Investigation of Noise-sensitivity of a Fixed Point Iteration-based Adaptive Controller for a Pendulum-like Electric Cart

In this paper the preliminary results obtained for a Fixed Pint Iteration-based adaptive control of a pendulum-like mobile robot are further investigated. The main idea in [1] was the application of a very simple adaptive solution that would be realizable by an embedded controller due to omitting the complicated calculation of the order 3 Lie derivatives occurring in the electro-mechanical dynamic model of the cart. In [1] promising simulation results were obtained but the noise-sensitivity of the relative order 3 control task was not investigated. In the present paper the originally suggested control algorithm is equipped with two different and simple algorithms that were developed for noise reduction in the time domain that can be simply applied in a combined way. Realistic sensor noise data were taken into consideration in the measurement of the tilting angle of the steering arm of the cart observed by rotational encoders. It was found via sequential Julia code-based numerical simulation that the suggested control method can be realized because the incorporated simple noise reduction algorithms can handle the expected noise which originates from the measurement of the rotational angle. The situation can be further improved by replacing the encoders with inertial measurement units (IMU acceleration sensors).