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�The space shuttle�consists of multiple�subsystems. Can you identify those that are control systems, or parts of control systems?

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�Components of a block diagram for�a linear, �time-invariant�system

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�a. Cascaded�subsystems;�b. equivalent transfer�function

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�Loading in cascaded�systems

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�a. Parallel�subsystems;�b. equivalent�transfer�function

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�a. Feedback control�system;�b. simplified model;�c. equivalent transfer�function

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�Block diagram�algebra for summing�junctions—�equivalent forms for moving a block�a. to the left past a�summing junction;�b. to the right past a�summing junction

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�Block diagram algebra for pickoff points—�equivalent forms for moving a block�a. to the left past a pickoff point;�b. to the right past a pickoff point

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�Block diagram�

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�Steps in solving�Example 5.1:�a. collapse summing�junctions;�b. form equivalent�cascaded system�in the forward path�and equivalent�parallel system in the�feedback path;�c. form equivalent�feedback system and�multiply by cascaded�G₁(s)�

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�Block diagram

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�Steps in the �block diagram �reduction

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�Steps in the �block diagram �reduction

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�Steps in the �block diagram �reduction

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�Steps in the �block diagram �reduction

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�Steps in the �block diagram �reduction

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�Steps in the �block diagram �reduction

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�Block diagram for�Skill-Assessment�Exercise

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�Second-order�feedback control�system

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�Feedback system

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�Feedback system for�

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�Signal-flow graph components:�a. system;�b. signal;�c. interconnection of systems and signals

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�Building signal-flow�graphs:�a. cascaded system�nodes (from Figure 5.3(a));�b. cascaded system�signal-flow graph;�c. parallel system�nodes (from Figure 5.5(a));�d. parallel system�signal-flow graph;�e. feedback system�nodes (from Figure�5.6(b));�f. feedback system�signal-flow graph

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�Signal-flow graph�development:�a. signal nodes;�b. signal-flow graph;�c. simplified signal-flow graph

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�Signal-flow graph�for demonstrating�Mason’s rule

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Loop Gain:-

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Forward Path gain

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Non-Touching loop gain

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Mason Gain Formulae

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�Forward Path gain��Loop Gains

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�Non-Touching loops taking two at a time

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�Non-Touching loops taking three at a time

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�Stages of�development of a�signal-flow graph�for the system of�Eqs. 5.36:�a. place nodes;�b. interconnect�state variables and�derivatives;�c. form dx₁/dt ;�d. form dx₂/dt�(figure continues)

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�(continued)�e. form dx₃/dt;�f. form output

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�Representation of�Figure as�cascaded first-order�systems

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�a. First-order subsystem;�b. signal-flow graph for Figure 5.23 system

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�Signal-flow�representation

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�Signal-flow�representation�

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Figure 5.27�Signal-flow graphs for obtaining forms for�G(s) = C(s)/R(s) = (s² + 7s + 2)/(s³+ 9s² + 26s + 24):�a. phase-variable form;�b. controller canonical form