Question 9.6.3: Consider a system under control, with transfer function G(s)...
Consider a system under control, with transfer function
G(s)=\frac{K}{(1+sT_1)(1+sT_2)}Show that using the PID controller (Eq. (9.6-1)), one can achieve arbitrary pole placement and simultaneously drive the position steady-state error to zero.
G_c(s)=K_p+\frac{K_i}{s}+K_ds=\frac{K_ps+K_i+K_ds²}{s}=\frac{K_d\left[s²+\frac{K_p}{K_d}s+\frac{K_i}{K_d}\right]}{s} (9.6-1a)
G_c(s)=K_p\left[1+\frac{1}{T_is}+T_ds\right], where T_i=\frac{K_p}{K_i} and T_d=\frac{K_d}{K_p} (9.6-1b)
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