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Introduction TO Automatic Control
Course: Process Control Systems 3B
22 Documents
Students shared 22 documents in this course
University: Durban University of Technology
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INTRODUCTION TO AUTOMATIC CONTROL
Several techniques used in solving engineering problems are based on the replacement of
functions of a real variable (usually time or distance) by certain frequency-dependent
representations, or by functions of a complex variable dependent upon frequency. A typical
example is the use of Fourier series to solve certain electrical problems. One such problem
consists of finding the current in some part of a linear electrical network in which the input
voltage is a periodic or repeating waveform. The periodic voltage may be replaced by its
Fourier series representation, and the current produced by each term of the series can then be
determined. The total current is the sum of the individual currents (superposition). This
technique often results in a substantial savings in computational effort.
Two very important transformation techniques for linear control system analysis are presented
in this chapter: the Laplace transform and the z-transform. The Laplace transform relates time
functions to frequency-dependent functions of a complex variable. The z-transform relates time
sequences to a different, but related, type of frequency-dependent function. Applications of
these mathematical transformations to solving linear constant-coefficient differential and
difference equations are also discussed here. Together these methods provide the basis for the
analysis and design techniques developed.
Differentiation and integration techniques (which should be known at this stage) are used to
find the Laplace and inverse Laplace transform of a function. It is also important to have a
thorough grasp of partial integration (integration of the product of two variables).
Partial integration:
f = f(x) (x)dx
where
1 df(x)
[derivative of f(x)] dx