Abstract:PurposeThe purpose of this paper is to present a comparison of nonlinear and linear simulations of aircraft dynamics to determine the divergence of the linear solution from the nonlinear solution.Design/methodology/approachThe general equations of motion of a transport aircraft are presented both in nonlinear and linear form. The nonlinear equations are solved by using the Runge Kutta method. Linear equations are solved numerically by using the Runge Kutta method and they are also solved exactly by using the L… Show more
“…When the solution algorithm with the GA summarized in Figure 3 is performed with the GA parameters in Table 6 within the limits specified in Table 5, results in Figures 10,11,12,13,and 14 and trim values in Table 7 are obtained. In the next section, we will use the trim values we found in Table 7 as the initial guess set (Set 3) for the Newton-Raphson method and check the result we obtained here.…”
Section: Solutions Using the Gamentioning
confidence: 99%
“…While lift changes linearly with the angle of attack until its stall value, drag cannot be expressed linearly in this range. However, the locally linearized drag equation can be written as presented in Figure 1 13,14 Figure 1.Linearized drag approach.…”
As the number of unknowns in trim analysis increases, the problem becomes more complicated, and traditional methods begin to fail. Common problems with conventional methods may be an ill-conditioned matrix, rounding errors, and division by zero. Furthermore, these methods are likely to find the local optimum, not the global optimum. In such cases, hybrid use with intelligent methods such as genetic algorithms is recommended. In this study, a flight situation that the Newton–Raphson method has for difficulty in solving is selected for a six-degree-of-freedom nonlinear trim analysis. Trim analysis was performed using the Newton–Raphson method, genetic algorithm, and by their hybrid use, respectively. The Newton–Raphson method had convergence problems despite very good initial guesses. The genetic algorithm was able to solve the same problem by itself. The unknowns in trim analysis, such as deflection angles of an elevator, a rudder, and an aileron, have physical limits, whereas the constraints make conventional methods more complicated, and the ability to use these limits in the genetic algorithm narrows the solution space and reduces the computation time. The hybrid use of the GA and Newton–Raphson method significantly increased the performance of the Newton–Raphson method and eliminated the convergence problem. It has been shown that a 6-degree-of-freedom trim problem, which traditional numerical methods such as the Newton–Raphson method have for difficulty in solving, can be solved easily and effectively with the hybrid use of the GA and the Newton–Raphson method. The strength of the proposed hybrid method to solve a highly nonlinear trim problem was demonstrated.
“…When the solution algorithm with the GA summarized in Figure 3 is performed with the GA parameters in Table 6 within the limits specified in Table 5, results in Figures 10,11,12,13,and 14 and trim values in Table 7 are obtained. In the next section, we will use the trim values we found in Table 7 as the initial guess set (Set 3) for the Newton-Raphson method and check the result we obtained here.…”
Section: Solutions Using the Gamentioning
confidence: 99%
“…While lift changes linearly with the angle of attack until its stall value, drag cannot be expressed linearly in this range. However, the locally linearized drag equation can be written as presented in Figure 1 13,14 Figure 1.Linearized drag approach.…”
As the number of unknowns in trim analysis increases, the problem becomes more complicated, and traditional methods begin to fail. Common problems with conventional methods may be an ill-conditioned matrix, rounding errors, and division by zero. Furthermore, these methods are likely to find the local optimum, not the global optimum. In such cases, hybrid use with intelligent methods such as genetic algorithms is recommended. In this study, a flight situation that the Newton–Raphson method has for difficulty in solving is selected for a six-degree-of-freedom nonlinear trim analysis. Trim analysis was performed using the Newton–Raphson method, genetic algorithm, and by their hybrid use, respectively. The Newton–Raphson method had convergence problems despite very good initial guesses. The genetic algorithm was able to solve the same problem by itself. The unknowns in trim analysis, such as deflection angles of an elevator, a rudder, and an aileron, have physical limits, whereas the constraints make conventional methods more complicated, and the ability to use these limits in the genetic algorithm narrows the solution space and reduces the computation time. The hybrid use of the GA and Newton–Raphson method significantly increased the performance of the Newton–Raphson method and eliminated the convergence problem. It has been shown that a 6-degree-of-freedom trim problem, which traditional numerical methods such as the Newton–Raphson method have for difficulty in solving, can be solved easily and effectively with the hybrid use of the GA and the Newton–Raphson method. The strength of the proposed hybrid method to solve a highly nonlinear trim problem was demonstrated.
“…The system equation that describes flight behavior can be solved using the Fourth Order Runge-Kutta Scheme, as demonstrated by Ozdemir and Kavsaoglu [4]. It is true that the system equation, which consists of 12 first-order differential equations, is non-linear and that the equations are coupled to each other.…”
The current study looks at flight behavior in lateral and directional motion.The investigation involves setting up the aircraft under an equilibrium condition with a small disturbance applied to it. Plotting the side slip angle, roll angle, and yaw angle with respect to time in the presence of disturbances can be used to investigate flight behavior in lateral and directional motion. Here the disturbance can be simulated by the movement of the aileron or rudder, in which these two control surfaces can be designed to move in a single impulse or multiple impulse disturbance mode. These two disturbance modes are used on the Beechcraft 99 and Cessna T37 aircraft. Both impulse disturbance models are used for the aileron and the rudder. However, in the current work, the Beechcraft 99 receives a single impulse, whereas the Cessna T37 receives multiple impulses. The implementation of such disturbances found that the Beechcraft 99 represented the aircraft that would be able to go back to its initial condition in response to a single impulse disturbance modewhile the Cessna T37 aircraft requires a little more time to return to its original yaw angle. Following the implementation of these twotypes of disturbances, it was discovered that each aircraft has the ability to return to its initial condition, but at varying times to reach its steady state solution.
“…Aircraft attitude by means of Euler angles and displacement with respect to Earth frame can be given as a function of these variables [11,12]: Indices G, A, and T represent gravity, aerodynamic and thrust contributions, respectively. Gravity forces on body axis are the functions of Euler angles and weight of the aircraft:…”
After a structural damage or component failure during any §ight mode, aircraft dynamics are dramatically altered. A quick and adequate stabilization e¨ort is crucial. Flight dynamics for several failure scenarios are analyzed. Necessary amounts of control de §ections for postfailure trim are calculated. These trim values are used as control input in an open loop manner and validity of this approach is tested via §ight simulations. Alternatively, a closed loop §ight control system, which does not need the postfailure trim values, is also designed. This closed loop controller is based on a linearized aircraft model whereas §ight simulations are based on nonlinear aircraft dynamics.
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