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Higher Order Sliding Mode-Based Guidance for Controlling Statically Unstable Missiles

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Abstract

A surface to air missile (SAM) typically operates at a wide range of Mach numbers, angles of attack and altitudes. This leads to an inevitable significant variation in center of pressure (CP) location. In addition, the propulsion burning changes the Center of Gravity (CG) location. The variation in CP and CG locations results in high variation in aerodynamic static stability in the flight envelope. The high variation of static stability makes operating at statically unstable regions inevitable and needs to be tackled through the missile on-board algorithm. The control design poses a requirement of high autopilot bandwidth to tackle the static instability, which leads to unrealistic actuator bandwidth requirements. Here, we propose a novel technique to handle the high static instability outside the purview of control design without burdening the control requirements. In this paper, the highly unstable operating conditions are avoided through judicious design of mid-course guidance. This paper also presents design of this guidance scheme through higher order sliding mode technique.

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Abbreviations

\(\alpha\) :

Angle of attack (AoA) (rad)

\(\delta\) :

Control deflection (rad)

\(\dot{q}\) :

Missile pitch angular acceleration (rad/s\(^2)\)

\(\gamma\) :

Missile flight path angle (rad)

\(a_Z\) :

Lateral acceleration (Latax) (m/s\(^2\))

\(C_A\) :

Axial force coefficient

\(C_l\) :

Rolling moment coefficient

\(C_m\) :

Pitching moment coefficient

\(C_N\) :

Normal force coefficient

\(C_n\) :

Yawing moment coefficient

\(C_Y\) :

Side force coefficient

\(C_{m_{\alpha }}\) :

Pitching moment coefficient slope with respect to AoA (rad\(^{-1}\))

\(C_{m_{\delta }}\) :

Pitching moment coefficient slope with respect to control deflection (rad\(^{-1}\))

\(C_{N_{\alpha }}\) :

Normal force coefficient slope with respect to AoA (rad\(^{-1}\))

\(C_{N_{\delta }}\) :

Normal force coefficient slope with respect to control deflection (rad\(^{-1}\))

\(I_{yy}\) :

Missile moment of inertia (kg-\(m^2)\)

\(V_{m}\) :

Missile velocity (m/s)

D :

Reference length (m)

m :

Missile mass (kg)

Q :

Dynamic pressure \(\left( N/m^2\right)\)

q :

Body rate (rad/s)

S :

Reference area \(\left( m^2\right)\)

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Correspondence to Ram B. Sankar.

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Sankar, R.B., Tiwari, P.K., Bandyopadhyay, B. et al. Higher Order Sliding Mode-Based Guidance for Controlling Statically Unstable Missiles. Trans Indian Natl. Acad. Eng. 6, 415–427 (2021). https://doi.org/10.1007/s41403-021-00215-0

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  • DOI: https://doi.org/10.1007/s41403-021-00215-0

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