Integrales En La Automatización

APPLICATIONS TO definite integrals Automation Engineering

Theoretical Framework

Given a function f (x) of a real variable x and an interval [a, b] of the real line, the definite integral is equal to the area bounded between the graph of f (x), the x-axis, and the vertical lines x = a and x = b.

Is represented by.

∫ is the integral sign.

a lower limit of integration.

b upper limit of integration.

f (x) is the integration or integrating function.

differential dx is x, and indicates which variable function that integrates

Properties of definite integrals

1. The value of the definite integral changes sign if they swapped the limits of integration.

2. If the integration boundaries coincide, the definite integral is zero.

3. If c is an interior point of the interval [a, b], the definite integral decomposes as a sum of two integrals extended to intervals [a, c] and [c, b].

4. The definite integral function of a sum equal to the sum of integrals

5. The integral of the product of a constant and a function is equal to the constant by the integral of the function.

After having this knowledge can enter clear applications in process automation, making very clear that engineering Automation is the integration of electronics, mechanical systems and high repetition processes requiring human hands, ie seeks to generate greater acceptance and use by the industry which have technology.

The application which is to deepen the electronics area, which is one of the most important in generating process automation.

In this area integrals play a key role in calculating the currents, capacitances, load times, among other current discharge. But fundamentally integral calculus is used in circuits RLC (resistor, capacitor and coil) to analyze their behavior in a circuit for example:

• To calculate the flow of electrons by a driver over time, the following equation is used:

q (t) = ∫ i (t) dt

Where:

Q = charge

I = current

• When we determine the energy possessed by a circuit, simply integrating the power output of a time circuit (t1) at a time (t2) as follows:

w (t) = ∫ 〖p (t) dt〗

Where: e

W = energy

P = power

• To determine the voltage on a capacitor within a given time have:

vc (t) = 1 / c ∫ 〖ic (t) dt〗

Where:

Vc = voltage across the capacitor

C = value of capacitor

Ic = current in the capacitor with respect to time (t) from t1 to t2 one.

• If we want to find the current in a coil or introducer in a given time, we have:

iL = 1 / (L ∫ 〖vL (t)〗) dt

Where:

iL = Coil current

L = value of the coil (mH)

VL = the inductor voltage with respect to time

These examples are but a clear demonstration of the importance of the integrals in electronic processes and thus in automation, just as we passed many clear examples such as calculating volumes which is essential to calculate the core a transformer.

We conclude that the importance of comprehensive and numeracy in all its forms within engineering plays a vital role, because the engineer must have two characteristics that distinguish him from other professionals, which are:

 Must be a good scientist

 Must be a good mathematician

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