L2-1_modeling - CDS 101 Lecture 2.1 System Modeling Richard...

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CDS 101: Lecture 2.1 System Modeling Richard M. Murray 4 October 2004 Goals: y Define what a model is and its use in answering questions about a system y Introduce the concepts of state, dynamics, inputs and outputs y Provide examples of common modeling techniques: differential equations, difference equations, finite state automata Reading: y Åström and Murray, Analysis and Design of Feedback Systems, Ch 2 y Advanced: Lewis, A Mathematical Approach to Classical Control , Ch 1
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4 Oct 04 R. M. Murray, Caltech CDS 2 Week 1: Introduction to Feedback and Control Sense Compute Actuate Control = Sensing + Computation + Actuation Feedback Principles y Robustness to Uncertainty y Design of Dynamics Many examples of feedback and control in natural & engineered systems: BIO BIO ESE ESE CS Review from last week
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4 Oct 04 R. M. Murray, Caltech CDS 3 Model-Based Analysis of Feedback Systems Analysis and design based on models y A model provides a prediction of how the system will behave y Feedback can give counter-intuitive behavior; models help sort out what is going on y For control design, models don’t have to be exact: feedback provides robustness Control-oriented models: inputs and outputs The model you use depends on the questions you want to answer y A single system may have many models y Time and spatial scale must be chosen to suit the questions you want to answer y Formulate questions before building a model Weather Forecasting 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 drought next summer? Different questions different models RMM16
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Slide 4 RMM16 Use a different model, more related to feedback and control Richard Murray, 10/4/2003
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4 Oct 04 R. M. Murray, Caltech CDS 4 Example #1: Spring Mass System Applications y Flexible structures (many apps) y Suspension systems (eg, “Bob”) y Molecular and quantum dynamics Questions we want to answer y How much do masses move as a function of the forcing frequency? y What happens if I change the values of the masses? y Will Bob fly into the air if I take that hill at 25 mph? Modeling assumptions y Mass, spring, and damper constants are fixed and known y Springs satisfy Hooke’s law y Damper is (linear) viscous force, proportional to velocity b k 3 m 1 m 2 q 1 u(t) q 2 k 2 k 1
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4 Oct 04 R. M. Murray, Caltech CDS 5
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This note was uploaded on 09/09/2009 for the course EE 4233 taught by Professor Georgio during the Spring '09 term at Minnesota Colleges.

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L2-1_modeling - CDS 101 Lecture 2.1 System Modeling Richard...

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