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A robust adaptive control approach to missile autopilot design

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Abstract

The huge developments in computational capabilities facilitate the design and implementation of adaptive and robust control. Furthermore, the great developments in nanotechnology and its availability in civilian level with less cost, weight, and size attract the researchers all over the world towards embedded systems especially the embedded flight control. One of the real applications are the guided missiles especially the anti-tank guided missile systems which are launched against the ground and short-range targets and is called command line of sight. The present work is concerned with improving the performance of an anti-tank guided missile system belonging to the first generation via adaptive synthesis of guidance systems. The online system identification is required to complete the cycle of adaptive autopilot design. This paper is devoted to designing an adaptive autopilot for the intended system using model reference and self-tuning regulator with justification against previous work and reference flight data concerning the performance requirements of time responses and flight path characteristics. The new design is implemented within the 6-DOF simulation from which the obtained results clarify its capability to stabilize the system in presence of unmodeled dynamics and satisfy the performance requirements with disturbance rejection and measurement noise attenuation. Also, the flight path is evaluated considering the HIL environment.

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Abbreviations

\(\hbox {X}_{1}, \hbox {Y}_{1}\), and \(\hbox {Z}_{1}\) :

Vectors components along the board reference axes

\(\hbox {X}_{\mathrm{g}}, \hbox {Yg}\), and \(\hbox {Z}_{\mathrm{g}}\) :

Vectors components along the ground reference axes

\(\hbox {X}, \hbox {Y}\), and \(\hbox {Z}\) :

Vectors components along the velocity reference axes

\(\hbox {T}_{\mathrm{bg}}\) :

Transformation matrix from board to ground reference axes

\(\hbox {T}_{\mathrm{vg}}\) :

Transformation matrix from velocity to ground reference axes

\(\hbox {T}_{\mathrm{bg}}\) :

Transformation matrix from board to ground reference axes

\({\updelta }_{\mathrm{jp}}\) and \({\updelta }_{\mathrm{jy}}\) :

Thrust jetivator angles in pitch and yaw planes

\(F_{{ TX}_1}, F_{{ TY}1} \hbox { and }F_{{ TZ}_1}\) :

Thrust forces along the board reference axes

\(F_{{ AX}}, F_{{ AY}}\) and \(F_{{ AZ}}\) :

Drag, lateral, and lift forces along the velocity axes

S:

Characteristic area

q:

Dynamic pressure given by \(\hbox {q} = 0.5\uprho \,(\hbox {V}_{\mathrm{m}})^{2}\,(\hbox {Kg/m/s}^{2}]\)

\(\uprho \) :

Air density (\(\hbox {kg/m}^{3}\))

\(\hbox {V}_{\mathrm{M}}\) :

Missile velocity

\(\hbox {C}_{\mathrm{x}}, \hbox {C}_{\mathrm{y}}\), and \(\hbox {C}_{\mathrm{z}}\) :

Dimension-less aerodynamic coefficients

\(\hbox {m}_{\mathrm{s}}\) :

Instantaneous total missile mass

\({\overline{g}}\) :

Vector of gravity acceleration

\(\hbox {m}_{\mathrm{o}}\) :

Initial missile mass

\(\hbox {m}_{\mathrm{sec}}\) :

Burnt quantity of fuel or propellant per second

M:

Mach number and given by \(\hbox {M}=\hbox {V}_{\mathrm{m}}/\hbox {V}_{\mathrm{a}}\)

\(\hbox {V}_{\mathrm{a}}\) :

Sound velocity at missile position

\(l_T\) :

Perpendicular distance between the missile C.G. and the point of lateral thrust forces action

\(l_{{ TX}}\) :

Perpendicular distance between longitudinal axis and thrust force line

\(l_x, l_y, l_z\) :

Characteristic linear dimensions of missile

\(m_{x_1}, m_{y_1}\) and \(m_{z_1}\) :

Dimensionless aerodynamic coefficients

\({\upomega }_{x_1 }, {\upomega }_{y_1} \hbox { and } {\upomega }_{z_1}\) :

Airframe-turn rates along board coordinate axes

\({\overline{J}}\) :

Acceleration of missile

\(\Omega \) :

Angular velocity of VCS w.r.t GCS

\(\hbox {I}_{\mathrm{XX}}, \hbox {I}_{\mathrm{YY}}\), and \(\hbox {I}_{\mathrm{ZZ}}\) :

Moments of inertia components along the BCS

\(\upalpha \) :

Angle of attack [angle of incidence] [Degree]

\(\upbeta \) :

Sideslip angle [angle of drift] [Degree]

\(\hbox {U, V}\), and \(\hbox {W}\) :

Velocities Along board coordinate axis

\(\hbox {U}_{\mathrm{d}}, \hbox {V}_{\mathrm{d}}\), and \(\hbox {W}_{\mathrm{d}}\) :

Derivative of velocities along board coordinate axis

\(\hbox {g}_{\mathrm{x}}, \hbox {g}_{\mathrm{y}}\), and \(\hbox {g}_{\mathrm{z}}\) :

Gravity acceleration along board coordinate axis

\(\upvarepsilon _{\mathrm{T}}\) and \({\updelta }_{\mathrm{T}}\) :

Elevation and azimuth angles of target

\(\upvarepsilon _{\mathrm{M}}\) and \(\upvarepsilon _{\mathrm{M}}\) :

Elevation and azimuth angles of missile

\(\Delta {\upvarepsilon }\) and \(\Delta _{{\updelta }}\) :

LOS angular error

\(\hbox {R}_{\mathrm{m}}\) and \(\hbox {R}_{\mathrm{t}}\) :

Missile and target range

\({\uptheta }_{\mathrm{p}}\) :

Pitch demand

\({\uppsi }_{\mathrm{s}}\) :

Angle between missile and LOS in yaw plane

\(\upvarepsilon _{1}, {\upsigma }_{1}\) :

LOS angular errors for the two planes expressed in meters

\(\hbox {e}\) :

Tracking error

\(\hbox {J}\,({\uptheta })\) :

Cost function of theta

\(\hbox {I}_{\mathrm{WP}}\) and \(\hbox {V}_{\mathrm{WP}}\) :

Pitch wire current and voltage

\(\hbox {V}_{\mathrm{ep}}\) :

Pitch error signal

\(\hbox {V}_{\mathrm{sp}}\) :

Pitch autopilot output

\(\hbox {V}_{\mathrm{gp}}\) :

Pitch gyro output

ADC:

Aero dynamic coefficients

AP:

Autopilot

BCS:

Board coordinate system

CLOS:

Commanded to line of sight

MRARC:

Model reference adaptive robust controller

LOS:

Line of sight

6-DOF :

Six degrees of freedom

Adaptive STR:

Adaptive self tuning regulator

TVC:

Thrust vector control

VCS:

Velocity coordinate system

c.g.:

Centre of gravity

HIL:

Hardware in loop

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Authors and Affiliations

  1. Department of Guidance, Military Technical College, madinet nasr, Cairo, Egypt

    A. N. Ouda

  2. UOIT, Ontario, Canada

    A. N. Ouda

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Ouda, A.N. A robust adaptive control approach to missile autopilot design. Int. J. Dynam. Control 6, 1239–1271 (2018). https://doi.org/10.1007/s40435-017-0352-4

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