Cybernetic Systems III Computer Controlled Feedback Systems (CY3A3) Course Overview

1. 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.reading.ac.uk/~sis01xh/ CY3A3 System identification

2. 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 can’t 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 CY3A3 System identification

3. 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 CY3A3 System identification

4. 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) CY3A3 System identification

5. Models require • Observation • Measurement • Hypothesis and model building • Testing/validation • A good model should encompass essential information without becoming too complex (KISS principle) CY3A3 System identification

6. CY3A3 System identification

7. 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 CY3A3 System identification

8. Matrix revision Dimensioning notation: Convenient way of confirming that the matrix calculation is achievable for transpositions/ multiplications etc A m×n 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. CY3A3 System identification

9. 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) CY3A3 System identification

10. 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) CY3A3 System identification

11. Algebra rules A+B = B+A Addition is commutative AB  BA Multiplication not commutative A(BC)=(AB)C Associative A(B+C)=AB+AC  BA+CA Associative but not commutative AI=IA=A Existence of an identity Existence of an inverse (when square and non singular) CY3A3 System identification

12. CY3A3 System identification