ENGR 315Mathematical Models of Systems2 - 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), 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).ReportENGR 315MATLAB / SIMULINK - Laboratory # 6Mathematical Models of SystemsObjectives:To learn about the 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 – The dynamics of a motorcycle open-loop transfer function is represented byGH(s) = K(s^2 + 30s +625) / s(s + 20)(s^2 + 20s + 200)(s^2 + 60s + 3400)Sketch the root locus for the system. Predict the behavior of the system from the root-locus, and investigate its response to a step input. Use different values of K (for example 30,000, 10,000 and 50,000).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), 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
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