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��Chapter 10�Digital Implementation of PID Controllers

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Course Overview

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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PID Controller Implementation

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Sample-Data Systems

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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z – Transform:

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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The z-transform is a sampled data equivalent to the Laplace transform

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Laplace Transform and Transfer functions

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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z – Transform and Transfer functions

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Discrete Integrator

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Tustin Approximation

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Dirty Differentiator

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Frequency range where�dirty derivative = pure derivative

dirty derivative

pure derivative

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Discrete (dirty) Differentiator

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Low Pass Filter

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Integrator Anti-windup

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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This is a classical anti-windup scheme, i.e., how you would do it�with an analog circuit.

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Integrator Anti-windup

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Design Study A

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Python Implementation:

https://github.com/randybeard/controlbook_public/blob/master/_A_arm/python

ctrlPID.py

hw10_armSim.py

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Design Study B

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Python Implementation:

https://github.com/randybeard/controlbook_public/tree/master/_B_pendulum/python

ctrlPID.py

hw10_pendulumSim.py

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Design Study C

Introduction to Feedback Control, Beard, McLain, Peterson, Killpack

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Python Implementation:

https://github.com/randybeard/controlbook_public/tree/master/_C_satellite/python

ctrlPID.py

hw10_satelliteSim.py