Chapter 6
note, typical algorithms are iterative and make use of the rigid-body equations analytically, while the proposed methodology is a global search method. It may not be as fast as an analytical method, but it is useful for complex maneuvers, since these require more free variables which increase the complexity of an analytical method. The search method only requires a definition of the non-linear model, the chosen free variables, a starting point for the free variables and a set of constraints.
The trimming functions, with the adequate search methods, allowed for realistic results, since these re- flect the instability increase with altitude due to effects of air rarefaction from the atmosphere model, the stalling speed from the aerodynamic model and the maximum flight ceiling from the propulsion model.
These are only some evident examples, as other dynamics present in the model are still occurring in the background in the form of coupling effects. Most of the obtained results regarding the trimming algorithm were consistent and the solutions were continuous. These tools allowed for the flight envelope for this aircraft to be defined for gliding and motorized flights, which will prove useful for studying the viability of the HABAIR concept, revealing many characteristics of the aircraft. For example, it was determined that gliding has no flight ceiling but will never achieve constant altitude but still, there are flight ceilings that delimit the use of motorization for ascent, descent and constant altitude flights. The detail regarding the servo-flap implementation detail was also noted, as small variations in the differential will provoke large lateral aerodynamic effects, displaying a need for high resolution in these actuators.
The set of equilibrium points that results from the trimming functions allows for the derivation of a linear model, which shows the decouplement between the longitudinal and lateral variables. This serves as evidence that the nonlinear model corresponds to a typical aircraft. Also, the pole analysis confirms this assumption, given that only the longitudinal model has a pair of complex poles that degenerated onto the real axis, while the other poles correspond to the commonly expected pole analysis of a generic aircraft. More information was extracted from this analysis, as the longitudinal mode short-period and the lateral-mode dutch-roll show that these become less damped with increase in altitude and decrease in airspeed.
As for the controller, two methods were achieved with classical and optimal control techniques, showing satisfactory results. One method relates to the PI-D controller, for the longitudinal model with a pitch feedback through the elevator deflection and a pitch damper, while the lateral model was controlled by a PI-D controller with roll feedback through the aileron deflection and a roll damper. These are simplified as SIMO systems and both provide stabilization results. The other method that was implemented for mo- torized flight considered the propeller actuator, which turns the longitudinal model into a MIMO system.
For this purpose, an LQR controller was implemented and achieved satisfactory results regarding sta- bilization. Although the lateral model still displayed an oscillatory component from the dutch-roll mode, this effect could have been attenuated with the use of a yaw rate feedback on the rudder deflection, but this control surface is not available.
Both control techniques allow for the linearization function to be validated as a tool to derive the longitu- dinal and lateral models, while still maintaining the key dynamics of the nonlinear model.
It can then be concluded that the flying wing vehicle is a valid option for the HABAIR concept.
6.2 Future Work
In order to complement this work, additional models should be integrated. For starters, the available information regarding the aerodynamic model is limited, so, a more refined analysis would yield a more detailed model using parameter identification and performing the model validation. Also, the model is ideal and does not contemplate the influence of sensor and flap-servo dynamics, which would add fur- ther detail to the simulator and add further evidence for proving the feasibility of the implementation.
To solve this, the sensor dynamics could benefit from the use of a Kalman filter implementation, either to remove noise components or to estimate a given state. An example for this estimation could be the altitude state being obtained through its relation to air pressure. As for the flap-servo model, the model could be approximated as a first order system with a fast time constant. Another detail to add would be the discretization of the simulator, since the physical implementation works with samples and this work only considers the continuous case.
To emphasize the contributions of this work, further results should be extracted with varying mass for the aircraft (in the case where probes or cargo are deployed during the flight). The limits for motorized flight ceilings should be further explored to better understand how they define the flight envelope, since this work only limits the values ofγbetween -2.5 to 5 degrees. Trimming functions for other maneuvers such as push-up, pull-down and turn-over are not considered and it would be of interest to understand how the aircraft behaves over the flight envelope while performing these maneuvers, with more information on this matter being available in [18]. The transition from drop to stabilized flight with a parachute is not modelled, as well as the landing maneuver. To solve this lack of information, the developed tools can be used with different settings and constraints to obtain further results.
Lastly, the importance of path planning would add the final details for the feasibility verification regard- ing the proposed mission, with the addition of a round-the-Earth reference frame for navigation. These navigation systems introduce further layers of detail, considering nonlinearities and disturbances, thus paving the way for nonlinear control techniques to guarantee that a flight mission can be executed from ascension to landing. As seen in the Chapter 5, stabilization is achieved but not assured as time goes to infinity, so adding further layers of controlled state variables such asψwould guarantee more stability conditions, as well as the control through estimation of theγ,Vtandαvariables, for example. These ad- ditional controlled variables could propose guidance control while also considering the wind disturbance.