L1-2_modeling

L1-2_modeling - CDS 101/110a Lecture 1.2 System Modeling Douglas G MacMynowski 29 September 2010 Goals Define a model and its use in answering

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1 CDS 101/110a: Lecture 1.2 System Modeling Douglas G. MacMynowski 29 September 2010 Goals: Define a “model” and its use in answering questions about a system Introduce the concepts of state, dynamics, inputs and outputs Review modeling using ordinary differential equations (ODEs) Reading: Åström and Murray Feedback Systems Sections 2 1–23 31[40m in Åström and Murray, Feedback Systems, Sections 2.1 2.3, 3.1 [40 min] Advanced: Lewis, A Mathematical Approach to Classical Control , Chapter 1 Monday: Introduction to Feedback and Control Sense Actuate Control = Sensing + Computation + Actuation Feedback Principles Compute Robustness to Uncertainty Design of Dynamics Many examples of feedback and control in natural & engineered systems: BIO Douglas G. MacMynowski, Caltech CDS CDS 101/110, 29 Sep 10 2 BIO ESE ESE CS
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2 Model-Based Analysis of Feedback Systems Analysis and design based on models A model provides a prediction of how the system will behave Feedback can give counter-intuitive behavior; models help sort out what is going on Weather Forecasting For control design, models don’t have to be exact: feedback provides robustness The model you use depends on the questions you want to answer A single system may have many models Time and spatial scale must be chosen to suit the questions you want to answer Question 1: how much will it rain tomorrow? Question 2: will it rain in the next 5-10 days? Question 3: will we have a Douglas G. MacMynowski, Caltech CDS CDS 101/110, 29 Sep 10 3 Formulate questions before building a model Control-oriented models: inputs and outputs Capture input/output behaviour “sufficiently” well Question 3: will we have a drought next summer? Different questions different models Example #1: Spring Mass System Applications Flexible structures (many apps) Suspension systems (eg, “Bob”) Molecular and quantum dynamics m 1 m 2 q 1 u(t) q 2 Questions we want to answer How much do masses move as a function of the forcing frequency? What happens if I change the values of the masses? Will Bob fly into the air if I take that speed bump at 25 mph? Modeling assumptions c k 3 k 2 k 1 Douglas G. MacMynowski, Caltech CDS CDS 101/110, 29 Sep 10 4 Mass, spring, and damper constants are fixed and known Springs satisfy Hooke’s law Damper is (linear) viscous force, proportional to velocity
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3 Modeling a Spring Mass System m 1 m 2 q 1 u(t) q 2 Model: rigid body physics (Ph 1) Sum of forces = mass * acceleration Hooke’s law: F = k ( x x rest ) Viscous friction: F = c v c k 3 k 2 k 1
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This note was uploaded on 01/04/2012 for the course CDS 101 taught by Professor Murray,r during the Fall '08 term at Caltech.

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L1-2_modeling - CDS 101/110a Lecture 1.2 System Modeling Douglas G MacMynowski 29 September 2010 Goals Define a model and its use in answering

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