Control of a small helicopter with linear matrix inequality-based design assuring stability and performance

Abstract

This article focuses on linear matrix inequality-based controller designs that can achieve stabilization and reference tracking for a small unmanned helicopter at various flight conditions. A nonlinear mathematical model of a small-scale helicopter is constructed. Then trim conditions are found and linearized around different equilibrium points. Local [Formula: see text] controllers are designed at trim conditions based on the local linear models. The pointwise controllers achieve local stability and performance, but fail at stabilization and tracking over the full envelope. A scheduling controller is built by blending the local controller outputs. In addition, grid-based [Formula: see text] controllers are designed at each operating point with common Lyapunov function. This allows controller scheduling between the adjacent design points with guaranteed stability and performance across the design envelope. Based on the family of linear systems which are obtained from the nonlinear model, an affine parameter-dependent model is built to exploit the approximate linear parameter dependency. Then, a parameter-dependent linear parameter varying controller is synthesized for the affine parameter-dependent model. Although local performance is satisfactory for all given design methods, local [Formula: see text] controllers and affine parameter-dependent controller cannot yield satisfactory performance over the full flight envelope apart from the grid-based controller with common Lyapunov function approach.

Integral-based robust LPV control of nonlinear flight systems

“…One of the scenarios is examined based on what mentioned in. 20 The analysis of trim points of longitudinal and altitudinal and transverse velocity control is done in the intervals of 0 to 10, 2, and 6.…”

“…In Figure 3, the velocity control is presented in the longitudinal direction without noise, and its response is compared to the gridding based method, which is shown in the reference. 20 The maximum velocity set for longitudinal directions is 10 m/sec. It is assumed that, the helicopter is flying at 10 m/s, and a trapezoidal pilot commands coming from 0 to 10 m/s in test full speed range.…”

“…Recently, control of a small helicopter is examined with a design based on LMI approach in. 20 In this paper, tracking of a small unmanned helicopter is investigated in different flight conditions. Although the design goal was based on H∞ control and affine parameters, it could not provide a good design performance other than the gridded LPV model.…”

H∞ Loop Shaping Using Polytopic Weights and Pole Assignment to Missile Autopilot

“…we obtain (46). Again, applying the congruence transformation on both ( 11) and ( 12), and recalling the closed-loop polytopic matrices in (19), we have…”

“…Previous work was grounded on a grid-based mixed sensitivity H ∞ approach to find an LPV controller for improving wheelset stability of railway vehicles [18], and for a small helicopter [19]. The latter linearizes the nonlinear plant model in a grid, which is composed of several operating conditions of the helicopter dynamics, and uses a common Lyapunov function to ensure robustness and performance to the entire flight envelope.…”