Team Vision for System-Level Design Phase
Functional DecompositionWhile the primary method of supporting the sample was assumed to be magnetic levitation during the first phase, this phase simply considered maglev as one possible way to support the test coupon. That way, when carrying out the analysis of the necessary functions of the device, the design process would not get bogged down by considering solutions instead of functions. The functional decomposition that identifies the necessary operations of the testing device is shown below.
Engineering Requirements (Metrics & Specifications)
Information source: PMIC Testing Services - Thermal Expansion
Further reading located here.
Morphological Chart and Concept Selection
Pugh Selection ProcessSelection criteria:
- Time to develop
- Ease of use
- Reduced contact with coupon
- Can accommodate various coupon geometries
- Setup time
- Accuracy of results
- Sensitivity to temperature changes
- Coupon stability
For a description of each concept, see here.
The Pugh selection process was employed to determine the best concept, with the datum set as the current Harris CTE test facility. Main Design 2 was determined to be the best overall, given the weighting system employed.
Once various functional solutions were brainstormed, the most feasible candidates were combined into full designs. The highly compartmentalized nature of our problem means that each functional solution is compatible with each other, i.e., the coupon support method will be sufficient regardless of which clamp design is selected. Therefore, the various functions were considered individually in order to select the best possible design from each.
Criteria for concept selection were determined based on the critical functions of the device. Weights were assigned to each based on their relative importance. For example, safety is still important, but the inherent safety hazards of the design are easy to guard against, provided proper operation by a trained technician. Therefore, the relative safety of the designs was not considered as important. Additionally, some of the key outcomes of this project involve quantifying and minimizing error, so the requirements that the design be accurate and isolate the sample are an attempt to account for this.
Since the exploration of maglev is one of the main goals of the project, weights were also assigned in such a way that prioritized the advantages offered by a maglev system, allowing it to overcome its inherent disadvantages and emerge as a viable concept.
Bottom Magnetic Levitation
- The coupon will need to expand against the force of gravity
- Supporting the coupon from the bottom is inherently unstable
Top Magnetic Levitation
- Supporting the coupon from the top end should be more stable than from the bottom end
- Slot prevents coupon from falling in the event of failure
No Magnetic Levitation
System ArchitectureBelow is a general concept of our high level system architecture. The system is controlled by a real time arduino. The arduino has multiple inputs including matlab/simulink input, and position and displacement sensors.
Risk AssessmentAs different functions and solutions were brainstormed, various risks that had not been considered during problem definition were brought to light. The updated risk assessment chart is shown below.
Link to the live document here.
Feasibility: Prototyping, Analysis, SimulationIn this portion of our system development we'll analyze the high level physics behind magnetic levitation. We'll also dive into magnetic levitation simulation using Matlab/Simulink and compare the use of PID control to sliding mode control.
Below we can see a generic magnetic levitation system. Analyzing the forces applied to the levitating object, we can see there is force from the electromagnet and force from gravity. These equations can be seen below.
Below we can see the characteristic of an object falling from a height of 1 meter. The position decreases quadratically, velocity is linearly increasing and acceleration is constant.
Using Equation 4 we can model the magnetic levitation system using Simulink. This model can be seen below. In the model we use a constant position(variable x in equation 4) which is initialized in the 2nd integral block.
Running the simulation we can observe how sensitive the system is. Below, we can see three responses, the first to analyze is the blue constant response. This response is obtained by equating equation 4 to zero and solving for current. Note, if the simulation is ran for enough time, this constant response will eventually follow a similar response as the perturbation's response. Next we'll analyze the perturbation response. Here we perturbed the current that was used for the constant response by 1pA. It is clear this minute change can have a significant effect on the system.
Using Mathwork's magnetic levitation simulation we can integrate different control schemes. Here we'll analyze PID control and Sliding Mode Control responses. Below we can see both schemes using simulink.
Within the PID and SMC control schemes we use the following plant model.
Using an optimization algorithm we can determine PID coefficients that produce a system response per given specifications. Below we use the algorithm to find an appropriate response for mass ranging from 1-5kg. We can see that as mass increases the time to reach steady state also increases.
Below is a phase plane portrait of the PID responses seen above. This plot tells us that the system responses are stable, converging to a central point.
Using SMC we can find variables that produce an appropriate response for masses ranging from 1-5kg. Here we can see there is nearly no oscillation in the responses. The responses are nearly identical even though mass is increases. Note, running this simulation with higher masses, there will be slight oscillation in the response.
Below is a phase plane portrait of the SMC responses seen above. This plot tells us that the system responses are stable, converging to a central point.
Additionally, as the first step for physical testing, the team constructed and tested a basic electromagnet.
Plans for next phase
Key Goals for Next Phase
- Prove magnetic levitation concept is or is not
- Initiate design (2) if magnetic levitation is NOT feasible.
- Start building prototype testing fixture.
- Purchase or “build” magnetic levitation device.
- Purchase sensor selection.
- Finalize CAD drawings.
- Material selection
Key Questions for Next PhaseIs the Magnetic Levitation Concept Feasible?
- Will be proved with a test fixture.
- Can we levitate a material sample?
- If so, what is the stability of that sample?
Is our designed electric system feasible?
- Electrical prototype will be built to prove our electrical design.
- Components for electrical prototype will be purchased.
Is the clamp design feasible?
- Will the clamp adequately secure the sample?
- Is the material selection of the clamp feasible?
Are the material selections feasible?
- Is the material implemented our best option?
- Does analysis validate our selection?