Control System Modeling Basic elements of control system - Open loop and closed loop systems - Differential equation - Transfer function, Modeling of electric systems, Translational and rotational mechanical systems - Block diagram reduction techniques - Signal flow graph. Time Response Analysis Time response analysis - First order systems - Impulse and step response analysis of second order systems - Steady state errors - P, PI, PD and PID compensation, Analysis using MATLAB. Frequency Response Analysis Frequency response - Bode plot, Polar plot, Nyquist plot - Frequency domain specifications from the plots - Constant M and N circles - Nichol's chart - Use of Nichol's chart in control system analysis. Series, Parallel, Series-parallel compensators - Lead, Lag, and lead lag compensators, Analysis using MATLAB. Stability Analysis Stability, Routh-Hurwitz criterion, Root locus technique, Construction of root locus, Stability, Dominant poles, Application of root locus diagram - Nyquist stability criterion - Relative stability, Analysis using MATLAB. State Variable Analysis and Digital Control Systems State space representation of continuous time systems - State equations - Transfer function from state variable representation - Solutions of the state equations - Concepts of controllability and observability - State space representation for discrete time systems. Sampled data control systems - Sampling theorem - Sample and hold open loop and closed loop sampled data systems. s.