4 research outputs found
Gain-scheduled H∞ control via parameter-dependent Lyapunov functions
Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques
Disturbance observer enhanced neural network LPV control for a blended-wing-body large aircraft
The problem of trajectory tracking control for a
Blended-Wing-Body (BWB) large aircraft with model
parameter uncertainties and unknown disturbances is
considered. A Linear Parameter-Varying (LPV) model is
derived from the nonlinear dynamics of the BWB aircraft from
which a robust linear parameter-varying controller is designed
to track a desired trajectory. Using a Single Quadratic
Lyapunov Function (SQLF) and an infinite number of linear
matrix inequalities to be evaluated at all vertices, a pair of
positive definite symmetric matrix solutions is determined via
Lyapunov stability theory and linear matrix inequality
technique. Furthermore, a disturbance-observer is designed to
process the unknown disturbances. Considering the plant exists
some model errors except for disturbances, a Radial Basis
Function Neural Network (RBFNN) approximation is
embedded into the SQLF LPV controller to improve tracking
performances, and a composite disturbance-observer based
Neural Network Single Quadratic Lyapunov Function
(NNSQLF) controller can realize desired trajectory tracking of
the linear parameter-varying system through regulating
performance weighting functions. The closed-loop system of
trajectory tracking control is proved to be asymptotically stable
by using Lyapunov theory. Simulation results of forward flight
speed and altitude tracking control of the BWB aircraft show
that the proposed disturbance-observer based NNSQLF control
can robustly stabilize the LPV system and precisely track the
desired trajectory by comparing with conventional SQLF
control and Parameter-Dependent Lyapunov Functions (PDLF)
control, even in unknown exterior disturbances and model
uncertainties
Robust gain-scheduled H [infinity] control for unmanned aerial vehicles
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
Gain-scheduled H-infinity control for tensor product type polytopic plants
A tensor product (TP) model transformation is a recently proposed technique for transforming a given linear parameter-varying (LPV) model into polytopic model form, for which there are many methods that can be used for controller design. This paper proposes an alternative approach to the design of a gain-scheduled output feedback H∞ controller with guaranteed L2-gain parameter-dependent performance for a class of TP type polytopic models using parameter-dependent Lyapunov functions where the linear matrix inequalities (LMIs) need only to be evaluated at all vertices of the system state-space model matrices and the variation rate of the scheduled parameters. In addition, a construction technique of the intermediate controller variables is also proposed as a matrix-valued function in the polytopic coordinates of the scheduled parameters. The performance of the proposed approach is tested on a missile autopilot design problem. Furthermore, nonlinear simulation results show the effectiveness of these proposed techniques