Reduced-order models are good for designing control systems because there are fewer parameters to explore for different algorithms. Higher-order systems have closed-loop responses that are similar to first-order systems, and underdamped 2nd-order systems. This happens because there are poles and zeros that cancel out or nearly cancel out. Low-order systems can be considered equivalent systems to the higher-order models as specific poles and zeros dominate the response. For example in aircraft, the lower-order models have the same form plus a time delay to approximate the phase-lag of higher-order subsystems in the actual aircraft. The reduced order models for aircraft are matched using the frequency response rather than the time response. It is important to properly reduce the model dynamics as phase delays can drastically influence coupling behaviors. such as in the case of the PIO.
When determining the dominant vs insignificant poles, the cut-off distance should be 6-10 times the magnitude of the real part of the dominant pole.
Lumped Parameter Model
Gas Path Dynamics – 10x the frequency of the fastest dynamic should be modeled.
State-Space Estimators – should have eigenvalues that are 5-10 times faster than the controller eigenvalues.
Dominant Mode Approximation – how to convert the desired dominant pole into a 2nd order system
MIL-F-8785C – models must be reduced to 4th order
EQS – MATLAB toolbox used to reduce aircraft models (F14 FCS)
[[Reaction Wheel]] – dynamic friction torque can be eliminated as it is multiple orders of magnitude smaller than other variables.
[[Equivalent Systems Formulation]] – is a form of reduced-order model
Point Reactor Kinetics Model – Fick’s law allows for the model reduction of reactor kinetics
Fick’s Law – used to reduce the model order of reactor kinetics
[[Simplified Sailplane Model]] – used a reduced-order model
[[RASCAL Model – reduced order model (not time varying)
Disadvantages of Dynamic Inversion Controllers – low-order inverse model may not be able to cancel out higher-order aircraft behavior
[[Reduced Order Controller]]
[[C_star Flight Control Law]] – requires a reduced-order model
[[F-4C Simplified Longitudinal Model]] – linearized 3rd-order model
[[Advanced Actuation System]] – assumes that inner loop filter bandwidth is so much higher that the transfer function is 1.
[[Equivalent System Time Delay]] – is a type of reduced-order model
[[Turing Patterns]] – complicated patterns may behave like a 2-species model
[[VAAC FCL005 Model Reduction]] – reduced dynamics that were constant between operating points
Sources
- SimbusProductsUser
- drhamelAdvancesAerodynamicModeling2001
- zywnoDominantSystemDynamics
Backlinks
[[Effects on Root-Locus of Poles and Zeros]]
[[Equivalent Time Delay]]
[[First-Order Systems]]
[[Frequency Response]]
Phase Lag
Pilot-Induced Oscillations
[[Pole-Zero Cancellation]]
[[Second-Order Systems]]