Unit 1 : Digital Control System Introduction, Configuration of the basic digital control system. Advantages and limitations of digital control; data conversion and quantization, Sampling and Reconstruction processes, Shannon's Sampling theorem, practical aspects of choice of sampling rate. Zero order hold (ZOH) and it's transfer function, Basic concepts and transfer function of first order hold. (Chapter - 1) Unit 2 : Z-Transform and Pulse-Transfer-Function Review of z-transform, Inverse z-transform, difference equations and solution using z transform method. Pulse transfer function and Z-transfer function, General procedure for obtaining Pulse-transfer-function, pulse transfer function of ZOH. (Chapter - 2) Unit 3 : Stability Analysis Sampled data closed loop systems, characteristic equation, causality and physical realizability of discrete data system, realization of digital controller by digital programming, direct digital programming, cascade digital programming, parallel digital programming. Mapping between S-plane and Z-plane, stability analysis of closed loop system in z-plane using Jury's test, Bilinear Transformation. (Chapter - 3) Unit 4 : Introduction to State Space Analysis Important definitions - state, state variable, state vector, state space, state equation, output equation. State space representation for electrical and mechanical system, order differential equation and transfer function. Conversion of transfer function to state model and vice versa. State model of armature control DC motor. (Chapter - 4) Unit 5 : Solution of State Equations Concept of diagonalization, eigen values, eigen vectors, diagonalization of system matrices with distinct and repeated eigen values, Vandermonde matrix. Solution of homogeneous and non-homogeneous state equation in standard form, state transition matrix, its properties, Evaluation of STM using Laplace transform method and infinite series method Cayley Hamilton theorem. (Chapter - 5) Unit 6 : Design of Control System using State Space Technique Concept of controllability and observability, controllability and observability Tests, condition for controllability and observability from the system matrices in Canonical form, Jordan canonical form, effect of pole zero cancellation on the controllability and observability of the system, duality property. Pole placement design by state variable feedback. Necessity of an observer, design of full order observer. (Chapter - 6)
