ENGR 315Mathematical Models of SystemsThan write a MATLAB script to compute and plot the close-loop transfer function poles within a certain selected range (see suggestion next page – please modify and explore possibilities).2 - The Bell-Boeing V-22 Osprey Tiltrotor is both an airplane and a helicopter. Its advantage is the ability to rotate its engine to 90 degrees from a vertical position, as shown below, for takeoffs and landings and then switch the engines to a horizontal position for cruising as an airplane. The altitude control system in the helicopter mode is shown below. a) Determine the root locus as K varies and determine the range for a stable system (use the stability criteria on the closed-loop transfer function) . b) For K = 280, find the actual y(t) for a unit step input r(t) and the percentage overshoot and settling time. C) When K=280 and r(t)=0, find y(t) for a unit step disturbance. d) Add a prefilter between R(s) and the summing node so thatGp(s) = 0.5 / (s^2 + 1.5s + 0.5) and repeat part b).ReportENGR 315MATLAB / SIMULINK - Laboratory # 5Mathematical Models of SystemsObjectives:To learn about the Stability Criteria (H-W Method) and Root Locus Method for designing and analyzing feedback control systems.Equipment:Computer Lab PCResources:1 - Modern Control Systems, Dorf and Bishop2 - Modern Control Systems - Analysis and Design, Bishop3 – MATLAB, Simulink, Control System Toolbox, Class NotesExperiments:1 – Consider the system below. Use R-H method to determine the range of K for stability.Than write a MATLAB script to compute and plot the close-loop transfer function poles within a certain selected range (see suggestion next page – please modify and explore possibilities).2 - The Bell-Boeing V-22 Osprey Tiltrotor is both an airplane and a helicopter. Its advantage is the ability to rotate its engine to 90 degrees from a vertical position, as shown below, for takeoffs and landings and then switch the engines to a horizontal position for cruising as an airplane. The altitude control system in the helicopter mode is shown below. a) Determine the root locus as K varies and determine the range for a stable system (use the stability criteria on the closed-loop transfer function) . b) For K = 280, find the actual y(t) for aunit step input r(t) and the percentage overshoot and settling time. C) When K=280 and r(t)=0, find y(t) for a unit step disturbance. d) Add a prefilter between R(s) and the summing node so that Gp(s) = 0.5 / (s^2 + 1.5s + 0.5) and repeat part b).ReportSummarize your observations and attach relevant MATLAB scripts, Simulink diagrams and plots.Report due next laboratory period.Example of MATLAB ScriptMatlab Script:K=[0:0.1:50];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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