Project
| # | Title | Team Members | TA | Documents | Sponsor |
|---|---|---|---|---|---|
| 26 | Analog Computer ODE Solver |
Dianxing Tang Haige Liu Shilong Shen Zixuan Qu |
design_document1.pdf final_paper1.pdf final_paper2.pdf other1.pdf proposal1.pdf |
Said Mikki | |
| # ANALOG COMPUTER ODE SOLVER ## Team Members: - Shilong Shen (shilong7) - Dianxing Tang (dt12) - Haige Liu (haigel2) - Zixuan Qu (zixuanq3) # Problem Analog computer is widely used in many mathematical calculations like ordinary differential equations (ODEs). ODEs have a wide range of applications in many fields, such as classical mechanics, electromagnetism, and engineering control. Especially in AI algorithms, such as in neural networks and deep learning, ODEs are used to adjust parameters during iterative training. Traditional software methods for solving ODEs often face issues like low response speed and insufficient efficiency. In addition, some types of ODEs do not have generalized solutions and therefore cannot be directly computed using traditional computational software. In some cases users prefer that the calculator can output the electrical signals of the solutions directly. Therefore, we need to design an **analog computer** using specialized hardware circuits to directly solve ODEs and other kinds of mathematical problems, which can efficiently obtain the numerical solutions of different types of ODEs and output them directly, aiming to improve computation speed, reduce latency, and meet the need for real-time processing. # Solution To design an analog computer for solving mathematical problems like ODEs, we plan to use operation amplifiers to build integrators, adders, and multipliers to create a feedback loop. We will convert the ODE into specific electrical signals, such as voltage, input these signals into the solving circuit, and then convert the output back to obtain the solution of the ODE, which will be shown directly to the user via an oscilloscope. From there we build a useful mathematical problem solver. All we need to do is select the types of ODEs and enter the coefficients, and the calculator outputs a numerical solution to the equation from the electrical signals and allows the user to visualize a picture of the solution. The main design process involves first building and simulating the analog circuit in MATLAB to verify its functionality. After successful simulation, we will implement the hardware circuit on a printed circuit board (PCB) and conduct further testing to ensure its performance. # Solution Components ## Subsystem I: Simulation Test MATLAB Simulation Circuit: Build and simulate analog circuit to verify the design. ## Subsystem II: Main PCB Hardware Circuit - Basic operational units: Build adders, multipliers and integrators with electrical components such as op-amps, resistors and capacitors - PCB hardware circuit: Construct the close-loop circuit with basic operational units on a printed circuit board (PCB) to solve ODE by multiple iterations. - ODE input recognition System: Identifies the type of ODE (e.g., order, whether it's homogeneous, etc.) and directs the signal to the corresponding circuit. ## Subsystem III: ODE Signal Conversion System - Arduino Main Control Board: Handles the input and output signals of the hardware circuit - Arduino Programming: Converts the ODE into electrical signals (e.g., voltage) to input into the hardware circuit and processes the output signal to extract the solution of the ODE. # Criterion For Success The MATLAB simulation circuit should solve 1st to 3rd order linear and nonlinear ODEs accurately, as demonstrated in testing. - The basic operational units on the PCB must function correctly, performing their intended tasks without errors. - The analog computer should solve ODEs with similar accuracy and timing as the MATLAB simulation. - The Arduino must accurately convert input and output signals for the hardware without error. ## Reference - https://i4cy.com/analog_computing/ - https://www.mathworks.com/matlabcentral/fileexchange/56756-solution-of-differential-equation-using-analog-computer - https://saching007.github.io/pubs/dpac.pdf - https://www.geeksforgeeks.org/what-is-an-analog-computer/ |
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