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) “Perspectives on System Identification” Lennart Ljung (2009)

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

lecture 1 Ali Karimpour Sep 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

lecture 1 Ali Karimpour Sep 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.

lecture 1 Ali Karimpour Sep Dynamic systems Stimuli It can be manipulated by the observer. Input Disturbance It can not be manipulated by the observer. Measured Unmeasured Dynamic system Input u Measured disturbance w Unmeasured disturbance v Output y

lecture 1 Ali Karimpour Sep A solar heated house Dynamic system Pump velocity u Solar radiation w Wind, outdoor temperature v Storage temperature y

lecture 1 Ali Karimpour Sep Speech generation Dynamic system chord, vibaration airflow v Sound y Time series: A dynamic system whose external stimuli are not observed.

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

lecture 1 Ali Karimpour Sep The fiction of a true model

lecture 1 Ali Karimpour Sep 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)

lecture 1 Ali Karimpour Sep Estimation A template problem: Curve fitting Squeeze out the relevant information in data. No more satisfaction All data contains signal and noise.

lecture 1 Ali Karimpour Sep Estimation The simplest explanation is usually the correct one. So the conceptual process for estimation is: Fit measure good agreement with data Complexity measure Not too complex is a random variable since of irrelevant part of data (noise).

lecture 1 Ali Karimpour Sep 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 If the model is not adequate, go to step 3 or 1.

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

lecture 1 Ali Karimpour Sep The Communities around the core 1- Statistics. ML Methods, Bootstrap method,… 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.

lecture 1 Ali Karimpour Sep 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.

lecture 1 Ali Karimpour Sep 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.

lecture 1 Ali Karimpour Sep Linear Systems – Linear Models Divide-Conquer-Reunite Helicopter data: 1 pulse input; 8 outputs (only 3 shown here) State space of order 20 wanted.

lecture 1 Ali Karimpour Sep Linear Systems – Linear Models Divide-Conquer-Reunite Next fit 8 SISO models of order 12, one for each output Reunite Order reduction

lecture 1 Ali Karimpour Sep Linear Systems – Linear Models Divide-Conquer-Reunite Reduce model from 96 to 20

lecture 1 Ali Karimpour Sep Convexification