Chapter 4 Flashcards
What are the three problems encountered in System Theory?
- Simulation
- Control
- System Identification
What is system identification?
System identification is the determination, on the basis of observation of input and output, of a system within a specified class of systems to which the system under test is equivalent.
What are the must haves of data gathering for system identification?
- Minimum sampling rate given by Nyquist frequency (twice the frequency of interest)
- A signal-to-noise ratio of significantly higher than 1 (literature: 10:1)
- Time-tagging of measurement channels
What are the types of sensors / measurements for an Aircraft? (6)
- Basic Aircraft Sensors
- Inertial Sensors
- GNSS
- Air Data Sensors
- Control Surface Deflections
- Pilot Forces
What are three important inertial sensors?
- Accelerometers
- Gyroscopes
- Angular Accelerometers
What is the difference between integrating and non-integrating sensors?
Non-Integrating sensors measure rates,
Integrating sensors measure increments
Where should accelerometers be installed?
Near the center of gravity
What are the components of a mechanical accelerometer? How does it work?
- proof mass
- suspension for mass
- pickoff providing signal related to the acceleration
Measures acceleration by measuring deflection of proof mass from initial position while also accounting for gravitational force
What are the three main types of gyroscopes and what physical effect do they use?
- Spinning mass : Gyroscopic moment
- Optical Laser Ring (RLG) / Fiber Optic (FOG) : Sagnac
- Micro Electro Mechanical Sensor (MEMS) : vibratory
What are the advantages and disadvantages of spinning mass gyros?
Advantages:
- Wide performance range of 0.0001 to >100 degree /h
- Low noise
Disadvantages:
- High cost
- Long warmup
- Fragile
What are the advantages and disadvantages of RLG/FOG gyros?
Advantages:
- Rapid reaction and turn on <1s
- No moving parts
Disadvantages:
- Performance increases with size
- High Voltage device
- Temperature sensitive
What are the advantages and disadvantages of MEMS gyros?
Advantages:
- Small
- No moving parts
- Low cost
Disadvantages:
- Higher precision to be developed
- Limited performance range
- Bias stability
What are the Air Data systems and what info do they provide?
- Air data systems (ADS) provide calibrated measurements of atmospheric conditions and the aircraft’s aerodynamic state:
- Static Pressure, pressure altitude, rate of climb
- Total Pressure, dynamic pressure
- Mach Number, calibrated and equivalent air speed
- AOA
- Angle of sideslip
- True airspeed, air density, temperature
What are pitot static probes?
- Probes that measure total pressure at the stagnation point, static pressure in cavities. Are different from pitot probes as they also give differential pressure
How are pilot forces meausred?
Strain gauges on control rods
What are the three types of Sensor errors?
- Systematic Errors
- Random Errors
- Sensor Dynamics
What is hysteresis error?
Different output for increasing and decreasing input
What is Bias instability?
Random medium to long-term bias variation
What is dead band error?
Small area around null where input is not detected
What is resolution / quantization error?
Minimum measurable input/floating point representation
What is turn on bias?
Variation of scale factor and bias from day-to-day
What are the error sources for GNSS? (6)
- Ephemeris Range error:
Difference between true and broadcast satellite position - Atmospheric Range Error: Speed of signal affected by atmosphere
- Multipath range error:
Due to reflected signals from surfaces near receiver - Receiver Clock Error:
- Satellite clock error:
- Receiver Noise
What does the integration of errors produce?
Large deviations
What are some values used in linear regression and what do they mean? (7)
- Independent variables x: Influence the output
- Regressors: Functions of the independent variables included in the model
- Regressor matrix X: All regressors in one matrix
- Dependent variable y
- Measurements z: Observation of output including error
- Parameters \theta
- Error r
What is the problem statement and Solution of the least squares method?
For an over-determined system z=x\theta the number of parameters is less than the number of equations so there doesn’t exist a solution that satisfies all equations
We find an approximate solution that minimizes the Euclidian-Norm of the vector x\theta - z
What are the assumptions for ordinary least square?
- Model is linear in parameters
- Regressors are deterministic
- White zero mean measurement noise with constant variance
What are some measures of accuracy for ordinary least squares?
Parameter Covariance and Correlation Matrix
Noise Covariance and Fit Error
Coefficient of Determination
What are the sum of squares for ordinary least squares?
Measure deviation from Model
- Total sum of Square
- Regression Sum of Square
- Residual Sum of Square
What is the coefficient of determination?
Ratio of Explained info to total info
What are some properties of ordinary least square estimators?
- Unbiased
- Minimum Variance
- Consistent
- Maximum Likelihood
What is the residual?
Shows model deficiencies and departure from the underlying assumptions
What are tests of residual analysis?
- Whiteness Test
- Graphical Analysis
- Tests for Normality
What are four additional least square methods?
- Multidimensional
- Generalized
- Total
- Recursive
What are regressors?
Regressors are explanatory functions, built from the independent variables, in order to explain the dependent variable
