ME 176Control Systems Engineering

Department of

Mechanical Engineering

Reduction of Multiple Subsystems

Block Diagrams: Elements:

Department of

Mechanical Engineering

Block Diagrams: Topologies Cascade Form:

Department of

Mechanical Engineering

Department of

Mechanical Engineering

Block Diagrams: Topologies Cascade Form:

Exception: Assumption that the interconnected subsystems do not load adjacent subsystems.

Use K (amplifier), it has high-impedance input so it does not load previus network. And has low impedance output so it looks like a pure voltage source to subsequent networks

Block Diagrams: Topologies Parallel Form:

Department of

Mechanical Engineering

Block Diagrams: Topologies Feedback Form:

Department of

Mechanical Engineering

Block Diagrams: Moving Blocks Algebra for Summing Junctions:

Department of

Mechanical Engineering

Block Diagrams: Moving Blocks Algebra for Pickoff Points:

Department of

Mechanical Engineering

Block Diagrams: Example Steps:a) Collapse suming junction.b) Form equivalent cascade system inthe forward and feedback paths.c) Form equivalent feedback systemand multiply by cascaded G1(s).

Department of

Mechanical Engineering

Block Diagrams: Example

Move G2(s) to the left past pickoff point to create parallel subsystems.Reduce feedback system consisting of G3(s) and H3(s).

Department of

Mechanical Engineering

Block Diagrams: Example

Reduce parallel pair of 1/G2(s) and unity.Push G1(s) past right summing junction.

Department of

Mechanical Engineering

Block Diagrams: Example

Collapse summing junction and two feedback elements.Combine last two cascade blocks.

Department of

Mechanical Engineering

Block Diagrams: Example

Reduce the remaining feedback system.

Combine last two cascade blocks.

Department of

Mechanical Engineering

Analysis and Design of Feedback Systems:

Department of

Mechanical Engineering

Analysis and Design of Feedback Systems:

Department of

Mechanical Engineering