hw1_f08 - Homework Set#1 MAE 4720/7720 Modern Control Fall...

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Homework Set #1: MAE 4720/7720 – Modern Control Fall 2008 Due September 11, 2008 Problem 1 . A simple RLC circuit has the following voltage equation (obtained by applying Kirchhoff’s law): + + = t a idt C Ri dt di L e 0 1 where e a is the applied voltage (input); L , R , and C are the inductance, resistance, and capacitance elements; and i is the circuit current. We can replace the above integro- differential equation by introducing the new variable q , which is the electric charge density, such that dq / dt = i , with initial condition q (0) = 0. Derive a complete state-space representation where the desired (single) output variable is the voltage across the capacitor C , i.e., e C = t idt C 0 1 . Be sure to identify all matrices ( A , B , C , and D ) and their dimensions (note that output matrix C is not to be confused with capacitance…) Problem 2 . Consider again the RLC circuit in Problem 1, but now let the inductance be a nonlinear function of current, i.e., L = L ( i ). Write the system equations in state-variable
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This note was uploaded on 01/12/2011 for the course MAE 4720 taught by Professor Dr.kluever during the Spring '10 term at Missouri (Mizzou).

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hw1_f08 - Homework Set#1 MAE 4720/7720 Modern Control Fall...

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