ENGR 315Mathematical Models of SystemsConsider the feedback control system below. Determine the maximum range of K for stability with the Routh-Hurwitz method. Compute the roots of the characteristic equation when K is the minimum value allowed for stability. Implement a Matlab script to compute the closed–loop transfer function poles for 0< K < 5 and plot the results denoting the poles with the “x” symbol (see next page). Try to use “rlocus” and compare results.ReportENGR 315MATLAB / SIMULINK - Laboratory # 5Mathematical Models of SystemsObjectives:Study the stability of linear feedback systems.Equipment:Computer Lab PCResources:1 - Modern Control Systems, Dorf and Bishop2 - Modern Control Systems - Analysis and Design, Bishop3 - MATLAB Control System Toolbox4 - Class NotesExperiments:Consider the feedback control system below. Determine the maximum range of K for stability with the Routh-Hurwitz method. Compute the roots of the characteristic equation when K is the minimum value allowed for stability. Implement a Matlab script to compute the closed–loop transfer function poles for 0< K < 5 and plot the results denoting the poles with the “x” symbol (see next page). Try to use “rlocus”and compare results.ReportSummarize your observations and attach relevant MATLAB scripts, Simulink diagrams and plots.Report due next laboratory period.Matlab ScriptK=[0:0.1:5];n=length(K);for i=1:nnumg=[1];deng=[1 5 K(i)-3 K(i)];sys_o=tf(numg,deng);sys_cl=feedback(sys_o,[1]);p(:,i)=pole(sys_cl);endplot(real(p),imag(p),’x’),gridtext(-0.9,0.95,’K=4-->’);text(-0.2, 1.3,’K=5’);text(0,0.2,’K=0’)Kmax=4;numg=[1]; deng=[1 5 Kmax-3
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