Neural Network-Based Adaptive Control Design of Dual-Spin Projectile with Rotating Canards

Abstract

Guided munition is composed of a highly rotating main body and a guidance/control fuze with two pairs of control canards. The guidance/control fuze rotates in an opposite direction at a slower rate than the main body. The first pair of canards, called pitch canards, is used as the pitch and yaw attitude control effector, and the second pair, called spin canards, is used to generate the rotation of the fuze. Due to the highly rotating motion of the munition, the cross coupling effect between the pitch and yaw axes is significant. To decouple the pitch and yaw axes, the neural network-based L1 adaptive control with dynamic model inversion is proposed in this paper. We also present a coordinate transformation for the controller of the rotating guided munition. The 7 DOF nonlinear simulation model was conducted to validate the results of the controller.

Appendix 1

Notation

$m_{\text{s}} ,m_{\text{f}}$	Mass of shell and fuze
$\bar{F}$	Force vector
$\bar{\omega }_{\text{NR}}$	Angular velocity in no-roll axis
$u,v,w$	Velocity component in body axis
$L_{\text{v}} ,L_{\text{b}}$	Roll moment of viscosity friction and roll brake
$B$	Coefficient of viscosity friction
$p_{\text{s}} ,p_{\text{f}}$	Shell and fuze angular velocity
$L,M,N$	Moment component
$I_{xx,yy,zz}$	Moment of inertia
$A_{y}^{B} ,A_{z}^{B}$	Side, normal acceleration in body axis
$A_{y0} ,A_{z0}$	Initial value of side, normal acceleration
$\delta_{y}^{\text{B}} ,\delta_{z}^{\text{B}}$	Deflection angles of yaw and pitch effectors in body axis, respectively
$\delta_{0}$	Initial value of control effector
$p_{0}$	Initial value of angular velocity in x axis
$t$	Flight time
$\phi_{A} ,\phi_{\delta }$	Phase of state and input
$A_{y}^{\text{NR}} ,A_{z}^{\text{NR}}$	Side, normal acceleration in no-roll axis
$A_{y}^{\text{m}} ,A_{z}^{\text{m}}$	Side, normal acceleration in maneuver axis
$x_{\text{c}}$	Command of angular velocity
$\delta_{\text{p}} ,\delta_{\text{y}}$	Pitch and yaw control effector
$v$	Pseudo control signal
$v_{\text{ad}}$	Neural network signals
$\Delta$	Modeling error
$W$	Unknown weighting vector of the neural network law
$\hat{W}$	Designed weighting vector of the neural network law
$\hat{A}$	Error model state matrix
$\sigma$	Sigma–pi basis function
$f(x)$	Nonlinear system model
$K$	Feedback gain matrix
$e$	State of error model