean value between the satellite and oscillator system. A clear discussion of the system in the presence of colored and white noise with perfect estimates derived from kalman filter and an adaptation law governing the evolution of system around equilibrium is done.