Effective Date: 15 June 98
Test and Analysis Techniques As mentioned in the introduction, this section will contain test and analysis techniques for some of the more common stability and control tests. The content of these sections is very general and should serve only as a guideline.
Parameter Identification Methods
Within the last 15 to 20 years, the use of parameter identification (PID) computer programs have been developed. These programs provide a method for extracting the basic aircraft stability and control derivatives directly from flight test data. These programs are essentially generalized equivalent system matching programs. Instead of a specific model based on aircraft wind tunnel data, a generalized aircraft model is used as the equivalent system. The stability and control derivatives in this general model are varied until the best match of flight test to model responses is achieved.
Initial programs such as the Modified Maximum Likelihood Estimator (MMLE) program developed by NASA Dryden Flight Research Center provided the capability to estimate derivatives using a linearized model of the aircraft equations of motions. This program is adequate for aircraft where the non-linear effects in the equations of motion are insignificant. For aircraft which contain significant non- linear effects, the MMLE program could produce results which have a significant amount of scatter and uncertainty.
The successor to MMLE, also developed at Dryden, was called simply Parameter Estimation (PEST). This program allowed the incorporation of some of the non-linear terms in the equations of motion. PEST also allows the use of several different types of convergence algorythms which help to cut down on the computer processing time required. The PEST program is an interactive program which allows the analyst to see what is happening during the convergence process. PEST also allows the equivalent model to be designed as required to fit the particular aircraft being analyzed.
The parameter identification process is not without pitfalls. PID programs are suceptable to errors introduced due to inaccurate initial conditions, a bad model, time lags introduced by instrumentation or data recording/reduction, multiple control surface effects, and inaccurate moments of inertia. Each of these items will be discussed briefly in the following paragraphs.
Without prior knowledge of some of the derivatives, the program is free to vary all derivatives to achieve a solution. Trade offs can be made between aerodynamic, control, and damping derivatives and a solution obtained which is totally wrong, yet produces a good match with the flight test data. To limit this effect, a good starting value of each derivative used in the model is required. Derivatives can be fixed or restricted to certain ranges if sufficient knowledge is available on its value. However, restricting derivatives runs the risk that you will corrupt the analysis based on predetermined results. A faulty initial estimate of a derivative can cause uncertain results.
PID programs depend on calculating the moments and forces contributed by controls, states and responses in each time increment of the whole maneuver. The model has only the inertial and aerodynamic lag between the control and response. If the flight test data contains additional lags between control and response parameters, then the PID program will attempt to account for these lags probably in the form of erroneous damping coefficients. The source of any time lags should be limited as much as possible in data which is to be used for PID analysis. Data should be pre- processed to remove known time lags.
For PID analysis it is best to use maneuvers which use only one control surface for each axis of motion. If this type of maneuver can be used, then there is only one set of control derivatives which need to be estimated. On aircraft which use a full time FCS, it is possible to have more then one surface being deflected at the same time. For instance, leading edge flaps may move as a function of angle of attack, and thus will change deflection as the aircraft goes through a pitch doublet. When this happens, forces and moments are generated from each of the control surfaces and it is difficult to discriminate the contributions from each of the surfaces. If more then one surface is allowed to vary, it is best to fix the control derivative on one of the surfaces until a good estimate for the other surface is determined. This often is an iterative process.
Moments of inertia directly affect the total moment equation. Errors in the values used for the PID analysis will normally produce errors in the damping derivatives. Therefore, it is essential that the moments of inertia be known with some certainty throughout the weight range being tested. Changes in configuration to the aircraft such as gear extension, or the addition of stores or other equipment which affect the moments of inertia should always be taken into account.
By using both PID and equivalent model matching techniques, it is possible to converge on a model which fully simulates the aircraft. It may be necessary to use results of PID analysis to modify the equivalent model, and use the equivalent model to form the PID model.