## Doctor of Philosophy (Electrical) under Faculty of Electrical & Computer Engineering

Linear estimation, Stochastic Gradient Algorithm, Mean Square performance, Transient Performance, Block Adaptive Filters, Least Square methods, Array algorithms, Fast RLS, Lattice Filters, and Robust Algorithms.

Speech recognition problem, Hidden Markov Models, Acoustic Models, Language modelling, Viterbi search, Hypothesis search, Elements of Information Theory, Decision Trees, Phonetics.

Review of discrete signals and systems in temporal and spectral domains acquisition, discrete transforms, digital filter design, spectral estimation, adaptive filtering, multi-rate signal processing, wavelets and joint time-frequency analysis.

Concept of Instantaneous Frequency, Generalization of Instantaneous frequency to non-stationary signals, Bandwidth Time Product, Relationship between IF and Joint TF distributions, Frequency Estimation for Stationary Signals, Review of IF Estimation techniques, Statistical/Computational Comparison of different IF Estimation Methods, Applications.

Fault Analysis, Fault Detection, Objectives of Power System Protection, Bus configurations, Zones of protection, Difference between Measuring CT and Protection CT, CT accuracy calculations, ratio correction factor (RCF) , Polarization, Directional relays, intro to Distance/Impedance relaying, differential protection, Connection of Differential Relay to delta-wye transformer, phase shift, Intro to Cap Bank Protection Applications; Cap Bank Wrap-up; Synchronous Switching , Generator Protection Basics - Volts/Hz; Smart Grid overview, SCADA, Wide Area Monitoring (WAM) and Control, Synchro-phasor Technology and its comparison with SCADA, IEEE C37.118, New trends in Power System Monitoring, Control and Protection, History of Blackouts and its phenomenon, How to avoid blackouts, Practical System stability aspects, Voltage Stability, Angle Stability, Instability avoidance techniques / opportunities using Synchro-phasor Technology **(Software’s to be used: MATLAB, ETAP).**

Power System Modeling, Introduction to power system stability problem, Small Signal Stability,

Fundamentals concepts of stability of dynamic systems, Eigen properties of state matrix, Small Signal Stability of single machine infinite bus system, Power System Stabilizer, Transient Stability, Performance of protective relaying, Voltage Stability, Basic concept related to voltage stability, Voltage collapse, Voltage stability analysis, Prevention of Voltage Collapse.

Supervised learning, Linear regression with single and multiple variables, Logistic Regression, Neural Networks and back propagation algorithm, Support Vector Machines, Unsupervised learning, K-means, Generative learning approaches, Convex optimization, Hidden Markov Models, Gaussian Mixture Models, EM-algorithm, Forward-backward algorithm, Viterbi decoding, Principal component Analysis, Independent component Analysis.

**Introduction:** Mathematical Modelling of Robots, Rigid Motions and Homogeneous Transformations,Forward Kinematics, The Denavit-Hartenberg Convention Inverse Kinematics, Velocity Kinematics- The Jacobian, Path and Trajectory Planning, Independent Joint Control, Dynamics, Stability Theorem, Multivariable Control, Force Control.**Computer Vision:** The Geometry of Image Formation, Camera Calibration, Segmentation by Thresholding, Position and Orientation.**Vision-Based Control:** Design Considerations, Camera Motion and the Interaction Matrix

Image-based Control Laws, End Effector and Camera Motions.

Neural Networks and Deep Learning Introduction to deep learning, Neural networks review, Shallow neural networks, Deep neural networks.

Improving Deep neural networks Hyper-parameter tuning, Regularization and Optimization, Practical Aspects of Deep Learning, Optimization Algorithms, Hyper-parameter tuning, Batch Normalization, & Programming Frameworks.

Structuring Machine Learning Projects ML Strategies, Convolutional Neural Networks, foundations of convolutional neural networks.

Deep Convolutional models Case Studies, Object Detection, Special Applications: Face Detection and neural style transfer.

Sequence Models Recurrent Neural networks, LSTMS, GRUs, Applications of Sequence Models in Speech Recognition & Synthesis.

Linear Models with Examples, Discrete-Time Systems (DTS) and z-Transform, Solution of Difference Equation, The Inverse z-Transform, State Variables Models and Solution, Sampling and Reconstruction, Sampled-Data Control Systems with ADC & DAC, Open/Closed Loop DTS, The Ideal Sampler, Starred Transform, Data Reconstruction, System Time-Response Characteristics, Pulse Transfer Function, Mapping of planes, Discrete Equivalents; Forward, Backward, Trapezoid Rule etc.

Advanced Design, Analysis and Stability Techniques, Pole Assignment, Controllability, Observability State Estimation, Stability Analysis Techniques, Linear Quadratic Optimal Control, Optimal State Estimation – Kalman Filters etc., Stability, Bilinear Transformation, Routh-Hurwitz Criterion & Jury’s Stability Test, Digital Controller Design, Lag, Lead, Leg-Lead Compensation, PID Controller Design, Design by Root Locus / Bode Plot, Microcontroller implementation of Digital Designs, Case Studies, Other Advanced Design.

Production and Classification of speech sounds, Acoustics of Speech Production, pole-zero speech models, Homomorphic filtering, STFT analysis and Synthesis, Filter bank analysis and synthesis, Pitch estimation, Non-linear measurement and modelling techniques.

Efficiency, Analysis and order, Divide and Conquer approach, Dynamic Programming, Greedy Approach, Back tracking, Branch and Bound, sorting problem, Searching problem: lower bounds, cost analysis.

Introduction and Historical Perspective, Distributions and their computing methods, Unified Approach, Wigner Distribution, Discrete Wigner Distribution, Smoother Distributions, Spectrogram and Ambiguity Function, TF Filtering and Synthesis, Instantaneous Frequency and Uncertainty Principle.

Three-Phase network analysis, Per-phase, Per-unit, Transformer basics. LTC, Transformer Connections, Transformers, paralleling, etc , Synchronous Machines. Synchronous Machines a-b-c -- d-q-0 analysis methods, Synch Machines recap: Over- vs. Under-excited, control via Ea and δ, Capability Curves, Transmission Line, Overhead Conductors, Overview of RLC effects, pi-equivalent, etc, Self-Inductance & Mutual Inductance recap, Transmission Lines as a two-port network, ABCD parameters, etc. shunt and series compensation, Ferranti Rise, Voltage Regulation, Transmission Line Performance Issues. Short-, medium-, and long-line models, Zc, propagation constants, Fault Calculation, X/R Ratio, Circuit Breaker Ratings, Practical Y|LS|bus|RS| and Z|LS|bus|RS| methods for SC calculation, Intro to Load-flow, Remedial actions for planning study, Contingencies, Security, System Stability, Swing Equation, Out-of-Step **(Software’s to be used: MATLAB, ATP, ETAP).**

Fundamental notions about Electrical Transients: Introduction, Circuit Parameters, Laplace Transforms and Simple switching transients, Circuit closing Transient, Impulsive transients, Oscillatory transients, Causes of transients, Circuit opening transients, Factors affecting TRC, Types of system grounding, Effect of load on TRV, Effect of fault location on TRV, Recovery transient initiated by removal of short circuit, Double frequency transients, Damping: RLC circuits, Series RLC circuit, Abnormal switching transients, Transients in three phase circuits, Travelling waves on Transmission lines **Software to be used (ETAP)**

**Transmission System Planning:** Introduction, Present Transmission-System-Planning Techniques, Models Used in Transmission System Planning, Transmission Route Identification and Selection, Transmission System Expansion Planning, Transmission System Planning in the Future.**Steady-State Performance of Transmission Lines:** Introduction, Complex Power in Balanced Transmission Lines, Constant-Impedance Representation of Loads, Factors Affecting Line Design, Transmission Line Constants, Inductance and Inductive Reactance, Capacitance and Capacitive Reactance, Equivalent Circuits for Transmission Lines, General Circuit Constants, Effect of Ground on Capacitance of Three-Phase Lines, Environmental Effects of Overhead Transmission Lines.**Transmission System Reliability: **Basic Definitions, Basic Probability Theory, Combinational Analysis, Probability Distributions, Basic Reliability Concepts, Systems with Repairable Components, Reliability Evaluation of Complex Systems, Markov Processes, Reliability Evaluation of Complex Systems, Markov Processes, Transmission System Reliability Methods.**Transient over-voltages and Insulation Coordination:** Introduction, Traveling Waves, Effects of Line Terminations, Junction of Two Lines, Junction of several Lines, Termination in Capacitance and Inductance, Bewley Lattice Diagram, Surge Attenuation and Distortion, Traveling Waves on Three-Phase Lines, Lightning and Lightning Surges, Switching and Switching Surges, Overvoltage Protection, Insulation Coordination.**Limiting Factors for Extra-High and Ultrahigh-Voltage Transmission:** Corona, Radio Noise, And Audible Noise Introduction, Corona, Radio Noise, Audible Noise, Conductor Size Selection. SAG and Tension Analysis Introduction, Effect of Change in Temperature, Line Sag and Tension Calculations.**Modelling and Performance Analysis of Transmission Lines Using Software’s:** Identification of important parameters of Transmission line on modelling, Simulation of Power transmission lines on different loadings, Simulation of Power flows on lines and interpretation of results, Simulation of typical problems of transmission lines and their solutions, Simulation of the transmission line termination effects.

Introduction, Matrices, Vectors, Inverse Matrix, Linear Vector Spaces, State Space Models and Solutions, Characteristic Value Problem, Definite Forms, Coordinate Transform, Maxima and minima, Lagrange Multiplier, Variation of Dynamic Systems, Variation of Deformable Bodies, Rayleigh-Ritz Method, Complex Functions, Mapping by Elementary Functions, Conformal Mapping, Application of Conformal Mapping, Statistical Estimation and Hypothetical Testing, Regression and Correlation, Analysis of Variance, Statistics and Sampling Distributions.

Review of Feedback Control Systems (FCS) Mathematical Modeling of Physical Systems, State space Models, Time Domain Specifications, Stability of FCS, SISO Control Design and Analysis via (Root Locus, Bode Plots, Nyquist Plots, Polar Plots) PID Controllers Design and Analysis via Emperical Tunning, Ziegler-Nichols (Z-N) Oscillation Method, Lead-Leg Compensators. Controllability and Stabilizability. Observability and Detectability. Pole-zero Cancellation and System Trade-offs in State Feedback and Observers. Frequency Domain Design Limitations. Control Design Based on Optimization. Parametric Sensitivity and Sensitivity Functions. Poisson and Bode’s Integral Constraints on Sensitivity. Feedforward Control, Cascade Control, Robust Control and applications. MIMO Control Essentials Model Based Controls and Quadratic Cost Functions Advanced Control Techniques such as Nonlinear control, Sliding Mode Control, and Predictive Control Design Case Studies.

Numerical methods for solving linear and non-linear equations, LU factorization, Sparse matrix techniques, Advanced power flow solutions using Newton-Raphson and fast decoupled methods, Continuation power flow, Three-phase power flow, Power system state estimation, Numerical integration and its application to power system transient stability, Eigenvalue analysis and its application to voltage stability.

Nonlinear Models and Nonlinear Phenomena with Examples, Common Nonlinearities, Second-Order Systems, Qualitative Behavior of Linear Systems, Multiple Equilibria, Qualitative Behavior Near Equilibrium Points, Limit Cycles, Numerical Construction of Phase Portraits, Existence of Periodic Orbits & Bifurcation.

Fundamental Properties, Existence and Uniqueness, Continuous Dependence on Initial Conditions and Parameters, Differentiability of Solutions and Sensitivity Equations, Comparison Principle, Lyapunov Stability, Autonomous Systems & Nonautonomous Systems, The Invariance Principle, Linear Systems and Linearization, Input-to-State Stability.

Advanced Nonlinear Control, Input-Output Stability, L Stability, State models, L2 Gains, Small Gain Theorem, Passivity, Advanced Stability Analysis, Stability of Perturbed Systems, Case Studies and more.