TUTORIAL ROOT LOCUS DESIGN

# TUTORIAL ROOT LOCUS DESIGN - Root-Locus Design The...

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For a given 1 1 s 1 j σ ω = + , the transfer function angle given by 0 ( c z p 0 ) θ θ θ = is positive if as shown in Figure 1 (a), and the compensator is known as the phase-lead controller . On the other hand if as shown in Figure 1 (b), the compensator angle 0 z p < 0 ( c z 0 0 0 z p > 0 ) p θ θ = θ is negative, and the compensator is known as the phase-lag controller In general, the open-loop transfer function is given by 1 2 1 2 ( )( ) ( ( ) ( ) ( )( ) ( m n K s z s z s z KG s H s s p s p s p + + + = + + + " " ) ) ) where is the number of finite zeros and is the number of finite poles of the loop transfer function. If , there are ( m n m n m > n zeros at infinity. The characteristic equation of the closed-loop transfer function is 1 ( ) ( ) KG s H s + = 0 Therefore 1 2 1 2 ( )( ) ( ) ( )( ) ( ) n m s p s p s p K s z s z s z + + + = − + + + " " From the above expression, it follows that for a point in the -plane to be on the root- locus, when 0 , it must satisfy the following two conditions.
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