Multiple Subsystem 2Dr. Aaron Don M. Africa

Basic Feedback ControlG1 = U / E

Superposition of Multiple InputsUsed to evaluate system performance when several inputs are simultaneously applied at a different points of a system

Step 1Set all inputs except one equal to zero We determine the output C due to inputs U and RPut U = 0

Step 2 Transform the block diagram to canonical form The system reduces to:

Step 3Calculate the response due to the chosen input acting aloneCR = [G1G2 / (1 + G1G2)] R

Step 4Repeat Steps to 3 for each remaining inputsPut R = 0 and Put a -1 into a block, representing a negative feedback effect.Rearranging the block diagram

Let the -1 block be absorbed by the summing pointThe output CU due to input U is CU = [G2 / (1 + G1G2)]U

Step 5Algebraically add all the responses

Example 1Determine the output C due to U1 , U2 and R for the figure

Let U1 = U2 = 0CR = [G1G2 / (1 G1G2H1H2) ] R

Let R = U2 = 0C1 = [G2 / (1 G1G2H1H2) ] U1

Let R = U1 = 0C2 = [G1G2H1 / (1 G1G2H1H2) ] U2

Analysis and Design of Feedback Systems

Example 2For the system shown in the figure find Peak TimePercent OvershootSettling Time

Natural FrequencyDamping RatioPeak TimePercent OvershootSettling Time

Example 3Design the value of gain K, for the feedback control system in the figure so that the system will respond at 10% overshoot (The damping ratio of 10% overshoot is 0.591)

10% overshoot has a damping ratio of 0.591

Example 4Determine the a) Loop Transfer Function b) Control Ratioc) Error Ratio d) Primary Feedback ratio

a) Loop Transfer Functionb) Control Ratio

c) Error Ratiod) Primary Feedback Ratio