HW 7 solutions - EML 4312 HW 7 Solutions 1a. The equation...

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Unformatted text preview: EML 4312 HW 7 Solutions 1a. The equation to find a transfer function from a state space representation: () ( [ ) [ [ [ [ ] () Or since the given A matrix is not in the controllable canonical form we must find a transformation matrix, P, to bring the given A, B, C matrices into that form. [ [ 2 Where a1 comes from the characteristic equation: s + a1s + a2. 2 The characteristic equation is: s – 5s + 3. Then we can calculate the transformation matrix P. [ Now we can obtain the controllable canonical form of our system. [ [ So using the controllable canonical form we can get the transfer function, H(s) () 1b. The given A matrix is in controllable canonical form so we don’t need to find a transformation matrix and we can find the transfer function from the state space representation without any calculations. () 1c. . The equation to find a transfer function from a state space representation: () ( [ ) [ [ [ () Or since the given A matrix is not in the controllable canonical form we must find a transformation matrix, P, to bring the given A, B, C matrices into that form. [ [ 3 2 Where a1 comes from the characteristic equation: s + a1s + a2s +a3. 3 2 The characteristic equation is: s – 3s – 5s + 7. Then we can calculate the transformation matrix P. [ Now we can obtain the controllable canonical form of our system. [ [ So using the controllable canonical form we can get the transfer function, H(s) () 2a. [ [ [ 2b. [ 2c. 3. Place closed loop poles at s = -5,-3±2j. Construct controllability matrix [ [ Find the closed loop scalar polynomial () ( )( )( ) Find the closed loop matrix polynomial () [ Use Ackermann’s Formula to find K [ () [ Place observer poles at s=-10,-1,-1. Construct Observability Matrix [ [ Find the closed loop scalar polynomial () ( )( )( ) Find the closed loop matrix polynomial () [ Use Ackermann’s Formula to find L () [ ...
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This note was uploaded on 09/05/2011 for the course EML 4312 taught by Professor Dixon during the Spring '07 term at University of Florida.

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