Question

please use root locus graphs to find amswer. thanks

The automatic control of an airplane is one example that requires multiple-variable feedback methods. In this system, the attitude of an aircraft is controlled by three sets of surfaces: elevators, a rudder, and ailerons, as shown in Figure DP7.13(a). By manipulating these surfacesi a pilot can set the aircraft on a desired flight path [20]. An autopilot, which will be considered here, is an automatic control system that controls the roll angle φ by adjusting aileron surfaces. The deflection of the aileron surfaces by an angle θ generates a torque due to air pressure on these surfaces. This causes a rolling motion of the aircraft. The aileron surfaces are controlled by a hydraulic actuator with a transfer function 1/s The actual roll angle ф is measured and compared with the input. The difference between the desired rollangle фd and the actual angle ф will drive the hydraulic actuator, which in turn adjusts the deflection of the aileron surface. A simplified model where the rolling motion can be considered independent of other motions is assumed, and its block diagram is shown in Figure DP713(b). Assume that K1 = 1 and that the roll rate ф is fed back using a rate gyro. The step response dcsired has an overshoot less than 10% and a settling time (with a 2% criterion) less than 9 seconds. Select the parameters Ka and K2.

Answer 1

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Step Response 1.4 System: sys Peak amplitude: 1.01 Overshoot (%): 1.01 At time (seconds): 11.7 1.2F Syste: sys Settling time (seconds): 9 0.8 E 0.6 0.4 0.2 10 15 20 25 Time (seconds)