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BlockDiagramLecture

# BlockDiagramLecture - ME 279 Automatic Control of Dynamic...

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ME 279 Automatic Control of Dynamic Systems Dr. Robert G. Landers Block Diagrams

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Introduction 2 Block diagrams are visual representations of dynamic systems. A block diagram can consist of one block with inputs and outputs or it can be an interconnection of blocks showing internal states and complex input–output characteristics. Block diagrams are used for graphical simulation and in control design, analysis, and implementation. So far we have dealt with a single system Block Diagrams Dr. Robert G. Landers U(s) is the input signal. Y(s) is the output signal. The arrows denote time varying signals (e.g., inputs, outputs) and blocks denote dynamic systems. The block diagram algebra is that the output signal is equal to the dynamic system multiplied by the input signal. In the block diagram given above, Y(s) = G(s)U(s). G(s) U(s) Y(s)
Introduction 3 Summing Junctions Block Diagrams Dr. Robert G. Landers Pickoff Point + + - U 1 (s) U 2 (s) U 3 (s) Y(s) = U 1 (s) + U 2 (s) – U 3 (s) U(s) U(s) U(s) U(s)

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Example 1 4 For the feedback control system below, determine the transfer functions Y(s)/R(s), U(s)/R(s), E m (s)/R(s), and E(s)/R(s), where E(s) = R(s) – Y(s) is the true error. R(s) is the reference, E m (s) is the measured error, U(s) is the control signal, and Y(s) is the output. Block Diagrams Dr. Robert G. Landers Plant G(s) Controller G C (s) U(s) R(s) + - Y(s) E m (s) Sensor H(s)
Example 1 5 ( 29 ( 29 ( 29 ( 29 m E s R s H s Y s = - Block Diagrams Dr. Robert G. Landers ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 C m C Y s G s U s G s G s E s G s G s R s H s Y s = = = - The measured error is The output is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 C C Y s G s G s R s G s G s H s = + The transfer function Y(s)/R(s) is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 C C U s G s R s G s G s H s = + The input is U(s) = C(s)/G(s) and the transfer function U(s)/R(s) is

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Example 1 6 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 m C E s R s G s G s H s = + Block Diagrams Dr. Robert G. Landers The measured error is E m (s) = C(s)/(G C (s) G(s)) and the transfer function E m (s)/R(s) is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 C C G s G s E s R s C s R s R s G s G s H s = - = - + The true error is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29
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BlockDiagramLecture - ME 279 Automatic Control of Dynamic...

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