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4 Qualifying Exam/2 Writing/1. QE Goals and Outcomes.md
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@ -36,4 +36,17 @@ If this research is successful, this diffusion model will accomplish three main
The diffusion generative model has shown great promise in creating novel and realistic samples from training data. This research will train a generative model to create Bode plots of transfer functions. This model will be given a nominal plant as an input and then generate a perturbed plant. Once created, this perturbed plant can be evaluated if it belongs to the set of controllable plants for a desired controller. This process will be repeated several times to generate enough plants to approximate the set of controllable plants.
These generated plants can be used to verify robustness of controller implementations. A model of a controller can use robust control theory to establish the set of controllable plants, but an actual implementation of a controller can not be verified as robust in the same way. Instead, it must be verified experimentally using elements of the set. Extracting elements of the set is not a trivial task, but if this research is successful, a generative model can reduce the effort required to create perturbed plants.
These generated plants can be used to verify robustness of controller implementations. A model of a controller can use robust control theory to establish the set of controllable plants, but an actual implementation of a controller can not be verified as robust in the same way. Instead, it must be verified experimentally using elements of the set. Extracting elements of the set is not a trivial task, but if this research is successful, a generative model can reduce the effort required to create perturbed plants.
## Edits
<mark style="background: #FFF3A3A6;">The goal of this research is to use a generative diffusion model to create unstructured perturbations of a nominal plant.</mark> <mark style="background: #FFB86CA6;">In the real world</mark>, there is always a perturbation between the dynamics of the physical process and the mathematical model. Stability and performance of the controller suffer when this difference is large, <mark style="background: #FFB8EBA6;"><mark style="background: #FFB86CA6;">but knowing that it is never zero, understanding how much performance is affected by the perturbation is important to know</mark></mark>. Robust control answers this problem for mathematical models of plants. We can know precisely how much a model of a controller will be affected by a perturbation, and we can define a set of allowable perturbations that fit within our engineering specifications.
A problem arises when we try to verify the robustness on an actual modern controller. In the actual implementation of control laws, there are several intermediate layers between the hardware, firmware, and software that can introduce mistakes. Unlike the model controller, we cannot easily verify that this controller has the same performance over the set of perturbed plants. The modern controller can only be tested with single elements from the set of plants. Because of this, we suggest using a diffusion generative model to generate elements from this set to validate implementations of controllers to be robust.
If this research is successful, this diffusion model will accomplish three main tasks:
1. It will approximate a set of controllable plants by generating a large number of perturbed examples
2. Perturb a nominal plant in an unstructured manner with a controllable amount of uncertainty
3. Generate time and frequency domain responses based on training data of example systems.
The diffusion generative model has shown great promise in creating novel and realistic samples from training data. This research will train a generative model to create Bode plots of transfer functions. This model will be given a nominal plant as an input and then generate a perturbed plant. Once created, this perturbed plant can be evaluated if it belongs to the set of controllable plants for a desired controller. This process will be repeated several times to generate enough plants to approximate the set of controllable plants.
These generated plants can be used to verify robustness of controller implementations. A model of a controller can use robust control theory to establish the set of controllable plants, but an actual implementation of a controller can not be verified as robust in the same way. Instead, it must be verified experimentally using elements of the set. Extracting elements of the set is not a trivial task, but if this research is successful, a generative model can reduce the effort required to create perturbed plants.