Transfer Function Models from Real-Flight Data

It is often advisable to fit a TF to the real flight data to quickly assess the dynamic characteristics of the aircraft. TF and the Bode plots can be easily obtained using the SID toolbox of MATLAB. The main principle is that an output/input mathematical form like the LS model is fitted to the discrete-time data and the Bode diagram from this model is determined [10]. Another approach is to fit a TF model to the frequency response data (the amplitude vs. frequency and the phase vs. frequency data) by the LS method [3]. From this TF again the Bode plot can be obtained. These two approaches are available in the MATLAB toolboxes. Basically, it is a system identification/ parameter-estimation problem and the criterion for the minimization would be the same as in time domain, except that here we are dealing with frequency domain data instead of time histories. One can fit a delta operator TF to the continuous-time data of a dynamic system [11], the merits of which are discussed in Section 2.2.1.

The ‘‘arx’’ model of second order was fitted to the real flight data (of a transport aircraft) using the following sequence in MATLAB:

Data = iddata(q, ele,0.4); model = arx(Data,[2 1 0])

A(q-1) = 1 – 1.981q-1 + 0.9898q-2 B(q-1) = -0.002198

The discrete time Bode diagram was then obtained by dbode([-0.002148], [1 -1.981 0.9898], 0.4). Figure 9.3 shows the Bode diagram of this pitch rate-elevator control input TF.

9.2.2 Expert Systems for System Identification

Although the SID procedure is well established, there is still some scope for improvement until perfection is achieved. A typical exercise would need a dozen steps. It should be possible to build an expert system that utilizes a set of rules that attempt to mimic the way in which an experienced SID expert proceeds while still using the ID toolbox of MATLAB. The expert system (SIDES) should be able to run without any intervention from an analyst. SIDES would start its iterative journey once driven by the data and rules. SIDES would have the following features: (1) an efficient sampling device with appropriate filters to select the data at lower sampling intervals without loss of information and (2) a set of permissible model structures. A typical expert system has the following steps [12]: (1) parsimonious walk through the model set defined by the analyst; (2) selection of best models based on a quality index; and (3) modification of the sampling interval. The first step avoids the examination and comparison of all the models in the model set. The quality index reflects the best trade-off among many validation tools. The rules are goal oriented and every set of rules is organized around a particular goal. Each rule would contain a conditional expression of one or more patterns, which would be followed by an unconditional action.