Modern Control
- 1-Introduction to modern control systems: Control system definition, Control system physical components, Control system conceptual components, Controller designing procedure, Advantages of state space representation over transfer function representation
- Introduction to linear algebra and matrix analysis: Vector space, Linear combination, Change of basis and coordinates in N-dimensional space, Linear transformation, Determinant, Eigenvalues and eigenvectors, Jordan canonical form, Matrix functions
- computing methods for state transition matrix (Laplace method, Caley-Hamilton method, Silvester method, Jordan form method), Similarity transformation, diagonal form, Block-diagonal form, System dynamic modes, Modal decomposition, solution of LTI system to exponential input
- State feedback: state feedback controller design in SISO systems, state feedback gain (Bass and Gura method, Ackerman method, Controllable canonical realization method, state feedback effect on controllability and observability, state feedback effect on system zeros, state feedback for uncontrollable systems, state feedback design for multivariable systems
- Controllability and observability: necessary and sufficient conditions for controllability, necessary and sufficient conditions for observability, Canonical Jordan form test method, Unstable pole-zero cancellation, Uncontrollable and unobservable systems decomposition, Kalman decomposition
- State estimator (State observer): full-order observer, Reduced-order observer, State feedback based controller with full-order observer, Separation property, Regulation and tracking, Tracking with disturbance rejection, State feedback based controller with reduced-order observer
- Linear systems representation: State space representation, system modelling based on physical principles, system modelling based on Lagrangian method, Linearization of Nonlinear differential equations, input-output representation of linear systems (transfer function, transmission zeros, transfer function poles), Linear system properties, Time-domain solution of LTI state equations
- Realization theory : Minimal Realization (definitions and conditions), Realization of SISO systems (Controllable canonical form, Observable canonical form, Jordan canonical realization, Parallel and serial realization), Realization of MIMO systems, Realization of MISO systems, Realization of SIMO systems
- Stability: Definitions (Lyapunov stability, Asymptotically stability, Global asymptotically stability, BIBO stability, Internal stability), stability in LTI systems, stability of Nonlinear systems ( linearization method, Lyapunov method)
- Linear Time-varying (LTV) systems: Fundamental matrix, State transition matrix, solution of LTV system, Equivalent LTV equations, Time-varying realization, internal stability for LTV systems