ADVANCED CONTROL SYSTEMS (18EE734)

ADVANCED CONTROL SYSTEMS

Course Code 18EE734
CIE Marks 40
Teaching Hours/Week (L: T:P) (3:0:0)
SEE Marks 60
Credits 03
Exam Hours 03

Course objectives:

• To introduce a state variable approach for linear time-invariant systems in both the continuous and discrete-time systems.
• To explain the development of state models for linear continuous-time and discrete-time systems.
• To explain the application of vector and matrix algebra to find the solution of state equations for linear continuous-time and discrete-time systems.
• To define controllability and observability of a system and testing techniques for controllability and observability of a given system.
• To explain design techniques of pole assignment and state observer using state feedback.
• To explain inherent and intentional nonlinearities that can occur in the control system and develop the describing function for the nonlinearities.
• To explain stability analysis of nonlinear systems using describing function analysis.
• To explain the analysis of nonlinear systems using Lyapunov function and design of Lyapunov function for stable systems.

Module-1

State Variable Analysis and Design: Introduction, Concept of State, State Variables and State Model,
State Models for Linear Continuous–Time Systems, State Variables and Linear Discrete– Time Systems.

Module-2

State Variable Analysis and Design (continued): Diagonalization, Solution of State Equations, Concepts
of Controllability and Observability.

Module-3

Pole Placement Design and State Observers: Introduction, Stability Improvements by State Feedback,
Necessary and Sufficient Conditions for Arbitrary Pole Placement, State Regulator Design, Design of State Observer, Compensator Design by the Separation Principle.

Module-4

Non-linear systems Analysis: Introduction, Common Nonlinear System Behaviours, Common
Nonlinearities in Control Systems, Fundamentals, Describing Functions of Common Nonlinearities,
Stability Analysis by Describing Function Method, Concept of Phase Plane Analysis, Construction
of Phase Portraits, System Analysis on the Phase Plane.

Module-5

Non-linear systems Analysis (continued): Simple Variable Structure Systems, Lyapunov Stability
Definitions, Lyapunov Stability Theorems, Lyapunov Functions for Nonlinear Systems.

Course Outcomes: At the end of the course the student will be able to:

• Discuss state variable approach for linear time-invariant systems in both the continuous and discrete-time systems.
• Develop of state models for linear continuous-time and discrete-time systems.
• Apply vector and matrix algebra to find the solution of state equations for linear continuous–
time and discrete-time systems.
• Define controllability and observability of a system and test for controllability and observability
of a given system.
• Design pole assignment and state observer using state feedback.
• Develop the describing function for the nonlinearity present to assess the stability of the system.
• Develop Lyapunov function for the stability analysis of nonlinear systems.

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub-questions) from each module.
• Each full question will have sub- questions covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

Textbooks

1 Control Systems Engineering (For the Modules1 and 2) I.J. Nagarathand M.Gopal NewAge 5th Edition,2007
2 Digital Control and State Variable Methods: Conventional and Intelligent Control Systems M.Gopal McGraw-Hill 3rd Edition,2008
3 Modern Control Theory R. V. Parvatikar Prism Books Pvt. Ltd. 1st Edition,2014