lecture_1

# lecture_1 - 2.160 Identification Estimation and Learning...

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2.160 Identification, Estimation, and Learning Lecture Notes No. 1 February 8, 2006 Mathematical models of real-world systems are often alone . ifi Figure by MIT OCW. Figure by MIT OCW. too difficult to build based on first principles System Ident cation; “Let the data speak about the system”. Image removed for copyright reasons. HVAC Courtesy of Prof. Asada. Used with permission. Physical Modeling 1. Passive elements: mass, damper, spring 2. Sources 3. Transducers 4. Junction structure Physically meaningful parameters ( ( m m 1 s G ) = s Y ) s b + s b + L + b = 0 1 m s n ( s U ) + s a n 1 + L + a 1 n , a i = a i ( M , K B ) ( , b i = M b , K B ) i 1

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System Identification Input u( t) Output y( t) Black Box m Y ( s ) s b + s b m 1 + L + b = 0 1 m G ( s ) = U ( s ) s n + s a n 1 + L + a 1 n Physical modeling Comparison Pros 1. Physical insight and knowledge 2. Modeling a conceived system before hardware is built Cons 1. Often leads to high system order with too many parameters 2. Input-output model has a complex parameter structure 3. Not convenient for parameter tuning 4. Complex system; too difficult to analyze Black Box Pros 1. Close to the actual input-output behavior 2. Convenient structure for parameter tuning 3. Useful for complex systems; too difficult to build physical model Cons 1. No direct connection to physical parameters 2. No solid ground to support a model structure 3. Not available until an actual system has been built 2
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