Controls and Robotics
Qualifying Exam Syllabus
Foundations (510 and undergraduate math)
- Linear algebra
- Function spaces
- Operators
- Differential equations
- Signals, causality, sampling, etc.
- Transforms
- Vector calculus
- Proof methods
Frequency domain methods (447)
- Modeling in the frequency domain
- Transfer functions
- Stability
- Interconnected systems
- Performance measures
- Root locus
- Nyquist plots, Bode plots
- PID
- Sensitivity, robustness
- Noise, disturbances
State space methods (547, 548)
- Modeling with state space
- Linearization
- Similarity, diagonalization
- Controllability, Observability
- Full state feedback
- LQR, LQG
- Relationship state space andtransfer functions
Control system design (448)
- Digital implementation of SISO controllers
- Analog implementation of SISO controllers
- System identification
- Modeling
- DC motor modeling
- Sensors and sensor models
- Controller design / performance / cost
Robot kinematics and dynamics (543)
- Rigid body transformations
- Forward kinematics
- Inverse kinematics
- The Jacobians
- Mechanics and Newton's Laws
- Lagrange's method
- Robot arm dynamics
- Force feedback / wrenches
- Control methods for a robot arm
