Control of slowly varying LPV systems - An application to flight control

Abstract

Recent results in parameter-dependent control of linear parameter-varying systems are applied to the problem of designing gain-scheduled pitch rate controllers for the F-16 Variable-Stability In-Flight Simulator Test Aircraft. These methods, based on parameter-dependent quadratic Liapunov functions, take advantage of known a priori bounds on the parameters' rates of variation (the bounds may themselves be parameter-varying). The controller achieves an induced-two-norm performance objective; Level 1 flying qualities are predicted. Suboptimal solutions are obtained by solving a convex optimization problem described by linear matrix inequalities. Incorporation of D-K iteration with 'constant D-scales' provides robustness to time-varying uncertainty. Parameter-varying performance weights are used to shape the desired performance at different points in the design envelope. (Author) AbstractRecent results in parameter-dependent control of linear parameter-varying (LPV) systems are applied to the problem of designing gain-scheduled pitch rate controllers for the F-16 VISTA (Variable-Stability In-Flight Simulator Test Aircraft). These methods, based on parameter-dependent quadratic Lyapunov functions, take advantage of known a priori bounds on the parameters' rates of variation (the bounds may themselves be parameter-varying). The controller achieves an induced-£2-norm performance objective; Level 1 flying qualities are predicted. Suboptimal solutions are obtained by solving a convex optimization problem described by linear matrix inequalities (LMIs). Incorporation of D-K iteration with "constant £)-scales" provides robustness to time-varying uncertainty. Parameter-varying performance weights are used to shape the desired performance at different points in the design envelope.

A Survey of Linear Parameter-Varying Control Applications Validated by Experiments or High-Fidelity Simulations

“…Parameter-varying performance weights are also encountered in aerospace applications [146], [149], and noise cancellation [177].…”

“…The first hifi simulation-based validations of LPV controllers were reported in [146], whereas the first experimental validations date back to [126] and [77]. In [77], both polytopic and small-gain theorem-based LFT LPV controller synthesis techniques are applied to the well-known academic example of an arm-driven inverted pendulum, whereas [126] implements a full-block multiplier-based LFT LPV design on microprocessor hardware for a compact disc player.…”

“…3) Mixed Scheduled/Robust LPV Controllers: Multiplicative input uncertainty and measurable time-varying parameters with PDLFs are considered in [146] and [149] on military flight control via a D/K -iteration [201].…”

Adaptive control of time-varying systems with gain-scheduling

“…One of the popular methods of nonlinear control design is the gain-scheduling [1], [2] and it has been used in a wide range of applications including flight control [3], [4], process control [5], and wind-turbine control [6]. The main idea behind the gain-scheduling approach is to decompose the nonlinear control design task into a family of linear control design methods and schedule this family of linear controllers based on the command signal so as to ensure that the original nonlinear system follows the desired dynamics.…”