Problem 3 (20 points) e-K,0 The DC motor system is modeled by the following governing equations: Jmm + bm = Kia La dia + Raia = va Kem dt 1 Due: March 24, 2023 Homework 7 (a) (10 points) Let the state variables be [0mm,a], so that the system can be described by the state equations in the form of: x = Ax + Bu y=Cx + Du where the input u = v and output y = 0. Determine the A, B, C, D matrices. For the following parts, we suggest you code it up in MATLAB for easy compu- tation and manipulation. (b) (5 points) Given the system parameters Jm=0.15kg-m,b=1.2 Nms N-m , K = 0.6 rad A V. S Ke=0.6- , La = 0.05H, Ra = 1.20 rad Determine the system stability and poles of the system. (c) (5 points) Based on state representation in (a) and parameters in (b), show that the system transfer function is given by: H(s) = 80 s3 +32s2+240s