Experimental Determination of Sampling Time in Hardware with Microcontrollers and Its Relationship to Mathematics in t, s and z
Abstract
The design of monitoring and/or control systems is based on mathematical models at time t, which involve differential equations and Laplace transforms for their solution. Associating these models with discrete systems and the use of microcontrollers or computers to digitize these systems involves the use of the z-transform, which requires knowledge of the sampling time used for all models to coincide in their results. The present work shows a practical method for determining the sampling time. The ESP-32-S2 development kit and a network with a resistor and a capacitor were used. Using a C/C++ language program and oscilloscope, the sampling time was measured. Experiments were performed for different operating conditions of the data acquisition system, recording the capacitor voltage in response to one unit step supply. The true results were compared graphically with the results in t,s and z and the error between the response in t and the practical results also was calculated. Demonstrating that the proposed method generates a good measure of the sampling time and that the model results in all planes coincide with those obtained in practice. Hoping to motivate students and professionals to apply mathematics in the design of digital systems. Encouraging the use of simulation tools that allow the development of faster and more efficient systems. Strengthening work related to embedded systems, intelligent sensors, internet of things and industry 4.0.
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