Block Diagram Algebra for Summing Junctions C-GR±X Block Diagram Algebra for Branch Point _R(s) GCs) GCs) IR(s) GCs) (a) 1 GCs) 1 GCs) R(s) GCs)
3
Block Diagram Reduction Rules Table 1: Block Diagram Reduction Rules Combine all cascade blocks Combine all parallel blocks Eliminate all minor (interior) feedback loops Shift summing points to left Shift takeoff points to the right Repeat Steps 1 to S until the canonical form is obtained Table 2: Basic rules with block diagram transformation 1. 2. 4, 5. 6. I I I I I Original Block Diagram Equivalent Block Diagram 1 2 4 5 6 Manipulation Combining Blcvks in Cascade Combining Blocks in Parallel: or Eliminating a Forward Loop Moving a pickoff behind a blfkk Moving pickoff point ahead of a block Moving a summing point tkhind block Moving a summing point ahead Of a block Equation 1 2 u 1 G G G y Y el —112 Y Guj y —u 2 — Ga)u
4
Example 1: (a) reduces to reduces to (c) equrvaent to I-I(s) (d) can be rearranqed thus to avoid the •nterl.nk•nq loops wh.ch U(s) equivalent to GCs) Gds) Gds) cm G sine C(s) • cm (s) H cm which r«iuces to H2(s) G7(s) Cts) cm
5
Example 2: X(s) + 1 + GIG2 KcGlG3 1 + GIG +
6
Example 3: GAS) R(s) (it(s) R(s) G2(S) 112(s) if3(s) (a) HI(s) H2(.s) 4 Gl and G2 are in series HI and 1-12 and 1-13 are in parallel Gl is in series with the feedback configuration. I + H2(s) + Hds)l (c)
If you have your own PowerPoint Presentations which you think can benefit others, please upload on MyPrivateTutor. For each approved PPT you will get 25 Credit Points and 25 Activity Score which will increase your profile visibility.
