Laboratory of
Embedded Control
Systems
Course Presentation
Teacher Luigi Palopoli
AA. 2011/2012
Aim of the course
The aim of this course it to introduce the student (you :=)
) to model based design of embedded control systems
This will be done with theoretical lectures (few) and lab
experiences (many)
The course is a laboratory course.
What we expect is that you deliver a complete working
project
You will organise yourself in groups of two students
Please start searching for your mate and let me know in the
next class
The project
The project will be developed in different phases
At the end of each phase, you will produce a different
artefact (e.g., a piece of code or a model), which has to
be documented by a report
There is a specific date for each delivery
Those of you who do not attend the class can deliver the
project all at once, but I warmly recommend not to (is possible)
We will do most of the work together in the class, but you
may need to work on your own to complete the different
phase
What this course
is not...
It is not a Signals and System course
It is not a Real

Time Operating Systems course
It is not an automatic control or a digital control
course.....
...but you will need a little bit
of all of this and we will help
you....
What this course
is...
In this course you will be offered a comprehensive look
on the entire model based development methodology
In detail, you will learn how to
1. Formulate
design specifications
2. Construct a model of the
system that you
want to control (plant)
3. Identify the physical
parameters of the system
4. Design a controller for the system that
fulfils your goals
5. Simulate the closed loop system and
asses its performance
6. Generate a Software implementation
for your controller
A plant
The objective of this course is to control a system that
we define a
plant
A plant is a continuous time system described by a set
of differential equations
Example (Spring + Damper)
Model of the Plant
Very often we will use the transfer function (Laplace
Transform) to express the plant in a mathematically
tractable way
In our example:
Model
We can easily translate this equation into a scicos
model
•
Double

clicking on the transfer function block we can
insert the physical parameters and simulate the
system
Simulation
Step Response
Physical Parameters
The behaviour of the system is obviously much different
if we change the physical parameters
Non

idealities
To make our model more realistic, we can refine our
model inserting blocks that model non

idealities
For instance, actuators are not able to produce
any
input
value
an utility car is different from a Formula 1 racing car
we can model this by inserting in the model a “saturation”
block
The system is no longer linear (why?) but we can consider its
behaviour as linear ad long as we do not exceed the bound of
the saturation
Non

idealities
Saturation
Performance
Specs
Once we have a model for our system we can formulate
performance specification (e.g., related to the step
response)
Rise
time
Overshoot
Settling
time
Physical
Parameters
Essential to our purpose is to determine the choice of
parameters whereby our model best fits the model
To do this we can
measure the physical quantities if easy/possible
Carry out the identification procedure
Identification:
carry out a large set of experiments and collect data
find the set of parameters that minimise the distance
between our system and the model
Control
Design
At this point, we are in condition to design a feedback
controller that fulfils the specs.
If we make a feedback connection of a plant P(s) with a
controller C(s), we get a new transfer function given by:
The presence
of the controller
at the denominator
moves the poles and
changes the dynamics
Feedback
Control
P(s)
C(s)
+

r
e
u
Digital
Implementation
The controller we have designed in this way is a
continuous time system (a differential equation)
If we want to implement it in a digital computer, we need
to transform it into a numeric algorithm
Instrumental to this goal is the introduction of a sampling
mechanism for the sensors and of a Zero order Hold
(ZoH) for the actuators
Feedback
Control
P(s)
C(z)
+

r
Sampler
ZoH
What is the digital
implementation C(z)?
Assume that our controller is given by
•
In terms of differential equations:
Digital
Implementation
If we sample periodically, the derivative can be
approximated
by the backward difference (we will see better
approximations
….)
Z

transform
notation
It is useful to express the difference equation in terms of
the Z

transform
It plays the same role in discrete
—
time as the Laplace
transform plays in continuous time
The one
—
step forward operator in the time domain
corresponds to multiplication by z in the Z domain and
the one step delay operator to multiplication by 1/z
The controller equation becomes:
Digital approximation
We can account for the digital approximation in our
scheme
and simulate the system
…
and finally
….
Once we are happy with the simulations, we can write a
real
—
time task (implemented in a RTOS) that translates
the algorithm into code
double e_1, u_1;
void task () {
double u, e;
e = get_from_sensor();
u = u_1 + kp (e

e_1)+ki*e;
output(u);
e_1 = e:
u_1 = u;
}
Schedule
Lecture 1: Introduction
Methodology
Introduction to Scicoslab
Lecture II: Scicoslab
Matrix computation
Scripts and functions
Plotting data
Modelling and simulating a CT system with Scicos
Schedule
Lecture III: Interfacing ScicosLab and Lego
Setup of the environment (step by step)
Example 1: turn on a motor and read the encoder through
USB and dump on file
Read the file with Scilab and plot it
Lecture IV: Recap on Laplace transform
Schedule
Lecture V: Modelling a second order system
Lecture VI: Identification of a second order system
Scicos

lab examples (identifying a second order system
using synthetic data)
Filtering
Schedule
Lecture VII: Identification of the Lego’s motors
Collection of Data
Lecture VIII: Identification of the Lego’s motors
Filtering
Identification
Schedule
Lecture IX: Control of SISO system
root locus
[
DELIVERY
] Lecture X: Identification of the Lego’s motors
Filtering
Identification
Schedule
Lecture XI: Control of SISO system
root locus
PID
Lecture XII: Example of design using scicoslab
Second order systems: from specs to control
Assesment by simulation
Schedule
Lecture XIII: Control of the motor
root locus
PID
Lecture XIV: Control of the motor
Schedule
Lecture XV: Digital Implementation of controllers
theory
practical application for the motor (SCICOSLAB)
Lecture XVI: Getting acquainted with Lego
Setup of the environment (step by step)
Example 1: Hello world and buttons
Example II: Read a sensor and print on display
Example III: Periodic tasks, signal activation, interrupts
Schedule
Lecture XVII: Modelling and simulation of the larger
system
[
Delivery
] Lecture XVIII: Implementing the digital
controller
Schedule
Lecture XIX: Control design based on State Space
Methods
Lecture XX: Control design based on State Space
Methods
Schedule
Lecture XXI: Design of the control in SCICOLAB
Lecture XXII: Design of the control in SCICOLAB
Schedule
Lecture XXIII: Design of the control in SCICOLAB
Digital implementation
Lecture XXIV: Design of the control in SCICOLAB
Coding
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