Automatic Control with Experiments

Abstract

Automatic control is one of the disciplines that support the technologically advanced lifestyle that we know today. Its applications are present in almost all the activities performed by humans in the twenty-first century. From the Hubble spatial telescope and spacecrafts, to the fridge at home used for food preservation. From residential water tanks to large industries producing all the products demanded by people: automobiles, aircrafts, food, drinks, and medicines, to name but some. Although it is known that applications of automatic control have existed for more than 2000 years, the Industrial Revolution motivated its development as scientific and technological knowledge oriented toward the solution of technological problems. Since then, automatic control has been instrumental in rendering human activities more efficient, increasing the quality and repeatability of products. It is for this reason that courses on automatic control have become common in academic programs on electrical engineering, electronics, mechanics, chemistry and, more recently, mechatronics and robotics. However, the fact that conventional automatic control techniques are based on mathematics has traditionally posed difficulties for education in this subject: to learn to design automatic control systems the student is required to understand how to solve ordinary, linear, differential equations with constant coefficients using Laplace transforms. This is an important obstacle because this subject is commonly difficult for most undergraduate students. The problem becomes worse because in automatic control the most important part of solving a differential equation is the physical interpretation of a solution, which is difficult for undergraduate students because most do not even understand how to find the solution. Another difficulty in automatic control education is how to teach students to relate abstract mathematical results to the practical issues in a control system. How do they implement a controller given in terms of the Laplace transform, i.e., as a transfer function in practice? How do they implement a controller using digital or analog electronics? How do they take into account sensors and power amplifier gains? How do they determine the gain of a pulse width modulation-based power amplifier? What are the effects of these gains in a control system?