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To understand the principles and qualities of the digital controller it is necessary to test this at concrete examples. To show the whole variety of the possibilities and problems, as many applications as possible have to be shown from the different disciplines. There is, however, the danger that one loses the summary of the essential, namely the digital controller. For this reason we will model only one example from the beginning of this eBook over the analogous and digital controller until the end of the eBook. On this MECHATRONIC example position-control of DC-motor we can show all the main features of the analog and digital control theory.
The eBook is so divided like a realistic development which structurally leads to the final result step by step.

At first gradual Scilab is explained and the linear model of the plant-model. After that, an analog and digital PID controller is developed for this linear plant.

After that, the plant will become some nonlinearities, quantisation and so on to see the robustness of the system. 

Everything what is here introduced can be summarized
under the concept mechatronics:

  • Model creation from different disciplines (electrical engineering, mechanical engineering and computer science)
  • Simulation of the complete system (analog-plant and digital-controller)
  • Analog- and digital-control engineering (controller-structure and parameter)
  • Implementing in an Embedded-System (C-program)
  • and this all with the Free software
     
    SCILAB and XCOS  
    the Open-Source for MATLAB and SIMULINK

 

You can free of charge download the current version of SCILAB on the page www.scilab.org. You must download the binary version for the corresponding operating system because you can install these. And do not forget to load the Help files.

To the end some further controller strategy will be shown.

Content

 
Introduction to SCILAB

Introduction
What is it?
Matlab and Simulink
What can Scilab?
The SCILAB window
Variables
Vectors and matrices
Creating and plotting signals
Arithmetic with signals
Series connection of signals
Cut out signals
Examining signals
Graphics
Animation
Scripts
Functions
Demos

Modelling

Introduction
Rotating and linear movement
Modelling
Model of DC-motor
What does signify a model?
The electrical coil
Mass, spring and damper
Motor torque
Feedback to the electrical part
What is a transfer function?
Set up the differential equation
Transfer function
Amplification and time constants
Parameters
Gearbox

Model in SCILAB

This chapter
Transfer function in SCILAB
Step response
Impulse response
Subplot
What is Bode-Diagram?
Disturbance transfer function

Different control plants

Control plants
P-plant
I-plant
PT1-plant
PT2-plant
Oscillation and reverse point
PTn-plants and dead time
ITn-plants
Dynamic in enumerator
Poles and zeros
State space
State space in Scilab
Series- and parallel connection
Identification

Introduction to XCOS

Introduction
Why Xcos?
Start Xcos
Drag and drop the blocks
Connect blocks
Start Simulation
Change blocks
TP1 block
Sinus and noise
Supperblock
Integral in series
Dead time
Limit
System in Xcos
State space
Xcos Demo

Simulation model

Simulation
Differential equation in integral equation
Integral blocks
Feedback
Force balance
Closed loop
Simulate mechanical part
Electrical part
Simulate electrical part
Electrical and mechanical part together
Simulate electrical and mechanical part together
Controller

Analog control

Open loop
Disturbance
P-controller
Steady state error
I-controller
PI-controller
PID-controller
PIDT1-controller

Analog control => parameter

How to adjust the parameter of the PID-controller?
Parameters from the step response
Adjustment rules
PID-controller structure
Results
Leadfilter
Ramp stimulus

Analog control => stability

What does it mean stability?
Stability in control theory
Stability in Bode-Diagram
Stability in Bode-Diagram
Controller design in Bode-Diagram
Script controller design
Adjust Kp
Adjust Kd
Adjust Ki
Requirements
Implementation

Discrete model

Why discrete model of the plant?
Sampling
A/D-converter, sampling and clock
Hardware implementation
FFT and antialiasing
Discrete plant
Discrete plant
z-transfer function
z-transfer function in SCICOS
Poles and zeros
Discrete controller

Discrete controller

Introduction
Sample and Hold
P-controller
Common control clock
I-controller
PI-controller
D-controller
PID-controller
Parallel- und recursive architecture
Parallel- und recursive architecture
Recursive architecture implementation
Controller higher order
Quasi-continuous discrete controller
Quasi-continuous discrete controller
Quasi-continuous discrete controller
Limit
I-part does not stop tp calculate
Anti-Wind-Up
DT1- and D-part
PI-controller
A/D-converter
Integer-calculation
Implementation
Controller design with poles and zeros adjustment
Controller design with poles and zeros adjustment
Preferred position of poles
Tools

Robustness and further controller

Robustness and further controller
Sensor noise
Temperature dependence
Nonlinear component
Nonlinear component
Spring defect
Friction
Cascade controller
Three controller in series
Simulation
Current controller
Speed controller
Position controller
Speed calculation
Disturbance adaption
Adaptive control
Two plants control

END

 


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PID-controller

SCILAB

SCICOS

plant

sampling time

xcos

scilab

matlab

simulink