Advanced Automatic Control
- Introduction and General Definitions
- Vector spaces, representations, and key properties of linear transformations
- Jordan form and matrix computations
- Inner Product Spaces and Normed Spaces
- Study of linear spaces with inner product structure
- Implications of this structure on the space and its transformations
- Exploration of normed spaces
- System Properties and State-Space Modeling
- Review of system characteristics such as linearity, time-invariance, causality, etc.
- Mathematical description of dynamic systems
- State-space realization using Lagrange and Hamilton equations
- Linearization techniques
- Use of simulation diagrams to describe state-space of linear time-invariant systems
- Presentation of various canonical forms
- Solving State Equations and Modal Analysis
- Solutions for time-varying and time-invariant linear systems
- Methods for computing the state transition matrix and analyzing its properties
- Dynamic modes and modal decomposition
- Input-output description using Markov parameters
- Equivalent realizations under coordinate transformations
- Augmented equations and periodic systems
- Structural Properties and Controllability/Observability
- Structural analysis of linear systems in ballistic and servomechanism control
- Concepts like reachability (controllability from origin), controllability to origin, and output controllability
- Observability and reconstructability of system states from output measurements
- Study of reachable and observable subspaces
- Canonical forms for controllable/uncontrollable and observable/unobservable systems
- Kalman and Ho canonical struc
- Feedback Control and Pole Placement
- Controllability as a structural feature in pole placement theorem
- State feedback and output feedback in single-input systems
- Various methods for computing state feedback gain
- Impact of feedback on system structure
- Stabilization problems and applications in servomechanisms
- Disturbance rejection and servo compensators
- Overview of state feedback in multi-input systems
- Smith and Smith-McMillan forms
- Observer Design
- Methods for designing state observers
- Full-order and reduced-order observers for time-varying and time-invariant systems
- Asymptotic observers and controllers based on the separation principle
- Stability Concepts
- Definitions and concepts of stability in linear systems
- Stability with zero and non-zero input
- Lyapunov stability analysis