Practice Final Problem 2 solution

Practice Final Problem 2 solution - / p E q C = + d and / R...

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(Spring 2001) Define state variables and write differential equations for the following model shown in bond graph form. The moduli of elements are constant except for the resistance which can be expressed as either R R e aq = d or 2 R R q ae = d a. Is the bond graph reducible to a tree like structure? Yes or No (please circle) b. Assign causality to all bonds. c. Is the system causal , under causal or over-causal (circle your answer)? d. What are the state variables? p , q . e. What is the state vector ( ) t x ? ( ) p t q   =     x f. What is the input vector ( ) t u ? ( ) { } t E = u g. Derive and write the first order differential equations for the system. From the bond graph first get
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Unformatted text preview: / p E q C = + d and / R q q p I =-d d . Noting 2 R R q ae = d and / / R e E T q C =-gives ( ) 2 / / / q a E T q C p I =--d . Thus the nonlinear differential equations become, ( ) 2 / / / / p E q C q a E T q C p I = + =--d d h. What is the state matrix A ? There is no linear state matrix for nonlinear differential equations. i. What is the matrix B ? There is no such matrix as the input is utilized in a nonlinear combination with a state in the differential equations. R 1 C 1 I E S E T E E p d / p I / p I / p I q d / q C / q C / q C / E T / / R e E T q C =-R e R q d 2 R R q ae = d R q d R q d / R q T d...
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