Nonlinear sub optimal mid course guidance with desired alinement using mpqc
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Nonlinear Sub-optimal Mid Course Guidance with Desired Alinement using MPQC. P. N. Dwivedi, Dr. A.Bhattacharya , Scientist, DRDO, Hyderabad-,INDIA Dr. Radhakant Padhi Asst. Professor, IISC, Banglore,INDIA. Outline. OBJECTIVE OF MID COURSE GUIDANCE

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Nonlinear Sub-optimal Mid Course Guidance with Desired Alinement using MPQC

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Nonlinear sub optimal mid course guidance with desired alinement using mpqc

Nonlinear Sub-optimal Mid Course Guidance withDesired Alinement using MPQC

P. N. Dwivedi, Dr. A.Bhattacharya,

Scientist, DRDO, Hyderabad-,INDIA

Dr. RadhakantPadhi

Asst. Professor, IISC, Banglore,INDIA


Outline

Outline

  • OBJECTIVE OF MID COURSE GUIDANCE

  • MODEL PREDICTIVE QUADRATIC CONTROL(MPQC) DESIGN

  • MID COURSE GUIDANCE WITH MPQC

  • RESULTS

  • CONCLUSION


Objective of mid course guidance

OBJECTIVE OF MID COURSE GUIDANCE

  • Interceptor must have sufficient capability and proper initial condition for terminal guidance phase .

  • Mid course guidance to provide proper initial condition to terminal guidance phase.

  • Interceptor spends most of its time during mid course phase Hence should be energy efficient

  • Hence Objective is:

    Interceptor has to reach desired point(xd, yd,zd) with desired heading angle (Φd) and flight path angle (γd) using minimum acceleration ηΦand ηγ.


Mpqc design mathematical development

Discretized

MPQC Design: Mathematical Development

System dynamics:

Goal: with additional (optimal) objective(s)


Mpqc design mathematical formulation

0

MPQC Design: Mathematical Formulation

(small error approximation)


Recursive relation for error coefficient computation

General formula

Recursive computation:

Recursive Relation for Error Coefficient Computation


Mpqc design mathematical formulation1

MPQC Design: Mathematical Formulation

Now the acceleration can be approximated as straight line

error in control can be given as

Substituting for dUk for k = 1,.....,N-1 in


Mpqc design mathematical formulation2

MPQC Design: Mathematical Formulation

We get


Mpqc design mathematical formulation3

MPQC Design: Mathematical Formulation

  • If no of eq is same as no of unknown

  • if number of unknowns is greater than the number of equations, the optimal solution can be obtained by minimizing the following objective (cost) function,


Nonlinear sub optimal mid course guidance with desired alinement using mpqc

MPQC algorithm

Start

Guess a control history

Update the control history

Propagate system dynamics

Compute Output

Check

Convergence

No

Compute sensitivity matrices

Yes

Converged control Solution

Stop


Mpqc design features

MPQC Design: Features

  • Advantages

    • Closed form control update

    • Computationally very efficient and can be implemented online

  • Limitations

    • Finite time formulation

    • Performance index isa function of control variable only


Mid course guidance with mpqc mathematical model

MID COURSE GUIDANCE WITH MPQC (Mathematical model)


Mid course guidance with mpqc

MID COURSE GUIDANCE WITH MPQC

  • In state equation of the interceptor, time is used as an independent variable.

  • Hence if we want to propagate state, we must have knowledge of final time which is quite difficult .

  • So instead of time, x can be used as independent variable as final position of x is known (because Missile has to reach at particular point(desired) after mid course).


Mid course guidance with mpqc1

MID COURSE GUIDANCE WITH MPQC

  • For this purpose missile model can be modified as where X’ represent the derivative of state with respect to position x.

  • For MPQC design, state model has to be in discreet form as

  • And dYN is define as


Results

RESULTS

  • To show the capability of guidance the initial position of missile and 2 different case for different final condition has been chosen as given in table.


Conclusion

CONCLUSION

  • A newly developed MPQC( MODEL PREDICTIVE QUADRATIC CONTROL) is utilized to solve optimal mid-course guidance problem for a homing interceptor.

  • Acceleration demand has been minimized for reaching desired position with desired velocity vector.

  • This technique is computationally efficient and can be applied online for getting closed form sub-optimal solution of mid course guidance problem.


Nonlinear sub optimal mid course guidance with desired alinement using mpqc

Thanks for the Attention….!!

Questions ... ??


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