As part of my work for the Columbia Laboratory for Unconventional Electronics (CLUE), I designed an analog computing system using cascaded op-amp integrators.
The circuit converted the equations of motion into real-time voltage waveforms that accurately modeled the flight dynamics of a rocket launch.
I began by deriving the equations of motion and defining the state variables so acceleration could be mapped to velocity and position in continuous time. With the math in place, I chose a circuit architecture of cascaded op-amp integrators, which allowed me to directly encode constants of the governing equations through resistor and capacitor values.
In LTSpice, I designed the circuit and mapped conversion factors between volts and physical units like ft/s and ft. I introduced voltage sources to represent initial conditions such as nonzero launch velocities, and adjusted damping and quality factors through targeted Resistor–Capacitor (RC) ratios to achieve the desired system dynamics.
After validating the design in simulation, I built the circuit on a breadboard. I tested each stage individually before driving the complete system with time-varying acceleration inputs.
Using an oscilloscope, I captured position, velocity, and acceleration waveforms and compared them against my LTSpice simulations. I iteratively adjusted the RC time constants at each stage, refining the system response and verifying that the hardware implementation tracked the expected dynamics.
The breadboard implementation of the analog computer generated rocket flight waveforms that matched my LTSpice simulations within <5% error. This validated the circuit design and confirmed the effectiveness of the op-amp integrator hardware implementation. Overall, the project was a resounding success.
