Question

1. The igure below zepreseats a sumplitied model oi a motut spplying a Inai. Th binck marked with an M is the motar. Assnne tbat the moteoris u. Durin opetion the motor geuerates an e..i known as the heck e.mf swn hy tuit doc The polaricies for to(0 are as showrn bwelos: Given thau u( T,n(t) k,?(t), where h and kt are constants. Find and). (12 points) Els Ra L ea(t) ,(t)

Answer 1

In this we need find theta_M (s)/ eq (s) given v_b (t) = k b d theta_m (t)/dt & T_M (t) = k_t I_a (t) where k_b & k_t are constant given diagram Rightarrow now apply K V L to the above circuit e_a (t) = (R_a + j w L_a) i_a (t) + v_b (t) Rightarrow replace the ' s' in ' t ' by laplace & j w = s ca (s) = (R a + s L a) i_a (s_0 + v_b (s) now T_M (t) = I_M d^2 theta_M/d t + D_M d theta_M/d t (by load motor) the above equation is from load motor \r\n rightarrow now taking laplace the equation becomes T_M (s) = I_M s^2 theta_M (s) + D_M s theta_M (s) now compare the given equation T_M (t) in laplace & above