# Nonlinear Sub-optimal Mid Course Guidance with Desired Alinement using MPQC - PowerPoint PPT Presentation

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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 withDesired Alinement using MPQC

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

Asst. Professor, IISC, Banglore,INDIA

### Outline

• OBJECTIVE OF MID COURSE GUIDANCE

• MODEL PREDICTIVE QUADRATIC CONTROL(MPQC) DESIGN

• MID COURSE GUIDANCE WITH MPQC

• RESULTS

• CONCLUSION

### 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.

Discretized

System dynamics:

0

### MPQC Design: Mathematical Formulation

(small error approximation)

General formula

Recursive computation:

### 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

We get

### 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

• 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

• 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 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

• 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

• 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.

Thanks for the Attention….!!

Questions ... ??