Module 7 Higher-Order Systems (I hour) TF in evans or bode form Approximate a higher order system with a first or second order one Effect of zeros and poles on the transient response Origins of zeros
Module 7 Higher – Order Systems (1 hour) • TF in Evans or Bode form • Approximate a higher order system with a first or second order one • Effect of zeros and poles on the transient response • Origins of zeros
7.1 Evans and Bode form Higher order systems: Consider the following transfer function B(s) F(S)A(s)(+P)s+p,).(s+p (Evans form) We can pull out the product of the poles and pre-multiply the conjugate pairs F(s)= B(S A(s)(s+PiXs+p2)s+p2) Pippa s+1 s+1 S+1 p2 Bo (Bode form Pippa s+1 +s+1 P F 0 2
7.1 Evans and Bode form
In general any transfer function can be re-written in bode form F(s)=Fo (Bode form) (s+1)z2s+1) 2S2+2 s+1 2 S-+ s+1 Q: What is the DC gain of F(s)? Example F(s)= S+15 s +35+4/(Evans form) (Bode form 154(0051025205+1 Q:What are the values of @ and 5 in the above example?
7.2 Approximate a higher order system with a first or second order one To approximate the system with a lower order transfer function, we keep only the dc gain and the dominant poles in its Bode form: F(s) 60067+1)0.2552+0.75+1 ( Bode form) (0.067+1)=0→s=-15 0.252+0.75s+1)=0→s=-1.5±1.32j 15 X 1.5 F(s 600.25s2+075s+1
7.2 Approximate a higher order system with a first or second order one
Step res pons e x10 16 pproximate F A 14 10 8 6 Original F 0 0.5 1.5 2 3.5 Time(s ec)