Analysis and implementation of second order differentiators in embedded systems

Differentiation plays a crucial role in estimating system states, especially in embedded systems where direct measurements might be noisy or unavailable. This study delves into various differentiation techniques tailored for the Arduino platform, an archetype of embedded systems. Beginning with a first-order differentiation method, the research provides a clear path from fundamental principles to practical implementation. Progressing to a second-order differentiator, we examine the nuanced advantages and complexities it introduces, particularly in real-world applications. The exploration culminates in the discussion of high-gain observers, highlighting their potential in specific scenarios while emphasizing the challenges in noisy environments. Through theoretical derivations juxtaposed with experimental insights, this paper furnishes a holistic perspective on differentiation techniques for Arduino and analogous embedded platforms.