Preface
Preface xvi
The system Identification Problem Basic Questions About System Identification 1-2 Common Terms Used in System Identification 1-4 Basic Information About Dynamic Models 1-6 The Signals 1-6 The Basic Dynamic Model Variants of Model Descriptions 1-7 How to Interpret the Noise Source 1-8 Terms to Characterize the Model Properties 1-10 The Basic Steps of System Identification 1-12 A Startup Identification Procedure Step 1: Looking at the Data 1-14 Step 2: Getting a Feel for the Difficulties 1-14 Step 3: Examining the Difficulties 1-15 Step 4: Fine Tuning Orders and Disturbance Structures 1-16 Multivariable Systems 8 Reading More About System Identification 1-21
1 The System Identification Problem Basic Questions About System Identification . . . . . 1-2 Common Terms Used in System Identification . . . . 1-4 Basic Information About Dynamic Models . . . . . . 1-6 The Signals . . . . . . . . . . . . . . . . . . . . . 1-6 The Basic Dynamic Model . . . . . . . . . . . . . . . 1-7 Variants of Model Descriptions . . . . . . . . . . . . . 1-7 How to Interpret the Noise Source . . . . . . . . . . . . 1-8 Terms to Characterize the Model Properties . . . . . . . 1-10 The Basic Steps of System Identification . . . . . . . 1-12 A Startup Identification Procedure . . . . . . . . . 1-14 Step 1: Looking at the Data . . . . . . . . . . . . . . 1-14 Step 2: Getting a Feel for the Difficulties . . . . . . . . . 1-14 Step 3: Examining the Difficulties . . . . . . . . . . . . 1-15 Step 4: Fine Tuning Orders and Disturbance Structures . . . 1-16 Multivariable Systems . . . . . . . . . . . . . . . . 1-18 Reading More About System Identification . . . . . . 1-21
1 The System Identification Problem Basic Questions About System Identification What is System Identification? System Identification allows you to build mathematical models of a dynamic system based on measured data How is that done? Essentially by adjusting parameters within a given model until its output coincides as well as possible with the measured output How do you know if the model is any good? a good test is to take a close look at the models output compared to the measured one on a data set that wasnt used for the fit ("Validation Data") Can the quality of the model be tested in other ways? It is also valuable to look at what the model couldn 't reproduce in the data (the residuals"). This should not be correlated with other available information such as the systems input. What models are most common? The techniques apply to very general models. Most common models are difference equations descriptions, such as ARX and aRMAX models, as well as all types of linear state-space models Do you have to assume a model of a particular type? For parametric models, you have to specify the structure. This could be as easy as just selecting a single integer, the model order or may involve several choices. If you just assume that the system is linear, you can directly estimate its impulse or step response using Correlation Analysis or its frequency response using Spectral Analysis. This allows useful comparisons with other estimated models What does the System Identification Toolbox contain? It contains all the common techniques to adjust parameters in all kinds of linear models. It also allows you to examine the models' properties, and check if they are any good, as well as to preprocess and polish the measured
1 The System Identification Problem 1-2 Basic Questions About System Identification What is System Identification? System Identification allows you to build mathematical models of a dynamic system based on measured data. How is that done? Essentially by adjusting parameters within a given model until its output coincides as well as possible with the measured output. How do you know if the model is any good? A good test is to take a close look at the model’s output compared to the measured one on a data set that wasn’t used for the fit (“Validation Data”). Can the quality of the model be tested in other ways? It is also valuable to look at what the model couldn’t reproduce in the data (“the residuals”). This should not be correlated with other available information, such as the system's input. What models are most common? The techniques apply to very general models. Most common models are difference equations descriptions, such as ARX and ARMAX models, as well as all types of linear state-space models. Do you have to assume a model of a particular type? For parametric models, you have to specify the structure. This could be as easy as just selecting a single integer, the model order, or may involve several choices.If you just assume that the system is linear, you can directly estimate its impulse or step response using Correlation Analysis or its frequency response using Spectral Analysis. This allows useful comparisons with other estimated models. What does the System Identification Toolbox contain? It contains all the common techniques to adjust parameters in all kinds of linear models. It also allows you to examine the models’ properties, and to check if they are any good, as well as to preprocess and polish the measured data
Basic Questions About System Identification Isn't it a big limitation to work only with linear models? No, actually not Many common model nonlinearities are such that the measured data should be nonlinearly transformed (like squaring a voltage nput if you think that it's the power that is the stimuli). Use physical insight about the system you are modeling and try out such transformations on models that are linear in the new variables, and you will cover a lot How do I get started? If you are a beginner, browse through Chapter 2, The graphical User Interface. Then try out a couple of the data sets that come with the toolbox. se the graphical user interface(GUi) and check out the built-in help functions to understand what you are doing Is this really all there is to System Identification? Actually, there is a huge amount written on the subject. Experience with real lata is the driving force to understand more. It is important to remember that ny estimated model, no matter how good it looks on your screen, has only icked up a simple reflection of reality. Surprisingly often, however this is sufficient for rational decision making 1-3
Basic Questions About System Identification 1-3 Isn’t it a big limitation to work only with linear models? No, actually not. Many common model nonlinearities are such that the measured data should be nonlinearly transformed (like squaring a voltage input if you think that it’s the power that is the stimuli). Use physical insight about the system you are modeling and try out such transformations on models that are linear in the new variables, and you will cover a lot! How do I get started? If you are a beginner, browse through Chapter 2, “The Graphical User Interface.” Then try out a couple of the data sets that come with the toolbox. Use the graphical user interface (GUI) and check out the built-in help functions to understand what you are doing. Is this really all there is to System Identification? Actually, there is a huge amount written on the subject. Experience with real data is the driving force to understand more. It is important to remember that any estimated model, no matter how good it looks on your screen, has only picked up a simple reflection of reality. Surprisingly often, however, this is sufficient for rational decision making
1 The System Identification Problem Common Terms Used in System Identification This section defines some of the terms that are fre used In System Identification Estimation data is the data set that is used to fit a model to data In the gui this is the same as the Working Data Validation Data is the data set that is used for model validation purpose This includes simulating the model for these data and computing the residuals from the model when applied to these data Model Views are various ways of inspecting the properties of a model. They include looking at zeros and poles, transient and frequency response, and Data Views are various ways of inspecting properties of data sets. A most common and useful thing is just to plot the data and scrutinize it. So-called outliers could be detected then these are unreliable measurements, perhaps arising from failures in the measurement equipment. The frequency contents of the data signals, in terms of eriodograms or spectral estimates, is also most revealing to study Model Sets or Model Structures are families of models with adjustable parameters. Parameter Estimation amounts to finding the"best"values of these parameters. The System Identification problem amounts to finding both a good model structure and good numerical values of its parameters Parametric Identification Methods are techniques to estimate parameters in given model structures. Basically it is a matter of finding(by numerical search) those numerical values of the parameters that give the best agreement between the models(simulated or predicted) output and the Nonparametric Identification Methods are techniques to estimate model behavior without necessarily using a given parametrized model set Typical nonparametric methods include Correlation analysis, which estimates a systems impulse response, and Spectral analysis, which estimates a systems frequency response 1-4
1 The System Identification Problem 1-4 Common Terms Used in System Identification This section defines some of the terms that are frequently used in System Identification: • Estimation Data is the data set that is used to fit a model to data. In the GUI this is the same as the Working Data. • Validation Data is the data set that is used for model validation purposes. This includes simulating the model for these data and computing the residuals from the model when applied to these data. • Model Views are various ways of inspecting the properties of a model. They include looking at zeros and poles, transient and frequency response, and similar things. • Data Views are various ways of inspecting properties of data sets. A most common and useful thing is just to plot the data and scrutinize it. So-called outliers could be detected then. These are unreliable measurements, perhaps arising from failures in the measurement equipment. The frequency contents of the data signals, in terms of periodograms or spectral estimates, is also most revealing to study. • Model Sets or Model Structures are families of models with adjustable parameters. Parameter Estimation amounts to finding the “best” values of these parameters. The System Identification problem amounts to finding both a good model structure and good numerical values of its parameters. • Parametric Identification Methods are techniques to estimate parameters in given model structures. Basically it is a matter of finding (by numerical search) those numerical values of the parameters that give the best agreement between the model’s (simulated or predicted) output and the measured one. • Nonparametric Identification Methods are techniques to estimate model behavior without necessarily using a given parametrized model set. Typical nonparametric methods include Correlation analysis, which estimates a system’s impulse response, and Spectral analysis, which estimates a system’s frequency response