Analysis of the X-15 Flight 3-65-97 Divergent Limit-Cycle Oscillation

Effect of Actuator Saturation on Pilot-Induced Oscillation: A Nonlinear Bifurcation Analysis

“…We continuation requires the system to be time-invariant (no on the right-hand side of the state equations). Therefore, it is necessary to convert the forcing term = sin( ) into the required form using equations (3)(4)(5). It can be shown that 6 = sin( ) and 7 = cos( ), essentially making them 'dummy states' to provide a harmonic forcing.…”

“…Actuator saturation has been identified as the leading cause of many high-profile pilot-induced oscillations (PIO) and limit-cycle oscillations. The problem stretches back to the early days of fly-by-wire technology with the X-15, which encountered both PIO [1,2] and a fatal limit-cycle oscillation [3] caused by rate saturation in the horizontal stabilizers. Due to its highly nonlinear nature, rate saturation can still be overlooked by many existing linear-based handling qualities criteria [4], which consider the X-15 to meet level-1 requirements and not PIO-prone [2].…”

“…In all these cases, the impact of rate limiting was not predicted before the accidents, and subsequent investigations only employed quasinonlinear methods (e.g. describing functions [2,3,5]), to supplement the original linear-based analysis. Therefore, there is a need to develop a more powerful toolbox for the industry that can not only handle nonlinearities efficiently, but also is presented in a familiar manner to facilitate its adoption by the practicing engineers.…”

Retrospective Cost Adaptive PID Control of Quadcopter/Fixed-Wing Mode Transition in a VTOL Aircraft

“…This model may represent a sampled-data version of a continuous-time plant with sample time T s , in which case x(k) denotes the state at time t = kT s . The goal is to develop an adaptive output feedback controller that minimizes z in the presence of the exogenous signal w with limited modeling information about (1), (2). The components of w can represent either command signals to be followed, external disturbances to be rejected, or both, depending on the choice of D 1 and E 0 .…”

“…Adaptive control has been viewed as an enabling technology for autopilots as early as the X-15 program 1,2 and as recently as the NASA Airborne Subscale Transport Aircraft Research (AirSTAR) testbed. 3 These and other techniques do not fulfill the vision of truly rapid prototyping since they depend on an autopilot designed for a nominal model and they have limited ability to accommodate high levels of uncertainty.…”