Work Plan

This is in addition to planned yearly project review/assessment trips to NASA. The team management structure can be visualized as shown in Figure 7.

Figure 7: Team Organization/Management Structure

• The PI will manage all technical and financial components of the project as well as regular meetings. An administrative assistant - provided by ASU - will handle trip logistics; e.g. yearly project review at NASA, summer visits to NASA by PI and research assistant. The PI will spend most of his time interacting with a PhD research assistant, guiding the development of modeling, analysis, and design tools - providing detailed templates throughout the project. In addition to attending relevant controls conferences each year, the PI may also attend relevant conferences addressing the modeling of hypersonic vehicles. In addition to exchanging information with relevant NASA personnel in a timely manner, and during summer trips to NASA, the PI will prepare yearly progress reports. The PI will ensure that all work and software is documented within these reports as well as in a comprehensive final document.

• A PhD research assistant will be responsible for developing relevant modeling, analysis, and design code using MATLAB, Simulink, toolboxes, Real-TimeWorkshop, C, etc.

• Dr. Ridgely and Professor Voulgaris will provide monthly feedback to the PI and his research assistant. Specific feedback will be provided by them on the relevant topics described within their letters of support. These individuals will also meet with the PI at relevant yearly controls conferences; e.g. American Control Conference (ACC), Conference on Guidance, Navigation and Control (GNC). They may also participate in planned trips to NASA.

• Advanced Control Methods NASA ARC researchers will assist the PI in developing tools that will directly contribute to the successful 2010 SOAREX mission. This will involve applying developed modeling, analysis, and design tools (see Figure 5) to data gathered from the 2008 SOAREX flight.

Tasks, Facilitators, Timeline, and Milestones

Table 1 provides a development schedule/ timeline listing tasks to be performed as well as relevant facilitators and important milestones.

Detailed work hours for each task are provided within Table 5.

Modeling: Aero-Thermo-Elastic-Propulsion

During Year 1, a large portion of the work effort will be spent on aero-thermo-elastic-propulsion modeling and uncertainty characterization for an X-43A/SOAREX like vehicle [22]-[32], [43], [53]. This will involve the following model components:

• Classic Rigid Body Aero-Elastic
  
  This will include classic modeling of nonlinear rigid body aerodynamics, lift-drag characteristics, aerocoefficients, actuators, basic propulsion, sensors, and elastic modes (see uncertain plant in Figure 3), over a wide range of flight conditions [213], [223]-[228]. Particular attention will be placed on servoelastic modeling.




• Aero-Thermal Effects
  
  This will involve capturing complex aero-thermal effects. Consequently, fundamental ideas from fluid mechanics, CFD, and kinetic gas theory must be brought together [28]-[29]. A major goal here is to understand the impact of Machinduced temperature effects on air properties (e.g. density, kinematic viscosity), air flow over the vehicle (e.g. Knudson and Reynolds numbers, approximate flow characteristics), lift, drag, center-of-pressure, and relevant aero coeffcients.




• Aero-Thermo-Elastic Effects
  
  This will involve capturing complex aero-elastic and thermo-elastic effects [43], [53]. Specifically, we seek to understand how Mach-induced heating influences elastic modes (e.g. servoelastic and flexible body modes). As discussed earlier, heating typically reduces (undamped natural) mode frequency and damping (see Figure 2) [53].




• Aero-Propulsion Effects
  
  This will involve developing a low fidelity model for a scramjet propulsion system to capture critical aero-propulsion interactions [11], [18], [21], [36]-[42]. A more complex model will be sought from parallel research efforts [4].



• Uncertainty Characterization
  
  Much of the first year will be spent on characterizing and quantifying uncertainty over a wide range of flight conditions to adequately preparefor the SOAREX 2010 flight and to permit maximum exploitation of 2008 SOAREX data for modeling, analysis, specification development, and design iteration purposes.

Analysis and Design Specifications

As described earlier, we will focus on worst-case analysis and determining fundamental performance limitations. The latter is achieved by exploiting LTI models, the so-called Youla-parameterization of all stabilizing controllers [158]- [160], [213]-[216], and convex optimization [218] as described within the seminal work [216]. Design specification will follow from this analysis. It is expected that 2008 SOAREX data will impact analysis and design specification development into Year 3.

Design

Design will begin in Year 1 with classical hierarchical sequential loop closing methods [223] (as used for the X-43A [6]-[7]). When this is combined with the above analysis, it will permit us to select design parameters associated with our more advanced methodologies; e.g. weighting matrices, frequency/parameter-dependent weighting matrices. Designs will be evaluated using a simulator developed by the team in collaboration with NASA researchers. This may include the use of an existing X-43A NASA simulator. It is expected that data from the planned 2008 SOAREX flight will significantly impact models, worst-case analysis, specifications, designs, and technical recommendations for the 2010 SOAREX flight.

Yearly Project Review, Milestones, 2010 SOAREX Mission

Yearly project reviews at NASA ARC, in addition to planned summer visits, will ensure that tasks are completed in a timely manner for the 2008 and 2010 SOAREX flights. Important project milestones include:

(1) Aero-elastic model with uncertainty characterization,

(2) Aero-thermo-elastic model with uncertainty characterization (Year 1),

(3) Aero-thermo-elastic-propulsion model with uncertainty characterization (Years 1-2) [22]-[27], [28]-[29], [30]-[32], [43], [53],

(4) Fundamental performance limitations and design specification over an X-43A/SOAREX like benchmark trajectory (Years 1-2),

(5) Control system designed via classical methods (Year 1) [6]-[7], [211], [220]-[223],

(6) Control system designed via quasi-LPV approach and constraint enforcement (Years 2-3) [43], [69]-[78], [187]-[199], [207]-[209],

(7) Control system designed via GPC (Years 2-3) [166]-[186],

(8) Detailed comparison of resulting control systems and methods using benchmark trajectory within simulator (Years 2-3),

(9) Analysis of 2008 SOAREX flight data to iterate on the above (Years 2-3),

(10) SOAREX 2010 aerocontrolled descent (Year 4 - post grant period).

Summary

In summary, we believe that the proposed technical approach, work plan, and planned collaboration with NASA ARC will significantly assist NASA in developing useful (interactive) modeling, analysis, and design tools so that we can maximally learn from 2008 SOAREX flight data and properly prepare for an enhanced (perhaps more aggressive) 2010 SOAREX mission [3]-[4].

The following tables show how time will be allocated to each task by the PI and the PhD RA. It should be noted that collarbaorator/constultant fees will be the cost of their travel to relevant project meetings. $6, 000 have been requested for this purpose.