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5. Some useful design curves

Figure 15 Unit step response vs normalised time $\omega_n t$ for various values of $\zeta$ (2nd order)

Figure 16 Bode diagram of a first order pole plotted against normalised frequency $\omega/p$

Figure 17 Bode diagram of a first order zero plotted against normalised frequency $\omega/z$

Figure 18 Bode diagram of a second order complex pair of poles plotted against normalised frequency $\omega/\omega_n$ for various values of $\zeta$

Figure 19 Effect of an extra pole at $s = -­p_r$ on a second order system

a) % overshoot $M_P$ vs $p_r/\zeta \omega_n$

b) normalised rise time $\omega_n t_r$ vs $p_r/\zeta \omega_n$

Figure 20 Effect of an extra zero at $s = -­z_r$ on a second order system

a) % overshoot $M_P$ vs $z_r/\zeta \omega_n$

b) normalised rise time $\omega_n t_r$ vs $z_r/\zeta \omega_n$

Figure 21 Maximum phase lead v $\alpha$ for a phase-lead compensator

Figure 22 Transient response overshoot $M_P$ and frequency response resonant peak vs phase margin for a second order system (note $M_r = M_\max$)

4. Design Criteria Acknowledgements