P17341: Harris Near-Zero CTE Test Apparatus
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Systems Design

Table of Contents

Team Vision for System-Level Design Phase

Tasks from Previous Phase

Tasks from Previous Phase

With the problem statement and scope well-defined in the previous phase, the team plan for this phase involved focusing on the specifics of the design and generating concepts. First, the specific functions of the design were broken down, and a morphological chart was populated with various concepts to fulfill each of those functions. While attention was given to the magnetic levitation concept, it was considered as one among others as a way of supporting the sample. Other functions of note included securing the entire fixture, clamping the sample, and how the sample's position will be controlled. The highly compartmentalized nature of the problem meant that the best of each individual functions were able to be combined together without interference into several proposed designs. These designs were weighed against each other in Pugh analysis to determine the best possible combination. Additionally, preliminary benchmarking and experimentation with electromagnets was carried out during this phase.

Functional Decomposition

While 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.
Functional Decomposition of CTE Tester

Functional Decomposition of CTE Tester


Engineering Requirements (Metrics & Specifications)

Engineering Requirements

Engineering Requirements

Benchmarking

Benchmarking - CTE Measurement Solutions

Benchmarking - CTE Measurement Solutions

Information source: PMIC Testing Services - Thermal Expansion

Further reading located here.

Benchmarking - Position Measurement Solutions

Benchmarking - Position Measurement Solutions



Morphological Chart and Concept Selection

Morphological Chart of Concepts

Morphological Chart of Concepts

Concept Selection

Pugh Selection Process

Selection criteria:

For a description of each concept, see here.

Selection Chart

Selection Chart

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

Bottom Maglev Concept

Bottom Maglev Concept

This concept was ultimately rejected for the following reasons:

Top Magnetic Levitation

Top Maglev Concept

Top Maglev Concept

No Magnetic Levitation

Concept Without Maglev

Concept Without Maglev

In the event that a magnetically levitated system is not feasible, this concept was chosen as an alternative. It features the same slot design as the previous concept, and is a very simple system with no need for a controller.

System Architecture

Below 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.
System Architecture

System Architecture

Risk Assessment

As 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.
Risk Assessment Chart

Risk Assessment Chart

Risk Explanation

Risk Explanation

Link to the live document here.

Feasibility: Prototyping, Analysis, Simulation

In 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.

Maglev Model

Maglev Model

Maglev simple equations

Maglev simple equations

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.

Characteristics of a free falling object

Characteristics of a free falling object

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.

Simulink model of maglev system without a controller

Simulink model of maglev system without a controller

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.

Maglev characteristics without controller

Maglev characteristics without controller

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.

Simulink model using discrete PID controller

Simulink model using discrete PID controller

Simulink model using SMC

Simulink model using SMC

Within the PID and SMC control schemes we use the following plant model.

Simulink maglev plant model

Simulink maglev 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.

Time domain response using PID controller

Time domain response using PID controller

Time domain response using PID controller

Time domain response using PID controller

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.

Phase Plane Portrait using PID controller

Phase Plane Portrait using PID controller

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.

Time domain response using SMC

Time domain response using SMC

Time domain response using SMC

Time domain response using SMC

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.

Phase Plane Portrait using SMC

Phase Plane Portrait using SMC

Additionally, as the first step for physical testing, the team constructed and tested a basic electromagnet.

Electromagnet Feasibility Test

Electromagnet Feasibility Test

Plans for next phase

Key Goals for Next Phase

  1. Prove magnetic levitation concept is or is not feasible.
    • Initiate design (2) if magnetic levitation is NOT feasible.
  2. Start building prototype testing fixture.
  3. Purchase or “build” magnetic levitation device.
  4. Purchase sensor selection.
  5. Finalize CAD drawings.
  6. Material selection

Key Questions for Next Phase

Is the Magnetic Levitation Concept Feasible?
  1. Will be proved with a test fixture.
  2. Can we levitate a material sample?
  3. If so, what is the stability of that sample?

Is our designed electric system feasible?

  1. Electrical prototype will be built to prove our electrical design.
  2. Components for electrical prototype will be purchased.

Is the clamp design feasible?

  1. Will the clamp adequately secure the sample?
  2. Is the material selection of the clamp feasible?

Are the material selections feasible?

  1. Is the material implemented our best option?
  2. Does analysis validate our selection?
Plans for Next Phase

Plans for Next Phase


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