## 3 Aircraft System Identification
### Input Design  
The objective of input design for aircraft system identification is to excite the aircraft so that the data contain sufficient information for accurate modeling, subjected to the practical constraints of the experiment [23]. The common longitudinal flight maneuvers for aircraft system identification consist of short-period maneuver, phugoid maneuver, thrust variation, et cetera, which will be able to excite the longitudinal motion of aircraft, that is, short-period mode or phugoid motion. According to [PERSON] [22], short-period motion is a fast responding longitudinal mode, provides the most information to enable the estimation of derivatives pertaining to the vertical and pitching motion. Since phugoid mode is the energy exchange, it is more suitable than short-period mode to excite the energy characteristic of the aircraft, which is the function of pitch angle, angle of attack, and longitudinal acceleration. The methods of utilizing the flight maneuvers in input design are called optimal input design, where the aircraft system identification uses the approach of a priori knowledge about the dynamic system response and the input is tailored accordingly. One of the popular optimal inputs is multistep input design where the range of aircraft natural frequencies are investigated, then followed by designing of suitable multistep input to cover the desired frequency range.  
A more common multistep input is doublet input, as shown in Figure 2. The doublet input is a two-sided pulse, resulting with a symmetrical signal, which has higher energy and wider frequency bandwidth compared to pulse input. The time step of doublet input can be approximated by:  
\[\Delta t_{\text{DBLT}}=\frac{1}{2.7}\times\ T_{\text{osc}} \tag{19}\]  
where \(\Delta t_{\text{DBLT}}\) is the time step of doublet input and \(T_{\text{osc}}\) is the period of aircraft oscillation.  
The input design is a part of the iterative process of system identification, until an adequate model is developed and finally the model is successfully with the implementation of the controller. In this study, the energy distribution model consists of elevator input and total energy model consists of throttle input. For aircraft longitudinal motion, without significant influence from lateral dynamics, we can assume that energy distribution model is independent of total energy model. The suitable input for elevator is a doublet signal with \(\Delta t_{\text{DBLT}}=1\) s. The maximum amplitude is eight degree and the minimum amplitude is \(-10\) degree, as shown in Figure 3. The maximum positive elevator deflection is smaller to prevent the aircraft from excessive pitch down. The multi-steps input in the Figure 3 was suggested by [PERSON] [23]. It is chosen due to the rich frequency spectrum covered in the input excitation which would result in better quality of dynamic response data.  
Figure 1: Flow chart of system identification process.  
The input of throttle is a pulse signal with \(\Delta t=3\) s, as shown in Figure 4. The determination of the duration and magnitude for this input was based on the results of flight simulations and experiments. Moreover, in throttle response, there is a lag time constant, which is typically of the order of 2 to 3 s. This is the reason why the duration of 3 s is chosen for the input design of throttle.