An aircraft model in a wind tunnel is constrained to pure pitching motion about its center...

 

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An aircraft model in a wind tunnel is constrained to pure pitching motion about its center of mass by mounting it on a vertically-aligned bearing Bearing Figure 2: Aircraft Model constrained to pure pitching motion The body and fixed frames are aligned at t-0 seconds such that The equation for the short-period pitching motion of the constrained aircraft model is then given by: Servo Where M,= -3.5 sec¹, M₂=-8 sec¹, M₂=0.5 sec-², M₁, -7 sec ³ A pitch auto-pilot system as shown in Figure is used to maintain the pitch at- titude. The elevator servo-motor has a transfer function that can be approximated as a first-order lag system: G₂(e) = Feedback is provided by a gyro with gain ko- 6(1) 1 k 26 Gyro Aircraft Dynamics 600 Figure 3: Schematic of the pitch auto-pilot system (s) Derive the transfer function G(s) for the aircraft's pitch angle (6) response to elevator input (6.). (b) Assume G(s) = A0/(A6), derive the transfer function for the closed loop feedback control system in terms of G(s), Ge(s), and kg. (c) If the transfer function G(s) has poles at -2+2i, sketch the root locus for the pitch auto-pilot system. Comment on the behaviour of the system as the gain k, is increased. (d) The pitch auto-pilot system is an example of Proportional Control. It is proposed to modify the system to implement Proportional-Derivative (PD) control. This requires the inclusion of a rate gyro, with gain k.. Draw a block diagram for the PD controller. (e) If an integral controller has been added to reduce the steady-state error, what issue occurs if the elevator is commanded to achieve deflections greater than its maximum deflection angle? What strategies could be used to treat this issue? (f) The auto-pilot system should be designed so that the model aircraft has a consistent response (flying qualities) to an elevator input over a range of airspeeds. Why would the response to a given elevator input change for different airspeeds? And how might the controller gains be adjusted to achieve a consistent response? An aircraft model in a wind tunnel is constrained to pure pitching motion about its center of mass by mounting it on a vertically-aligned bearing Bearing Figure 2: Aircraft Model constrained to pure pitching motion The body and fixed frames are aligned at t-0 seconds such that The equation for the short-period pitching motion of the constrained aircraft model is then given by: Servo Where M,= -3.5 sec¹, M₂=-8 sec¹, M₂=0.5 sec-², M₁, -7 sec ³ A pitch auto-pilot system as shown in Figure is used to maintain the pitch at- titude. The elevator servo-motor has a transfer function that can be approximated as a first-order lag system: G₂(e) = Feedback is provided by a gyro with gain ko- 6(1) 1 k 26 Gyro Aircraft Dynamics 600 Figure 3: Schematic of the pitch auto-pilot system (s) Derive the transfer function G(s) for the aircraft's pitch angle (6) response to elevator input (6.). (b) Assume G(s) = A0/(A6), derive the transfer function for the closed loop feedback control system in terms of G(s), Ge(s), and kg. (c) If the transfer function G(s) has poles at -2+2i, sketch the root locus for the pitch auto-pilot system. Comment on the behaviour of the system as the gain k, is increased. (d) The pitch auto-pilot system is an example of Proportional Control. It is proposed to modify the system to implement Proportional-Derivative (PD) control. This requires the inclusion of a rate gyro, with gain k.. Draw a block diagram for the PD controller. (e) If an integral controller has been added to reduce the steady-state error, what issue occurs if the elevator is commanded to achieve deflections greater than its maximum deflection angle? What strategies could be used to treat this issue? (f) The auto-pilot system should be designed so that the model aircraft has a consistent response (flying qualities) to an elevator input over a range of airspeeds. Why would the response to a given elevator input change for different airspeeds? And how might the controller gains be adjusted to achieve a consistent response?

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Steps Step 1 of 3 a To derive the transfer function Gs for the aircrafts pitch angle 0 response to elevator input Se you can use the principles of con... View the full answer