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Investigative design of missile longitudinal dynamics using LQR-LQG controller in presence of measurement noise and inaccurate model

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Abstract

The paper presents the design and development of a Linear Quadratic Gaussian (LQG) controller for a longitudinal dynamics of a high maneuvering missile. The Linear Quadratic Regulator (LQR) in association with Linear Quadratic Estimator (LQE) is realized through extensive numerical simulations to address the plant dynamics associated with measurement noise and inaccurate plant model. The LQR gives the minimum cost function to the proposed optimal solution for a missile control design application. The LQR and LQE design has been tested for its robustness subjecting it to parametric variation of disturbances and plant uncertainties. The study brings out the efficacy of the LQG controller over traditional methods in missile control system design.

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Abbreviations

X, Y, Z:

Forces in x, y and z directions

m:

Mass of the missile

\(\phi \) :

Roll angle

\(\alpha \) :

Angle of attack

\(\hbox {I}_{\mathrm{xx}}\), \(\hbox {I}_{\mathrm{yy}}\), \(\hbox {I}_{\mathrm{zz}}\) :

Moment of inertia about x, y and z axes

u, v, w :

Components of missile velocity three axes

p, q, r :

Roll rate, Pitch rate and Yaw rate

\(\theta \) :

Pitch angle

\(\delta _{pitch}\) :

Pitch control deflection

L, M, N:

Rolling moment, Pitch moment, Yawing moment

x(t):

State vector

u(t):

Control input vector

A, B, C, D:

Plant matrix, input matrix, output matrix and feed-forward matrix

\(C_{AT}\) :

Axial force coefficient

\(C_{N}\) :

Normal force coefficient

IMU:

Inertial Measurement Unit

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Authors and Affiliations

  1. DRDL, DRDO, Ministry of Defence, Kanchanbagh, Hyderabad, India

    V S N Murthy Arikapalli, Shiladitya Bhowmick & P V R R Bhogendra Rao

  2. National Institute of Technology, Tiruchirapalli, Tamilnadu, India

    Ramakalyan Ayyagari

Authors
  1. V S N Murthy Arikapalli
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  2. Shiladitya Bhowmick
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  3. P V R R Bhogendra Rao
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  4. Ramakalyan Ayyagari
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Correspondence to P V R R Bhogendra Rao.

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Arikapalli, V.S.N.M., Bhowmick, S., Rao, P.V.R.R.B. et al. Investigative design of missile longitudinal dynamics using LQR-LQG controller in presence of measurement noise and inaccurate model. Sādhanā 47, 38 (2022). https://doi.org/10.1007/s12046-021-01784-0

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  • DOI: https://doi.org/10.1007/s12046-021-01784-0

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