ENGR 315 CALVIN COLLEGE Engineering DepartmentMathematical Models of Systems1 – Read and implement functions of Section 2.10 (to gain further familiarity with MATLAB). You may skip this part if you have already used of the functions on the section.3 – Implement the MATLAB and Simulink solution of Problem MP2.6. Use a step input to verify the response of the system. Vary gains and constants and discuss the responses.ReportENGR 315 CALVIN COLLEGE Engineering DepartmentMATLAB / SIMULINK - Laboratory # 2Mathematical Models of SystemsObjectives:In this lab we consider some of the issues surrounding the modeling of physical systems. Equipment:Computer Lab PCResources:1 - Modern Control Systems, Dorf and Bishop2 - MATLAB Control System Toolbox3 - Class NotesExperiments:1 – Read and implement functions of Section 2.10 (to gain further familiarity with MATLAB). You may skip this part if you have already used of the functions on the section.2 – Implement (using Simulink) the filed-controlled dc motor (open-loop) and armature-controlled dc motor (closed-loop) of Example 2.5. (Section 2.5 page 52-56). Assume the following parameters: moment of inertia of the rotor (J) = 3.2284E-6 kg.m^2/s^2 damping ratio of the mechanical system (b) = 3.5077E-6 Nms electromotive force constant (Km) = 0.0274 Nm/Amp electric resistance (Rf) = 4 ohm electric inductance (Lf) = 2.75E-6 HStudy and expand the analytical equations, transfer functions and block diagrams beforeperforming the computer simulations.3 – Implement the MATLAB and Simulink solution of Problem MP2.6. Use a step input to verify the response of the system. Vary gains and constants and discuss the responses.ReportSummarize your observations and attach relevant MATLAB scripts, diagrams and plots.Report due next laboratory period.M-File for the field-controlled dc motor example (open-loop)J=3.2284E-6;b=3.5077E-6;Km=0.0274;Rf=4;Lf=2.75E-6;num=Km;den=[(J*Lf) ((J*Rf)+(Lf*b)) ((b*Rf)+Km^2) 0];step(num,den,0:0.001:0.2);M-File for the armature-controlled dc motor example (closed-loop)J=3.2284E-6;b=3.5077E-6;Km=0.0274;Kb=Km;Ra=4;La=2.75E-6;num1=Km;den1=[(J*La) ((J*Ra)+(La*b)) ((b*Ra)+Km^2) 0];sys1=tf(num1,den1);sys=feedback(sys1,[1]);step(sys,0:0.001:0.2);M –File for Problem MP2.6num1=[1]; den1=[1 1]; sys1=tf(num1, den1);num2=[1 0]; den2=[1 0 2]; sys2=tf(num2, den2);num3=[1]; den3=[1 0 0]; sys3=tf(num3, den3);num4=[4 2]; den4=[1 2 1]; sys4=tf(num4, den4);num5=[50]; den5=[1]; sys5=tf(num5, den5);num6=[1 0 2]; den6=[1 0 0 14]; sys6=tf(num6, den6);num7=[4]; den7=[1]; sys7=tf(num7, den7);sys8=feedback(sys3,sys5,1)sys9=series(sys1,sys2)sys10=feedback(sys9,sys4)sys11=series(sys8,sys10)sys12=feedback(sys11,sys6)sys=series(sys7,sys12)step(sys,0:0.001:10)p=pole(sys)z=zero(sys)pzmap(sys)
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