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SYSTEMS Identification

SYSTEMS Identification. Ali Karimpour Assistant Professor Ferdowsi University of Mashhad. Reference: “System Identification Theory For The User” Lennart Ljung(1999) “Practical Issues of System Identification” Lennart Ljung (2007)

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SYSTEMS Identification

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  1. SYSTEMSIdentification Ali Karimpour Assistant Professor Ferdowsi University of Mashhad Reference: “System Identification Theory For The User” Lennart Ljung(1999) “Practical Issues of System Identification” Lennart Ljung (2007) “Perspectives on System Identification” Lennart Ljung (2009)

  2. Lecture 1 Perspective on System Identification Topics to be covered include: • System Identification. • Place System Identification on the global map. Who are our neighbors in this part of universe? • Discuss some open areas in System Identification.

  3. System Identification System Identification:The art and science of building mathematical models of dynamic systems from observed input-output data. System Identification is look for sustainable description by proper decision on: Model complexity Information contents in the data Effective Validation

  4. Dynamic systems System:An object in which variables of different kinds interact and produce observable signals. Stimuli:External signals that affects system. Dynamic System:A system that the current output value depends not only on the current external stimuli but also on their earlier value. Time series:A dynamic system whose external stimuli are not observed.

  5. Unmeasured disturbance v Measured disturbance y w u Output Input Dynamic systems Stimuli Input Disturbance It can be manipulated by the observer. It can not be manipulated by the observer. Measured Unmeasured Dynamic system

  6. Wind, outdoor temperature v Solar radiation y w u Storage temperature Pump velocity A solar heated house Dynamic system

  7. chord, vibaration airflow v y Sound Speech generation Dynamic system Time series:A dynamic system whose external stimuli are not observed.

  8. Model types Buildingmodels Models Model:Relationship among observed signals. 1- Mental models 2- Graphical models 3- Mathematical (analytical) models 4- Software models • Split up system into subsystems, • Joined subsystems mathematically, 1- Modeling • Does not necessarily involve any experimentation on the actual system. • It is directly based on experimentation. 2- System identification • Input and output signals from the system are recorded. 3- Combined

  9. The fiction of a true model

  10. The Core The Core:The core of estimating models is statistical theory. • Model: m • True Description: S • Model Class: M • Complexity (Flexibility): C • Information: Z • Estimation • Validation • Model Fit: F(m,Z)

  11. Squeeze out the relevant information in data. Estimation A template problem: Curve fitting No more satisfaction All data contains signal and noise.

  12. Fit measuregood agreement with data Complexity measureNot too complex is a random variable since of irrelevant part of data (noise). Estimation The simplest explanation is usually the correct one. So the conceptual process for estimation is:

  13. The System Identification Problem 1- Select an input signal to apply to the process. 2- Collect the corresponding output data. 3- Scrutinize the corresponding output data to find out if some preprocessing … 4- Specify a model structure. 5- Find the best model in this structure. 6- Evaluate the property of model. 7- Test a new structure, go to step 4. 8- If the model is not adequate, go to step 3 or 1.

  14. The System Identification Problem 1- Choice of Input Signals. • Filtered Gaussian White Noise. • Random Binary Noise. • Pseudo Random Binary Noise, PRBS. • Multi-Sines. • Chirp Signals or Swept Sinusoids. • Periodic Inputs. 2- Preprocessing Data. • Drifts and Detrending. • Prefiltering. 3- Selecting Model Structures. • Looking at the Data. • Getting a Feel for the Difficulties. • Examining the Difficulties. • Fine Tuning Orders and Noise Structures . • Accepting the Models .

  15. The Communities around the core ML Methods, Bootstrap method,… 1- Statistics. 2- Econometrics and time series analysis. 3- Statistical learning theory. 4- Machine learning. 5- Manifold learning. 6- Chemo metrics. 7- Data Mining. 8- Artificial Neural Network. 9- Fitting Ordinary Differential equation to data. 10- System Identification.

  16. Some Open Areas in System Identification • Spend more time with neighbors. • Model Reduction and System Identification. • Issues in Identification of Non-linear Systems. • Meet Demand from Industry. • Convexification.

  17. Model Reduction System identification is really “system approximation” and therefore closely related to model reduction. Linear systems – Linear models. Divide, conquer and reunite. Non-linear systems – Linear models. Is it good for control? Non-linear systems – nonlinear reduced models. Much work remains.

  18. Linear Systems – Linear ModelsDivide-Conquer-Reunite Helicopter data: 1 pulse input; 8 outputs (only 3 shown here) State space of order 20 wanted.

  19. Reunite Order reduction Linear Systems – Linear ModelsDivide-Conquer-Reunite Next fit 8 SISO models of order 12, one for each output

  20. Linear Systems – Linear ModelsDivide-Conquer-Reunite Reduce model from 96 to 20

  21. Convexification

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