Dynamic gain scheduled control of a Hawk scale model

Abstract

A state matrix A cl closed-loop state matrix B input matrix I yy moment of inertia about y-body axis K feedback (static) gain matrix m aircraft mass M aerodynamic pitching moment q pitch rate u control input V t total translational velocity V achievable closed-loop eigenvalues x state vector Z w z-wind axis aerodynamic force Abbreviations CGS conventional gain schedule DGS dynamic gain schedule Greek letters α angle-of-attack ABSTRACTWhen designing flight control laws using linearisations of an aircraft model about different flight conditions, some form of scheduling of the resultant gains will often be required to implement the controller over wide operating regions. In practice, the controller gains are often scheduled against relatively slowlyvarying system states such as altitude or velocity. However, it may also be desirable to schedule gains against rapidly-varying states such as angle-of-attack, thereby generating a cyclic dependence through hidden coupling terms. Previous published work at Bristol has developed a numerical method of accounting for this dependence when scheduling state feedback gains against coupled states. The resulting `dynamic gain schedule' is shown to significantly improve the transient response of the aircraft model during rapid manoeuvring and to reduce the chances of control surface actuator position limit saturation. In this paper, the novel design process, using eigenstructure assignment, is applied to a mathematical second-order longitudinal aircraft model which represents an approximate BAe Hawk wind-tunnel model. The dynamic gain scheduled controller is shown to work extremely well in practice when applied to the closed-loop experimental rig. Despite the highly nonlinear characteristics of the model aerodynamics and tailplane actuation system, as well as unmodelled high turbulence levels, dynamic gain scheduling demonstrates stable closed loop control even in regions where the nonlinearities are such that conventional gain scheduling fails to produce a stable response.

Aircraft longitudinal decoupling based on a singular perturbation approach

“…Rosa et al 8 described an application of a new fault detection and isolation technique based on set-valued observers to a linear parameter varying longitudinal aircraft dynamic model. Richardson et al 9 designed a gain scheduled controllers for a mathematical second-order longitudinal aircraft model which represents an approximate BAE Hawk wind-tunnel model. Naldi and Marconi 10 solved numerically both minimum-time and minimumenergy optimal transition problems in order to compute reference maneuvers to be employed by the onboard flight control system to change the current flight condition.…”

Dynamic gain-scheduled control and extended linearisation: extensions, explicit formulae and stability

“…demand. Significant results of work on DGS can be found in papers (Hammoudi & Lowenberg, 2008;Jones, 2005;Jones, Lowenberg, & Richardson, 2006;Richardson, Lowenberg, Jones, & Dubs, 2007), including an experimental validation of the approach.…”

Dynamic gain scheduled control of a satellite with a robot manipulator

“…However, it is well-known that simple continuous gain-scheduling of linear design may not retain stability. To counter this, dynamic gain scheduling (DGS) [10][11][12][13][14][15] is adopted.…”