Gain-Scheduled Control: Relaxing Slow Variation Requirements by Velocity-Based Design

Abstract

This paper investigates the application of the gain-scheduling approach to flight control tasks where the conditions required by conventional techniques need not be satisfied. The conditions required by conventional techniques are progressively relaxed and the design of gain-scheduled controllers under a range of conditions is addressed. In particular, the paper considers gain-scheduled control design in situations where the vehicle is manoeuvring aggressively far from equilibrium, the airspeed need not be slowly varying and/or scheduling on the instantaneous incidence angle is required.

Application of velocity-based gain-scheduling to lateral auto-pilot design for an agile missile

“…These traditional gain-scheduling conditions are, however, conservative in nature. By nonlinear analysis of the resulting closed-loop system, the classical gain-scheduling approach (including the foregoing, on the face of it rather ad hoc, implementation technique) may lead to a soundly based controller design which is globally valid (not restricted to near equilibrium operation) provided that appropriate conditions are satisfied (Leith & Leithead, 2000b). Namely, it is required that the aerodynamic moment and force are linear with respect to lateral velocity and fin angle and that qN=qv; qN=qr; qN=qd; qY=qv and qY=qd do not depend on the lateral velocity, v; or the fin angle, d; that is,…”

“…It is, therefore, also necessary to ensure that the state-space realisations of the members of the controller linearisation family are suitably compatible with one another. When the rate of variation of a nonlinear system is sufficiently slow, it can be shown that the controller becomes insensitive to the choice of realisation (Leith & Leithead, 2000b). However, in general, it is straightforward to confirm the closed-loop dynamics may be extremely sensitive to the choice of realisation.…”

“…In addition, the requirement to operate at high angles of attack can necessitate scheduling on rapidly varying quantities such as the instantaneous incidence angle (rather than, for example, conventional flap scheduling on averaged incidence, McLean, 1990, p. 523). It should be noted that scheduling on instantaneous incidence is wellknown to be problematical and is almost always avoided in classical scheduling arrangements (see, for example, Leith & Leithead, 2000b). Specifically, in the example considered in this paper, a conventional gain-scheduling design approach fails to lead to a stabilising controller.…”

Nonsingular finite-time second order sliding mode attitude control for reentry vehicle

“…In this approach, the system is linearized at multiple trimmed flight conditions throughout the flight envelope and a corresponding set of linear controllers are defined. Then overall attitude control system is realized with scheduled gains defined by interpolation online with respect to some meaningful flight conditions such as dynamic pressure, Mach number, etc [5,6]. However, the design of gain scheduling controller is time-consuming and relies extensively on experience of control designers.…”

Stability of Gain Scheduling Control for Aircraft with Highly Nonlinear Behavior

“…Since the flight dynamics have nonlinear nature, the linear approximation of the system leads to controllers with stability and performance limitations. To overcome such limitations there exist in the literature a variety of control methodologies which provide important advances in GSC and hybrid and nonlinear approaches [5][6][7][8]; see also GSC surveys [1,[9][10][11][12][13][14][15][16][17][18][19].…”