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chapter_3_model_typesrev09 [Compatibility Mode]

# chapter_3_model_typesrev09 [Compatibility Mode] - ME 375...

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1 ME 375 System Modeling and Analysis Section 3 – State Variable and Input-Output Modeling Frameworks j j j j i i i i dt u d b dt y d a = } ]{ [ } ]{ [ } { } ]{ [ } ]{ [ } { u D q C y u B q A q + = + = & Spring 2009 School of Mechanical Engineering Douglas E. Adams Associate Professor

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2 Key points to remember Different frameworks for expressing models We are only observers of the system’s behavior: We only measure a portion of the system dynamics 3.1 We only measure a portion of the system dynamics. Input-output models are unique. State variable models are not unique. Why choose state variable models? All integrators solve first order differential equations, and state variable models contain only first order equations. State variable models provide an easy way to identify all the natural frequencies, time constants, etc. of the system by solving an eigenvalue problem. Which model form to choose? Time domain-MIMO-numerical solution state-variable Frequency domain-SISO-analytical solution input-output © 2009 D. E. Adams ME 375 – State variable and input-output models
3 State variable models Specific example 1.Select state variables If we know ALL the state variables, , initially, q 3.2 If we know ALL the state variables, we should be able to evaluate ALL variables at any later time. What does that mean? i K B g Vibration examples (SDOF) ) ( t f Ky y B y M d d d = + + & & & E.O.M. We need to know d y f y M because it determines the POTENTIAL ENERGY We need to know because it determines the KINETIC ENERGY d y & Conclusion The initial energy in all elements must be known because the dynamics are determined by the transfer of this energy. and are independent energy storage elements d y & d y © 2009 D. E. Adams ME 375 – State variable and input-output models

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4 State variable models Specific example (cont.) 1.Select state variables (continued) di d d t t h t b d 3.3 2. Solve for the derivatives of state variables and are independent, so they cannot be expressed as
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chapter_3_model_typesrev09 [Compatibility Mode] - ME 375...

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