Robust gain-scheduled H [infinity] control for unmanned aerial vehicles - Chumalee, Sunan (Cranfield University, 2010)
This thesis considers the problem of the design of robust gain-scheduled ight controllers for conventional xed-wing unmanned aerial vehicles (UAVs). The design approaches employ a linear parameter-varying (LPV) control technique, that is based on the principle of the gain-scheduled output feedback H1 control, because a conventional gain-scheduling technique is both expensive and time-consuming for many UAV applications. In addition, importantly, an LPV controller can guarantee the stability, robustness and performance properties of the closed-loop system across the full or de ned ight envelope. A ight control application problem for conventional xed-wing UAVs is considered in this thesis. This is an autopilot design (i.e. speed-hold, altitude-hold, and heading-hold) that is used to demonstrate the impacts of the proposed scheme in robustness and performance improvement of the ight controller design over a fuller range of ight conditions. The LPV ight controllers are synthesized using single quadratic (SQLF) or parameterdependent (PDLF) Lyapunov functions where the synthesis problems involve solving the linear matrix inequality (LMI) constraints that can be e ciently solved using standard software. To synthesize an LPV autopilot of a Jindivik UAV, the longitudinal and lateral LPV models are required in which they are derived from a six degree-of-fredoom (6-DOF) nonlinear model of the vehicle using Jacobian linearization. However, the derived LPV models are nonlinearly dependent on the time-varying parameters, i.e. speed and altitude. To obtain a nite number of LMIs and avoid the gridding parameter technique, the Tensor-Product (TP) model transformation is applied to transform the nonlinearly parameter-dependent LPV model into a TP-type convex polytopic model form. Hence, the gain-scheduled output feedback H1 control technique can be applied to the resulting TP convex polytopic model using the single quadratic Lyapunov functions. The parameter-dependent Lyapunov functions is also used to synthesize another LPV controller that is less conservative than the SQLF-based LPV controller. However, using the parameter-dependent Lyapunov functions involves solving an in nite number of LMIs for which a number of convexifying techniques exist, based on an a ne LPV model, for obtaining a nite number of LMIs. In this thesis, an a ne LPV model is converted from the nonlinearly parameter-dependent LPV model using a minimum least-squares method. In addition, an alternative approach for obtaining a nite number of LMIs is proposed, by simple manipulations on the bounded reallemma inequality, a symmetric matrix polytope inequality form is obtained. Hence, the LMIs need only be evaluated at all vertices. A technique to construct the intermediate controller variables as an a ne matrix-valued function in the polytopic coordinates of the scheduled parameter is also proposed. The time-varying real parametric uncertainties are included in the system statespace model matrices of an a ne LPV model as a linear fractional transformation (LFT) form in order to improve robustness of the designed LPV controllers in the presence of mismatch uncertainties between the nonlinearly parameter-dependent LPV model and the a ne LPV model. Hence, a new class of LPV models is obtained called an uncertain a ne LPV model which is less conservative than the existing parameter-dependent linear fractional transformation model (LPV/LFT). New algorithms of robust stability analysis and gain-scheduled controller synthesis for this uncertain a ne LPV model using single quadratic and parameter-dependent Lyapunov functions are proposed. The analysis and synthesis conditions are represented in the form of a nite number of LMIs. Moreover, the proposed method is applied to synthesize a lateral autopilot, i.e. heading-hold, for a bounded ight envelope of the Jindivik UAV. The simulation results on a full 6-DOF Jindivik nonlinear model are presented to show the e ectiveness of the approach.