EET401 ADVANCED CONTROL SYSTEMS

Course Code: EET 401

Course Name: Advanced Control Systems

Preamble: This course aims to provide a strong foundation on advanced control methods for
modelling, time domain analysis, and stability analysis of linear and nonlinear systems. The
course also includes the design of feedback controllers and observers.
Prerequisite: EET 305 Signals and Systems, EET 302 Linear Control Systems
Course Outcomes: After the completion of the course the student will be able to:
CO 1 Develop the state variable representation of physical systems
CO 2 Analyse the performance of linear and nonlinear systems using state variable
approach
CO 3 Design state feedback controller for a given system
CO 4 Explain the characteristics of nonlinear systems
CO 5 Apply the tools like describing function approach or phase plane approach for
assessing the performance of nonlinear systems
CO 6 Apply Lyapunov method for the stability analysis of physical systems

Syllabus
Module 1
State Space Representation of Systems (7 hours)
Introduction to state space and state model concepts- State equation of linear continuous time
systems, matrix representation- features- Examples of electrical circuits and dc servomotors.
Phase variable forms of state representation- Diagonal Canonical forms- Similarity
transformations to diagonal canonical form.
Module 2
State Space Analysis (9 hours)
State transition matrix- Properties of state transition matrix- Computation of state transition
matrix using Laplace transform and Cayley Hamilton method.
Derivation of transfer functions from state equations.
Solution of time invariant systems: Solution of time response of autonomous systems and
forced systems.
State space analysis of Discrete Time control systems: Phase variable form and Diagonal
canonical form representations- Pulse transfer function from state matrix- Computation of
State Transition Matrix (problems from 2nd order systems only).
Module 3
State Feedback Controller Design (6 hours)
Controllability & observability: Kalman’s, Gilbert’s and PBH tests.- Duality principle
State feedback controller design: State feed-back design via pole placement technique
State observers for LTI systems- types- Design of full order observer.
Module 4
Nonlinear Systems (7 hours)
Types and characteristics of nonlinear systems- Jump resonance, Limit cycles and Frequency
entrainment
Describing function method: Analysis through harmonic linearization- Determination of
describing function of nonlinearities.
Application of describing function for stability analysis of autonomous system with single
nonlinearity (relay, dead zone and saturation only).
Module 5
Phase Plane and Lyapunov Stability Analysis (8 hours)
Phase plots: Concepts- Singular points – Classification of singular points.
ELECTRICAL AND ELECTRONICS
Definition of stability- asymptotic stability and instability.
Construction of phase trajectories using Isocline method for linear and nonlinear systems.
Lyapunov stability analysis: Lyapunov function- Lyapunov methods to stability of nonlinear
systems- Lyapunov methods to LTI continuous time systems.
Text Books:
1. Nagarath I. J. and Gopal M., Control System Engineering, 5/e, New Age Publishers, 2007
2. Ogata K., Modern Control Engineering, 5/e, Prentice Hall of India, 2010.
3. Gopal M, Modern Control System Theory, 2/e, New Age Publishers, 1984
4. Kuo B.C, Analysis and Synthesis of Sampled Data Systems, Prentice Hall Publications,
2012.

References:
1. Khalil H. K, Nonlinear Systems, 3/e, Prentice Hall, 2002
2. Gibson J.E. Nonlinear Automatic Control, Mc Graw Hill, 1963.
3. Gopal M., Control Systems Principles and Design, 4/e, Tata McGraw Hill, 2012.
4. Slotine J. E and Weiping Li, Applied Nonlinear Control, Prentice-Hall, 1991,
5. Gopal M, Digital Control and State Variable Methods, 2/e, Tata McGraw Hill, 2003
6. Imthias Ahamed T. P, Control Systems, Phasor Books, 2016
7. Ogata K., Discrete Time Control Systems, 2/e, Pearson Education, Asia, 2015
8. Thomas Kailath, Linear Systems, Prentice-Hall, 1980