Empirical Modeling

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# Empirical Modeling - PowerPoint PPT Presentation

Empirical Modeling. Introduction Regression models First-order transfer function models Second-order transfer function models Integrating models Matlab System Identification Toolbox. Motivation. Fundamental models Derived from conservation principles Typically comprised of ODEs

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## PowerPoint Slideshow about 'Empirical Modeling' - dolf

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Presentation Transcript
Empirical Modeling
• Introduction
• Regression models
• First-order transfer function models
• Second-order transfer function models
• Integrating models
• Matlab System Identification Toolbox
Motivation
• Fundamental models
• Derived from conservation principles
• Typically comprised of ODEs
• Preferred modeling approach when possible
• Limitations of fundamental modeling
• Often lack fundamental knowledge of process
• Unknown parameters must be determined
• Complex models may not be suitable for controller design
• Alternative approach
• Derive model directly from process data
• Procedure known as process identification
• Yields empirical models
Process Identification
• Basic idea
• Vary process input u(t)
• Collect measurements of the process output y(t)
• Use data to construct dynamic model M relating u(t) and y(t)
• Goal is to obtain the simplest model possible
• Limitations
• Model only represents process dynamics over range of data collected
• No fundamental knowledge is gained
General Modeling Procedure
• Formulate model objectives
• Select input and output variables
• Develop plant testing plan and collect data
• Analyze dataset and remove “bad” data
• Select model structure
• Estimate unknown model parameters by regressing the available data
• Validate model using data not used for regression
Linear Regression Models
• Steady-state data: (u1,Y1), (u2,Y2),…, (uN,YN)
• Assume linear steady-state model structure
• Least-squares problem
• Solution:
Linearly Parameterized Models
• Can apply linear regression if the unknown parameters appear linearly
• Model structure
• Least-squares problem
• Solution:
First-Order Models
• Model structure
• Step response:
• Gain calculation
• Time constant calculation
First-Order Model Example
• Gain calculation
• Time constant calculation
• Model
First-Order Plus Time Delay Models
• Model structure
• Calculation of q and t
• Determine times when output has reached 35.3% (t35) and 85.3% (t85) of its final value with the time delay removed
• Calculate q and t
• The inflection-free method is preferred
Second-Order Models
• Model structure
• Estimate q from step response
• Calculation of z and t
• Determine times when output has reached 20% (t20) and 60% (t60) of its final value with the time delay removed
• Calculate z and t from graph
Second-Order Model Example
• Normalized step response data
• Assume K is known and q = 0
• Time constant calculation
Integrating Models
• Model structure
• Step response
• Calculation of K
• Select two times t1 and t2
• Compute
Matlab System Identification Toolbox
• Data import and processing: represent, process, analyze and manipulate data
• Linear model identification: estimate transfer function and state-space models from time domain data
• Analysis: validate and analyze models by comparing model output, computing parameter confidence intervals and prediction errors
• Simulation and prediction: simulate and predict linear model output
• Not used in this class