Control Challenges and Issues
Constrained Operation in Presence of Significant Uncertainty. The paramount challenge associated with controlling waveriders/gliders is maintaining robust
and reliable constrained angle-of-attack operation (for air-breathing propulsion efficiency) over a wide range of Mach numbers (e.g. Mach 4-15) and in the presence of significant
sources of uncertainty. Key sources of uncertainty include complex dynamic aero-thermo-elastic
effects associated with fundamental physical phenomena [22]-[27], [28]-[29], [30]-[32],
[43], [53] described below. These effects manifest themselves in a variety of ways which can
be visualized as shown in Figure 2.
 Figure 2: Aero-Thermo-Elastic Effects for a Variety
of Hypersonic Vehicles
- Shock Layer Uncertainty. Shock layer variability (which occurs for >Mach 3) results
in significant variations in the proximity of the shock wave with respect to the lower
surface. This significantly impacts “compression lift.” Compression lift is what gives
waveriders/gliders their unparalleled lift-to-drag characteristics. Shock layer variability
leads to highly uncertain aerodynamics [28]-[29]; i.e. lift-drag properties. L/D
variability is seen in Figure 2(a) with the ratio exhibiting a clear decreasing trend with
increasing Mach number. See how rigid body lateral modes change with increasing
Mach number in Figures 2(b), (c) - with the (stable) spiral mode moving closer to the origin (i.e. becoming slower) while one of the Dutch roll mode poles becomes more
unstable for large Mach numbers [30].
- Boundary Layer Uncertainty. Boundary-layer growth effects (proportional to temperature
and the square of the Mach number) can result in significant viscous interaction
effects [28]-[29] and drag increases.
- Chemically Reacting Flow. Thermal heating causes the air flowing over the vehicle to
react chemically (occurs when >Mach 7, 2000◦K). This leads to large changes in fluid
properties (e.g. density, viscosity, Reynolds number) and hence aerodynamic characteristics
(i.e. lift-drag properties). When very low density flow conditions prevail (e.g. sufficiently high altitudes/temperature), the classic continuous Euler-Navier-Stokes equations
break down because fluid particles are far apart (i.e. large Knudson number)
and kinetic gas theory is required for prediction [28]-[29]. As the Knudson number
increases, the drag coefficient CD can increase significantly. (One can therefore use
density and hence Knudson number information to obtain useful bounds on CD.)
- Thermo-Elastic. Thermal heating can also exacerbate aero-elastic coupling - reducing flexible and aero-servo-elastic mode frequencies by 20%-30% in some application [43],
[53]. Such a loss of rigidity generally places an upperbound on the achievable bandwidth
with a fixed structure control system (which lacks sufficient lead to compensate for the flexible mode lag). In short, if adequate (closed loop) stability robustness margins are
not present, aero-elastic instability can ensue (e.g. control reversal, control surface flutter, wing divergence). Figure 2(d) shows shows how flexible
body mode frequencies decrease upon hypersonic induced heating; (e) and (f) show that
the achievable disturbance attenuation bandwidth (see low frequency behavior) is lower
(as expected) for higher temperatures.
Complex aero-propulsion interactions will also contribute significantly to the above formidable control challenges.
Given the above, great effort will be spent to (approximately) model
key nonlinear aero-thermo-elastic-propulsion interactions
and characterize/bound associated uncertainty that will impact overall
control system performance, robustness, and reliability.
We now discuss our overall control approach.
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