Application of Optimal Input Synthesis to Aircraft Parameter Identification

Abstract

This paper considers an application of the Frequency Domain Input Synthesis procedure reference [12] for identifying the stability and control derivatives of an aircraft. In previous studies, the input design has mostly been carried out in the time-domain. However, by using a frequency-domain approach, one can handle criteria that are not easily handled by the time-domain approaches. Numerical results are presented for optimal elevator deflections to estimate the longitudinal stability and control derivatives subject to root-mean square constraints on the input. The applicability of the steady state optimal inputs to finite duration flight testing is investigated. It is shown that the steady state approximation of frequency-domain synthesis is good for data lengths greater than two time cycles for the short period mode of the aircraft longitudinal motions. For data lengths shorter than this, the phase relationships between different frequency components becomes important. The frequency domain inputs are shown to be much better than the conventional doublet inputs.

Online greedy identification of linear dynamical systems

“…This could be explained by the fact that the signal-to-noise ratio in this system is of order 1, hence the estimation bias in planning is large and it is more effective to plan one-step-ahead than to do planning over large epochs. We obtain similar results for the longitudinal system of a C-8 Buffalo aircraft [4].…”

“…System identification is a problem of great interest in many fields such as econometrics, robotics, aeronautics, mechanical engineering or reinforcement learning [1,2,3,4,5]. The task consists in estimating the parameters of an unknown system by sampling trajectories from it as fast as possible.…”

“…The control variables are the aileron and rudder angles (δ a , δ r ) := u. The linear dynamics for an aircraft flying at 573.7 meters/sec at 6.096 meters are given by the following matrix, obtained after discretization and normalization of the continuous-time system[4]:…”

Online greedy identification of linear dynamical systems

“…For the agent to find an effective control policy, the mathematical model of the environment must faithfully capture the dynamics of the system and thus must be fit with data. However, collecting observations can be expensive: consider for example an aircraft system, for which running experiments costs a lot of energy and time (Gupta et al, 1976). In this regard, active exploration (or system identification) aims at exciting the system in order to collect informative data and learn the system globally in a sample-efficient manner (Yang et al, 2021), independent of any control task.…”

Experimental Design Considerations for Dynamic Systems

“…While numerous heuristic and optimal input design methodologies have been proposed, very few direct comparisons have been made among them. Exceptions include Gupta et al (1976), Zarrop (1979), andSoderstrom andStoica (1983), who have presented results comparing different alphabetic optimal designs for the case of no model mismatch. The main purpose of this paper is to compare several different input signal designs in their ability to provide good controller The following sections of this paper summarize existing methods for designing input signals for dynamic systems, with special emphasis on the contributions of Ljung (1987).…”