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

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,


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
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.



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