For the forward-path transfer functions given below, determine the type of the unity-feedback system and calculate the step, ramp, and parabolic error constants of the unity-feedback control system. Also, determine the steady-state error for a unit-step input, unit-ramp input, and parabolic input. Check the stability of the system before applying the final-value theorem.
(a) G(s) = (1+5)(s+10)(s+20) / (s+1)(s+5)(s+10)(s+20)
(b) G(s) = 1 / (s^6+5s^6+6s^2+6)
(c) G(s) = s / (s+5)(s+6)(s^2+6s+4)
(d) G(s) = 8(s+5s+5) / (s+10)(s+6s+4)
(e) G(s) = 8(s+2) / (5s+6s+2)
(f) G(s) = 8(s+4) / (8s+4)
(g) G(s) = (s^2+25s+3) / (6s+1)