This design project simulates and controls a beam and ball system. A ball rolls on a pivoting beam. The beam is connected through DC motor through a linkage arm. The objective is to create an output feedback control system. The project simulates the system using Matlab and Simulink.

Ball and beam geometry

The physical system consists of coupled linkages and a free-to-roll ball. The linkage motion is nonlinearly coupled to the gear angle. The beam has a length of 1 meter. The gear arm has a radius of 0.03 meters, and the linking arm has a length of 0.2 meters. The ball is steel with a radius of 15 millimeters. The system has 2 energy storage components: beam inertia and ball inertia. System control is allowed through a voltage input into the DC motor, which provides a torque applied at the gear arm. The gear arm motion is harmonic; the gear can go past topdead-center in the straight up and down positions.

The document is available here.

I recently found an old photo from 1983 of me next to a trike. Judging from the background hanger’s appearance, this is apparently the large north hanger at KELK.

This project developed an one degree-of-freedom electronic aircraft directional
gyro (DG). The mechanical inertial gyro in a 1960’s vintage DG was removed
and replaced with an stepping motor driven by a micro controller connected to
an electronic rate gyro.

Directional Gyro Retrofit

The project document is available here

The goal is to determine possible soccer ball launch configurations that result in the ball returning to the launch site. A returning soccer ball is possible with the proper launch angle and velocity. A headwind is required except for the purely vertical case.

Trajectories with long free fall times are extremely sensitive to their initial conditions. These critical trajectories have outgoing and incoming paths that are vastly different.

Flow regimes and the resulting drag coefficients dominate the launch configuration. The transition to fully turbulent flow increases the required launch angle. Higher headwinds quicken the appearance of the turbulent region.

The document is available here

Conceptually, a high endurance aircraft circles over a service area to provide high-bandwidth communication. The objective is to maximize endurance. The basic physical geometry is a conventional aircraft powered by a small fan-jet engine.

Aircraft Configuration Feasible Space

The project is available endure.pdf.

This project investigates aerodynamic system identification. An airfoil produces time varying loads based on the current and past boundary conditions; this project seeks to identify the lift loads resulting from pitch motion.
The first part discusses some unsteady aerodynamic theory. The second part discusses the identification process. The final part discusses conclusions and observations.

A Box-Jenkins model successfully modeled the lowand moderate airfoil reduced frequencies, but was  troublesome at higher frequencies. Interestingly, the Theodorsen theory qualitatively matches the CFD results except above approximately a reduced frequency of unity. The moderate frequency lift deficiency predicted by Theodorsen was found in the CFD solution and the Box-Jenkins model. Interestingly, as the high frequencies were resolved, the system appears more distributed. The final Box-Jenkins model accurately predicted the forces resulting from a validation input signal.

Bode Frequency Response of Data and Box-Jenkins Model

The project document is at sifinal.pdf.

This project surveys nonlinear analysis and control methods for a specific two-degree-of-freedom analytical delta wing model. Linearization, phase plane analysis and existence theorems are used to describe the overall system behavior without solving the differential equations. A describing function is developed for the nonlinear system and favorably compares to the actual limit cycle amplitudes and frequencies. Linear pole placement and Ricatti control methods and nonlinear sliding mode and Lyapunov control laws are developed for stabilization and tracking.

Sliding Mode Control Schematic

See the full project at wingrock.pdf