Module I (14hours)
State-space analysis of systems – Concept of state-state space and state variables-advantages over transfer function approach-state equations for typical electrical, mechanical and electromechanical systemsrepresentation for linear time-varying and time-invariant systems- Phase variable and canonical formsdiagonalization- transfer function and state equations-matrix exponential- solution by state transition matrixtransfer function decomposition-Discrete-time state models-solution of discrete-time state equation-z transform decomposition.
Module II (10hours)
Design using conventional methods – Cascade compensation – PI, PD and PID control – lead and lag compensation using RC networks – design of lead, lag and lead-lag compensators using frequency response and root locus methods.
Module III (12 hours)
Non-linear systems – characteristics of non-linear systems – types of nonlinearities -phase plane analysis – construction –isocline method and delta method- singular points – classification of singular points. Describing function analysis – definition – describing functions of common non-linearities –ideal relay,dead zone, saturation, combined dead zone and saturation-relay with hysteresis- stability analysis using DF – amplitude and frequency of limit cycle using DF.
Module IV (16 hours)
Liapunov methods – Sign definiteness of a function, Sylvester’s criteria-stability in the sense of Liapunov – definition of stability, asymptotic stability and instability –Liapunov’s second method – Liapunov stability analysis of LTIV continuous time and discrete time systems. Controllability, observability and introduction to optimal control – concept and criteria for controllability and observability – state feed back – design via pole placement – formulation of the optimal control problem – performance measure – optimal control using second method of Liapunov – the quadratic regulator problem – solution of the reduced matrix Riccati equation

Reference books
1.Ogata K., Modern Control Engineering, Prentice Hall
2.Nagarath & Gopal, Control System Engineering, Wiley Eastern
3.Kuo B.C., Automatic Control Systems, Prentice Hall
4.Ogata K., Discrete-Time Control Systems, Prentice Hall
5.Donald E. Kirk, Optimal Control Theory, Prentice Hall