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PID Controller

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A possible representation in the time domain The same in the frequency domain That's a second-order controller The simplest: P-control Why I part Problems Windup Noise

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A Standard Representation

Equation

Block diagram

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And in the Laplace-Domain

Equation

Block diagram

Second order

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Series Representation in Laplace

Standard representation from series representation

Series representation from standard

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Problem: Differentiation

Differentiation can strictly speaking not be done. Differentiation amplifies high frequencies. Noise gets thus a particular problem.

One can zoom in as much as one want, one does need information from the past to get the slope. 5

Fix: Delay Measurement with Filter

Filter delays and smoothens signal

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Windup

Input to the process is usually limited What happens if the controller asks for more input than there is available?

The error increases and the integrator is accumulating and accumulating whilst the process does not proceed.

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Effect of Input Saturation

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Effect of different feedback level of saturation

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PID with without and with anti windup Simulink modules

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Process without and with saturation Simulink modules

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#### Information

##### PID Controller

12 pages

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