State Function and Lyapunov Functions:
Review of the concept of stability and state variable representation,
Stability by the direct method of Lyapunov, Its advantage over classical methods; Lyapunov stability theorems,
Generation of Lyapunov functions for autonomous linear systems, Estimation of settling time using Lyapunov
functions, Examples,
Sampled Data Control System:
Advantage and Disadvantage of Digital Control:
The Z Transform, The Residue Method, Inverse Z Transforms
Block Diagram Algebra for Discrete Data System, Limitations of the Z-Transformation Method, Frequency
Domain Analysis of Sampling Process, Data Reconstruction
Zero Order Hold, Discrete State Equation, The Solution of Discrete State Equations, the Recursive Method,
Stability of Discrete Linear Systems
Jury’s Stability Test, Steady State Error for Discrete Systems
State Feedback Design for Discrete Systems, Predictor Estimator.
Fuzzy Logic for Control systems :
The Concept of Fuzzy Logic and Relevance of Fuzzy Control , Advantages of Fuzzy Controller Potential Areas
of Fuzzy Control, Benefits of Fuzzy Logic and Fuzzy Logic Based Control System, Fuzzy Sets and
Membership
Basic Definitions of Fuzzy Sets and Terminologies, Set-Theoretic Operations on Fuzzy Sets, Fuzzy
Complement, Union and Intersection, T-Norm, T-Conorm, MF Formulation and Parameterization, MF’s of
One Dimension,
From Numerical Variables to Linguistic Variables , Term Sets of Linguistic Variables
Classical Relations and Fuzzy Relations, Cartesian Product, Relations: Crisp
and Fuzzy, Extension Principle, Modus Ponens, Modus Tollens, Hypothetical Syllogism:
Interpretations of Fuzzy If-Then Rules, Basic Principles of Approximate Reasoning
Representation of a Set of Rules, Approximate Reasoning with Multiple Conditional Rules.
Fuzzy Logic-Based Control:
The Structure of Fuzzy Logic-Based Controller, Knowledge Base
Rule Base, Contents of Antecedent and Consequent of Rules
Derivation of Production Rules, Cardinality of a Term Set, Inference Engine, Special Cases of Fuzzy
Singleton, Reasoning Types
Fuzzification Module, Fuzzifier and Fuzzy Singleton, Center of Area Defuzzifier, Center Average
Defuzzifier,Examples of Fuzzy Control System Design : Inverted Pendulum
Design of Fuzzy Logic Controller in SIMULINK and MATLAB Environment
Iterative Design Procedure of a PID Controller in MATLAB Environment
Simulation of System Dynamics in SIMULINK for PID Controller Design
Simulation of System Dynamics in SIMULINK for Fuzzy Logic Controller Design
Optimal Control:
Introduction to Optimal Control Problem:
Performance Index ;Calculus of Variations, Functions and Functionals
The Fundamental theorem of the Calculus of Variations, Extrema of Functionals of a Single Function and n
Functions, Euler Equation
Optimal Control Problem, Pontryagin’s Minimum Principle
The LQ Problem, the Hamilton-Jacobi Approach
The Matrix Riccati Equation, Finite Control Horizon
Linear Regulator Design (Infinite-Time Problem ), Optimal Controller for Discrete System, Linear Digital
Regulator Design (Infinite-Time Problem)