Problem 3 Consider the DC motor system shown below: R La -0000- TL i ia Τω TITIT Motor The above circuit diagram represents a speed-control system in which the DC motor voltage is V=2. Parameters are R=2,L, =1,1=1, and c = 2. The external load, T, =0 di V-Ri-L -K,w=0 dt dw dt -Ki+T₁₂+coo=0 (a) The number of coils in the armature, n, is 20 and the flux density of the field, B, is 1 Wb/m². Also, the length of the conductor, L, is 1 m and the armature radius, r, is 0.1 m. Then calculate the motor constants, Km, (motor constant), Kr (torque constant) and K (back emf constant). Provide the values of all the three constants. (5 points) (b) After substituting the parameters given in the problem, find the steady-state current, i.. from the state variable form. (10 points) (c) When the transfer function of the system is given as Is+c V LIs²+(RI+cL¸)s+cR¸+K² what is the current, i, at the steady state? Use the Final Value Theorem and show your work clearly. (10 points)