ECE 455/555 Project 1 Due March 25, 2019 φ K Nef x RLl iv + – + – xf D f fe M Figure 1: U-I electromagnet (labeled Figure 2.2-3 in EMD). Consider the U-I electromagnet of Figure 1. The magnetizing...

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ECE 455/555 Project 1 Due March 25, 2019 φ K Nef x RLl iv + – + – xf D f fe M Figure 1: U-I electromagnet (labeled Figure 2.2-3 in EMD). Consider the U-I electromagnet of Figure 1. The magnetizing inductance of this system may be expressed Lm(x) = k k0 + x . Write the state equations, choosing either i or λ as your electrical state and build the system model in Simulink. The system parameters are detailed in Table 1. Simulate the system for 0.2 seconds for each of the two stimuli detailed in the task descriptions below. Timing parameters are listed in Table 2. These studies are similar to those on pp. 77–78 of Electromechanical Motion Devices. The initial conditions of the states should be set such that each simulation begins from equi- librium (i.e., no motion/variation should occur prior to a change in the inputs). The appropriate initial conditions should be determined from steady-state analysis. For each simulation, plot 1. the back-emf ef , 2. total flux-linkage λ, 3. current i, 4. electromagnetic force fe, 5. displacement x, 6. electrical energy supplied to the field We, 7. field energy Wf , 8. mechanical energy supplied to the field Wm. A plotting script and project report template will be provided. 1 ECE 455/555 Project 1 Due March 25, 2019 Task 1. Electrical stimulus The applied force f(t) is set to zero. The voltage source is stepped up and then back down as follows: Vs(t) =  0 V t0 ≤ t < t1,="" 5="" v="" t1="" ≤="" t="">< t2,="" 0="" v="" t="" ≤="" t2="" ≤="" tf="" .="" task="" 2.="" mechanical="" stimulus="" the="" voltage="" source="" is="" set="" to="" a="" constant="" 5="" v.="" the="" applied="" force="" is="" stepped="" up="" and="" then="" back="" down="" as="" follows:="" f(t)="" 0="" n="" t0="" ≤="" t="">< t1,="" 4="" n="" t1="" ≤="" t="">< t2, 0 n t ≤ t2 ≤ tf . task 3. ece 555 only—nonlinear material repeat tasks 1 and 2 for a core with nonlinear magnetic permeability such that the inductance coefficient k is a function of current of the given form: k(i) , α√ 1 + i2 . (1) 2 ece 455/555 project 1 due march 25, 2019 table 1: physical and system parameters for u-i electromagnet. parameter description value units r resistance 10 ω k inductance coeff. 6.283× 10−5 h ·m k0 inductance parameter 10 −4 m α nonlinear inductance coeff. 6.283× 10−5 h ·m ll leakage inductance 0.1 h m mass 55 g d damping factor 4 n · s/m k spring rate 2667 n/m xf spring free pos. 3 mm table 2: simulation parameters for project 2. parameter description value units t0 initial time 0 s t1 first step time 0.02 s t2 second step time 0.1 s tf final time 0.2 s 3 t2,="" 0="" n="" t="" ≤="" t2="" ≤="" tf="" .="" task="" 3.="" ece="" 555="" only—nonlinear="" material="" repeat="" tasks="" 1="" and="" 2="" for="" a="" core="" with="" nonlinear="" magnetic="" permeability="" such="" that="" the="" inductance="" coefficient="" k="" is="" a="" function="" of="" current="" of="" the="" given="" form:="" k(i)="" ,="" α√="" 1="" +="" i2="" .="" (1)="" 2="" ece="" 455/555="" project="" 1="" due="" march="" 25,="" 2019="" table="" 1:="" physical="" and="" system="" parameters="" for="" u-i="" electromagnet.="" parameter="" description="" value="" units="" r="" resistance="" 10="" ω="" k="" inductance="" coeff.="" 6.283×="" 10−5="" h="" ·m="" k0="" inductance="" parameter="" 10="" −4="" m="" α="" nonlinear="" inductance="" coeff.="" 6.283×="" 10−5="" h="" ·m="" ll="" leakage="" inductance="" 0.1="" h="" m="" mass="" 55="" g="" d="" damping="" factor="" 4="" n="" ·="" s/m="" k="" spring="" rate="" 2667="" n/m="" xf="" spring="" free="" pos.="" 3="" mm="" table="" 2:="" simulation="" parameters="" for="" project="" 2.="" parameter="" description="" value="" units="" t0="" initial="" time="" 0="" s="" t1="" first="" step="" time="" 0.02="" s="" t2="" second="" step="" time="" 0.1="" s="" tf="" final="" time="" 0.2="" s="">