Defining Model Structures Polynomial Black-Box Models: The idpoly Model 3-36 Multivariable arx models: The idarx mode Black-Box State-Space Models: the idss Model 3-3 Structured State-Space Models with Free Parameters: the idss model State-Space Models with Coupled Parameters State-Space Structures: Initial Values and Numerical Derivatives 3-47 Examining Models 349 Parametric Models: idmodel and its children 3-49 Frequency Function Format: the idfrd model 3-55 Graphs of Model Properti 3-56 Transformations to Other Model Representations 3-59 Discrete and Continuous Time models Model structure selection and validation Comparing Different Structures 3- Impulse Response to Determine Delays 3-66 Checking Pole-Zero Cancellations Residual analysis 3-66 Model error models 3-67 Noise- Free simulations Assessing the Model Uncertainty 368 Comparing Different Models 3-70 Selecting Model Structures for Multivariable Systems 3-70 Dealing with Data Offset levels 3-74 Outliers and Bad Data; Multi-Experiment Data 3-74 Missing Data 3-75 Filtering Data: Focus 3-75 Feedback in Data 376 Delaysiv Contents Defining Model Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35 Polynomial Black-Box Models: The idpoly Model . . . . . . . . . . 3-36 Multivariable ARX Models: The idarx Model . . . . . . . . . . . . . . 3-37 Black-Box State-Space Models: the idss Model . . . . . . . . . . . . 3-39 Structured State-Space Models with Free Parameters: the idss Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-42 State-Space Models with Coupled Parameters: the idgrey Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-44 State-Space Structures: Initial Values and Numerical Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-47 Examining Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-49 Parametric Models: idmodel and its children . . . . . . . . . . . . . . 3-49 Frequency Function Format: the idfrd model . . . . . . . . . . . . . 3-55 Graphs of Model Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-56 Transformations to Other Model Representations . . . . . . . . . 3-59 Discrete and Continuous Time Models . . . . . . . . . . . . . . . . . . . 3-60 Model Structure Selection and Validation . . . . . . . . . . . . . . 3-63 Comparing Different Structures . . . . . . . . . . . . . . . . . . . . . . . . 3-63 Impulse Response to Determine Delays . . . . . . . . . . . . . . . . . . 3-66 Checking Pole-Zero Cancellations . . . . . . . . . . . . . . . . . . . . . . . 3-66 Residual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-66 Model Error Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-67 Noise-Free Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-68 Assessing the Model Uncertainty . . . . . . . . . . . . . . . . . . . . . . . 3-68 Comparing Different Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-70 Selecting Model Structures for Multivariable Systems . . . . . . 3-70 Dealing with Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-74 Offset Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-74 Outliers and Bad Data; Multi-Experiment Data . . . . . . . . . . . 3-74 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-75 Filtering Data: Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-75 Feedback in Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-76 Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-77