Cybernetic Systems III

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Cybernetic Systems III Computer Controlled
Feedback Systems (CY3A3) Course Overview
Systems identification ( Xia Hong) Adaptive
systems ( Xia Hong) Principles of feedback
(R. Mitchell) System Identification and
Modelling This module has approx 10 lectures and
tutorial. Assessment is via examination and an
assignment. This URL is at http//www.personal.re
ading.ac.uk/sis01xh/
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• System modelling and identification
• What is system identification?
• Define a system as a collection of outputs and
  (possibly) inputs as well as possible
  disturbances. We can measure the outputs, and may
  be able to measure the inputs. We cant measure
  the disturbances. We may also be able to
  influence the inputs.
• We would like to
• Predict future behaviour (very useful for making
  money)
• Gain a meaningful insight and understanding of
  the system

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• We can use this information for
• Research - Encompass a lot of information in an
  understandable form and use this to predict
  behaviours (e.g. Keplars laws of planetary
  motion)
• Design -Use the models to ensure that what we
  are building will work as expected without having
  to build complex prototypes. Predict the limit of
  our designs (e.g. why do bridges fall down?)
• Control - Push a systems behaviour
  to meet our requirements

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• Types of model
• Conceptual - A collection of ideas
• Physical - A scaled or analogous
  version of the system
• Mathematical - A collection of algorithms,
  that predict behaviour
• Mathematical models can be further distinguished
  into
• Parametric models - Represent fundamental
  characteristics where different behaviours are
  observed when parameters are changed (e.g. a
  system transfer function)
• Non-parametric models - Represent typical
  descriptive behaviours, (e.g. a frequency
  response, an impulse/step response)

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• Models require
• Observation
• Measurement
• Hypothesis and model building
• Testing/validation
• A good model should encompass essential
  information without becoming too complex (KISS
  principle)

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System ID example Given a set of data, we need
to decide a model or set of models to fit. We
then need to fit it with minimal error. We can
then use the model to make a future time
prediction (beyond the range of our data)
Data
Model
Prediction
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Matrix revision Dimensioning notation
Convenient way of confirming that the matrix
calculation is achievable for transpositions/
multiplications etc A mn is a matrix with m
rows and n columns b n 1 a
column vector with n rows Traditionally
vectors are assumed to be in column form.
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Matrix operations Multiplication (The number
of columns of A must be the same as number
of rows of B) Addition (A and B must be the
same size) Transpose
Symmetric (If C is symmetric it must also be
square)
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Identity The identity matrix I is square and has
1s on the major diagonal, elsewhere 0s.
Inverse exists
only if A is square and not singular. A is
singular if A 0 (determinant of A)
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Algebra rules AB BA Addition is
commutative AB ? BA Multiplication not
commutative A(BC)(AB)C Associative A(BC)ABAC
? BACA Associative but not commutative AIIAA
Existence of an identity
Existence of an inverse (when square and non
singular)
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