Courses Taught


Control Systems

Course Contents: Modeling of physical systems: time-domain, frequency-domain and state-variable models; Block Diagrams, Signal Flow Graphs; Time and frequency response of first and second order systems; Control system characteristics: stability, sensitivity, disturbance rejection and steady-state accuracy; Stability analysis: Routh-Hurwitz test, relative stability, root locus, Bode and Nyquist plots; Controller types: lag, lead, lag-lead, PID and variants of PID; Controller design based on root-locus and frequency response plots; Modern design techniques: canonical state-variable models, Equivalence between frequency and time-domain representations, diagonalization, controllability and observability; Pole placement by state feedback; State feedback with integral control; Observer and observer based state feedback control.


Advanced Control Systems

Course Contents: Frequency response design: Design of lag, lead, lag-lead and PID controllers, the Nyquist criterion, analysis and design, relative stability and the Bode diagram, closed-loop response, sensitivity, time delays; Root locus design: construction of root loci, phase-lead and phase-lag design, PID controller design; Modern design: controllability and observability, state feedback with integral control, reduced order observer; Optimal control design: Solution-time criterion, Control-area criterion, Performance indices, Zero steady state step error systems; Modern control performance index: Quadratic performance index, Ricatti equation; Digital controllers: Use of z-transform for closed loop transient response, stability analysis using bilinear transform and Jury method, deadbeat control, Digital control design using state feedback; On-line identification and control: On-line estimation of model and controller parameters.


Digital Control

Course Contents: Discrete-time system representations: modeling discrete-time systems by linear difference equations and pulse transfer functions, time responses of discrete systems; discrete state-space models, stability of discrete-time systems. Finite settling-time control design: deadbeat systems, inter sample behavior, time-domain approach to ripple-free controllers, limitations and extensions of the deadbeat controller. State-feedback design techniques: linear system properties, state feedback using Ackermann's formula, tracking of known reference inputs. Output-feedback design techniques: observer design , observer-based output feedback design.


Modeling and Simulation of Dynamical Systems

Course Contents: Review of ordinary differential equations. State space modeling of linear time invariant systems, Partial differential equations, State space modeling of time varying systems, Solution of state equations, matrix inversion, SVD, Difference equations, State space modeling of discrete time systems, Modeling of stochastic systems, Modeling examples of various practical systems. Simulation diagrams of state space models, Simulation of dynamic systems using MATLAB SIMULINK toolboxes.


Optimal and Adaptive Control

Course Contents: Basic mathematical concepts, Conditions for optimality, Calculus of variations, Pontryagin’s maximum principle, Hamilton Jacobi-Bellman theory, dynamic programming, structures and properties of optimal systems, various types of constraints, singular solutions, minimum time problems, optimal tracking control problem
Model reference adaptive control, gain scheduling, adaptive internal model control, adaptive variable structure control, adaptive back- stepping design, introduction to system identification, direct and indirect adaptive control.


Linear Systems Theory

Course Contents: Essentials of linear algebra: vector spaces, subspaces, singular value decomposition; state variable modeling of linear dynamical systems; transfer function matrices; Stability theory: Lyapunov theorems; controllability and observability; realization theory: balanced realization, Kalman canonical decomposition; linear state feedback and estimation. Introduction to linear robust control: model uncertainty, model reduction and co-prime factorization; robust stability and robust performance.