This exam will be involving the modeling of a butterfly valve shown in Fig. 1. The equations that model the electrical and mechanical parts of the sysetm are Eq. 1 through7 Tk Tn Problem 1: Find the transfer function as H(s) with all the values sylnbolic. You may find the transfer function by hand or in MATLAB. After do the following: (a) What is the transfer function with the numeric values for constants plugged in? (n - 19.225, Ra-5 , La = 1.1 mH, J = 1.1347527 kgm2, kb = 0.0829 Vsec/rad, ki = 0.0892 Nm/A,K = 0.1 Nmrad-1) (b) Make your sampling rate at twice your highest pole frequency. (c) Find the discrete transfer function of the system H(z) i. with Impulse Invariant ii. with Bilinear Transform (d) Plot the open loop discrete time response to a step input for the Impulse Invariant system and the Bilinear Transformed system on the same graph. Label both in a legend (e) Show the discrete frequency response of the system for the Impulse Invariant (f) Print out the above results and turn in a hard copy. (g) Submit your m-file (or live script) to blackboard 4 2 A wA, MA eb UK MR MP electromagnetic subsystem mechanical subsystem This exam will be involving the modeling of a butterfly valve shown in Fig. 1. The equations that model the electrical and mechanical parts of the sysetm are Eq. 1 through7 Tk Tn Problem 1: Find the transfer function as H(s) with all the values sylnbolic. You may find the transfer function by hand or in MATLAB. After do the following: (a) What is the transfer function with the numeric values for constants plugged in? (n - 19.225, Ra-5 , La = 1.1 mH, J = 1.1347527 kgm2, kb = 0.0829 Vsec/rad, ki = 0.0892 Nm/A,K = 0.1 Nmrad-1) (b) Make your sampling rate at twice your highest pole frequency. (c) Find the discrete transfer function of the system H(z) i. with Impulse Invariant ii. with Bilinear Transform (d) Plot the open loop discrete time response to a step input for the Impulse Invariant system and the Bilinear Transformed system on the same graph. Label both in a legend (e) Show the discrete frequency response of the system for the Impulse Invariant (f) Print out the above results and turn in a hard copy. (g) Submit your m-file (or live script) to blackboard 4 2 A wA, MA eb UK MR MP electromagnetic subsystem mechanical subsystem