Mechatronics (JEM) Curriculum

The deliverables for this project were normalized models of the thruster, pitch and yaw. In this, the thruster and pitch were represented as as single-input, single-output linear differential equations, and the yaw was represented as a multi-input, single-output differential equation.

Each of these models were derived from schematics of the product which required teams to think critically about interactions between the subsystems. Ultimately, the project required us to construct differential equations based on an electrical-to-rotational transducer, equations of motion, and nonlinear relationships between pitch and yaw angle.

Once the differential equations were constructed of both known and unknown terms, they were ready to be taken to the next stage of the project: modeling and simulating potential responses.

After derivation, the next task was to use experimental data to validate the accuracy of the calculated model. This is done by running the system through an experiment where the input and output of that system is observed and comparing that real output to a simulated output given the same input, all of which can be done using MatLab Simulink. First, the differential equations must be re-expressed in terms of either a transfer function, or a state-space model.

Using Laplace transforms, characteristics of underdamped systems, interpolation from experimental data, state space, logarithmic decrement, and a polynomial expression of a line of best fit, our team was able to represent the pitch, thruster, and thruster forces associated with defined initial conditions and experimentally gathered responses.

The differences between our calculated model and the experimental data likely originated from our linearization of a trigonometric term under the assumption of small angles (tan(θ) ≈ θ) .