Help with Response Optmization

I am working on optimizing a Simulink model for unpowered flight to demonstrate dynamic soaring phenomenon. My goal is to increase the range by adjusting the control surfaces. I am struggling to create the function that will maximize the distance traveled. Can anyone provide guidance or help with this optimization task?

Answer 1

[Manikanta Aditya]

Hi Krishnan,

I see you are working on optimizing a Simulink model for unpowered flight to demonstrate dynamic soaring phenomen and you are looking to increase the range by adjusting the control surfaces.

To create a function that maximizes the distance traveled, you’ll need to set up an optimization problem. Here’s a high-level approach:

1. Objective Function: This is the function you want to maximize or minimize. In your case, it’s the distance traveled by the aircraft. You’ll need to create a function that calculates this distance based on the aircraft’s flight path.
2. Design Variables: These are the variables you’ll be changing in order to optimize the objective function. In your case, these could be the angles or positions of the control surfaces.
3. Constraints: These are the limits within which the design variables can change. For example, the angles of the control surfaces likely have a minimum and maximum value.
4. Optimization Algorithm: This is the method by which you’ll iteratively adjust the design variables to find the optimal solution. There are many algorithms to choose from, such as gradient descent, genetic algorithms, or even machine learning-based methods.

For further assistance, check the following reference to know about:

• Simulink Optimization Blockset documentation: https://www.mathworks.com/products/sl-design-optimization.html

Hope this gives help you to create the function.

[Sam Chak]

Hi @Manikanta Aditya

Your response aligns with what's typically found in optimization documentation. However, the actual challenge the OP is facing is to determine the mathematical function that maximizes the distance traveled, which serves as the cost function. Without this crucial component, the optimization problem cannot be solved, regardless of the availability of generic optimization code or successful examples.

Only the OP, if they possess expertise in aerodynamics (even if they are unfamiliar with optimization tasks), can provide the accurate cost function. How would you advise the OP in deriving the cost function from the Newton's laws of motion?

[Manikanta Aditya]

Hi @Sam Chak,

Thanks for replying back.

Yes, You’re correct that deriving the cost function is a crucial step in this optimization problem. The cost function should ideally be derived from the fundamental principles of flight dynamics and the specific characteristics of the aircraft.

In this case, the Newton’s laws of motion can be applied to the forces acting on the aircraft during flight. These forces include lift, drag, weight, and thrust. The relationships between these forces, the control surface angles, and the aircraft’s velocity and direction can be used to derive a mathematical model of the aircraft’s motion.

According to Newton’s second law, the sum of these forces is equal to the mass of the aircraft times its acceleration.

• In the vertical direction, we have Lift - Weight = Mass * vertical acceleration.
• In the horizontal direction, we have Thrust - Drag = Mass * horizontal acceleration.
• Since it’s an unpowered flight, the thrust is zero. So, the equation becomes -Drag = Mass * horizontal acceleration.

This mathematical model can then be integrated over time to calculate the total distance traveled for a given set of control surface angles. This gives us the cost function for the optimization problem.

However, deriving this cost function can be complex and requires a deep understanding of aerodynamics and flight dynamics. If not familiar with these topics, I would recommend consulting with an expert or studying more about them. Even I am not sure exactly on about the derivation. There are also many resources available online and in textbooks that can help with this task.

Gathered some useful and helpful resources:

• Aerodynamics and Aircraft Performance - 3rd edition - Open Textbook Library (umn.edu)
• Flight Dynamics | Princeton University Press

Thanks!

[Sam Chak]

@Manikanta Aditya: deriving this cost function can be complex and requires a deep understanding of aerodynamics and flight dynamics.

That largely depends on the specific unpowered flight vehicle that the OP has modeled. Assuming the OP is a trained individual, such as a student or professor from a flight school, I would assume he has a solid grasp of calculus and integration concepts, so that shouldn't be a concern.

When neglecting lateral motion, computing the total distance traveled by the aircraft in a 2D plane is likely not as simple as taking the square root of the sum of horizontal and vertical distances. The total distance traveled may need to be computed as an arc length, which can be found using an integration formula.

Let's wait for OP's response if he is truly motivated to solve this problem in MATLAB.