TF Models

Studies of electric/electronic circuits, basic linear control-systems, mechanical systems, and related analyses lend to the TF analysis [2]. For single-input single­output (SISO) linear systems, a TF is defined as the ratio of the Laplace transform of the output and that of the input. It is often important to quickly determine the frequencies and damping ratios of the dynamic systems. This is true also for aircraft modes and aircraft-control system loop TF to assess the key dynamic characteristics (the stability/gain – and phase-margins of the feedback control system; see Appendix C) for longitudinal and lateral-directional modes from small perturbation maneuvers (Chapters 5 and 9) [5]. Often this is termed as Z-transform analysis; however, we will consider it as TF analysis in which case the coefficients of numerator and denominator polynomials (in “z” or “s”—complex frequency) are estimated using a least-squares method from the real test data. This estimation can be performed to obtain either discrete time-series models (to obtain pulse TF—in z domain) or directly the continuous-time models (by using appropriate methods [10] in s domain). Additionally, one can obtain the Bode diagram, the amplitude ratio, and the phase of the TF as a function of frequency (Appendix C).