State space Representation of Continuous Time Systems:
Introduction, concepts of state, consistency conditions, State space representation using physical variables, phase variables, canonical variables. Eigen values, Eigen vectors, state equations for dynamic systems, Nonuniqueness of state model, state diagrams- state diagrams for continuous time state models.
State Space Representation of Discrete Time Systems:
Digital control system, quantizing and quantization error, Data acquisition and conversion, Impulse sampling and data hold, pulse transfer function, State space representation of discrete time systems, State diagrams - state diagrams for discrete time state models.
Solution of State Equations:
Introduction, Existence and Uniqueness of solution to continuous time state equations, Solution of Linear time invariant continuous time state equations – Evaluation of matrix exponential, series evaluation, Evaluation using symmetry transformation, Evaluation using Cayley- Hamilton technique, Evaluation using Inverse Laplace transformation. Solution of Discrete time state equations – Z transform approach, Pulse transfer function matrix, Discretization of continuous time state space equations.
Controllability and Observability of Systems:
Introduction, General Concept of Controllability, General Concept of Observability, Controllability Tests For Continuous Time Systems – Time Invariant Case, Observability Tests For Continuous Time Systems – Time Invariant Case, Controllability and Observability of Discrete Time Systems – Time Invariant Case Controllability and Observability of State Model in Jordan Canonical Form. Loss of Controllability and Observability due to Sampling
Model Control:
Introduction, Controllable and Observable Companion Forms – Single Input /Single Output Systems, Effect of State feedback on Controllability and Observability, Pole Placement by State Feedback- Single Input Systems, Stabilizability, Full Oder Observer, Reduced Order Observer, Deadbeat Observer.