State variable model of continuous dynamic systems:
Converting higher order linear differential equations into state variable form. Obtaining SV model from
transfer functions. Obtaining characteristic equation and transfer functions from SV model. Obtaining SV
equations directly for R-L-C and spring-mass-dashpot systems.
Concept and properties associated with state equations. Linear Transformations on state variables.
Canonical forms of SV equations. Companion forms. Solutions of state equations, state transition matrix,
properties of state transition matrix.
Controllability and observability. Linear State variable feedback controller, the pole allocation problems.
Linear system design by state variable feedback.
Analysis of discrete time (sampled data) systems using Z-transform:
Difference Equations. Inverse Z transform. Stability and damping in z-domain.
Practical sampled data systems and computer control. Practical and theoretical samplers. Sampling as
Impulse modulation. Sampled spectra and aliasing. Anti-aliasing filters. Zero order hold. Approximation of
discrete (Z-domain) controllers with ZOH by Tustin transform and other methods. State variable analysis of
sampled data system. Digital compensator design using frequency response.
Introduction to non-linear systems:
Block diagram and state variable representations. Characteristics of common nonlinearities.
Phase plane analysis of linear and non-linear second order systems. Methods of obtaining phase plane
trajectories by graphical method – isoclines method. Qualitative analysis of simple control systems by
phase plane methods.
Describing Function method. Limit cycles in non-linear systems. Prediction of limit cycles using describing
function.
Stability concepts for nonlinear systems. BIBO vs. State stability. Lyapunov’s definition. Asymptotic
stability, Global asymptotic stability. The first and second methods of Lyapunov methods to analyse nonlinear
systems.
Text Books
1. Gopal M : Digital Control and State Variable Methods, 2e, – TMH
2. Roy Choudhuri, D., Control System Engineering, PHI
3. Nagrath I J & Gopal M : Control Systems Engg. - New Age International
4. Anand,D.K, Zmood, R.B., Introduction to Control Systems 3e, (Butterworth-Heinemann )Asian
Books
Reference Books
1. Goodwin, Control System Design, Pearson Education
2. Bandyopadhyaya, Control Engg.Theory and Practice, PHI
3. Kuo B.C. : Digital Control System- Oxford University Press.
4. Houpis, C.H, Digital Control Systems, Mc Graw Hill International.
5. Ogata, K., Discrete Time Control Systems, Prentice Hall, 1995
6. Jury E.I. : Sampled Data Control System- John Wiley & Sons Inc.
7. Umez-Eronini, Eronini., System Dynamics and Control, Thomson
8. Dorf R.C. & Bishop R H : Modern Control System- Pearson Education.
9. Ramakalyan, Control Engineering, Vikas
10. Natarajan A/Reddy, Control Systems Engg., Scitech
11. Lyshevski, Control System Theory with Engineering Applications, Jaico
12. Gibson J E : Nonlinear Control System - McGraw Hill Book Co.