Syllabus (Core courses) : M.Tech (Systems, Control and Automation)

EE 550 |
Linear Systems Theory |
3-0-0-6 |

Course Contents:

Maths Preliminaries: Vector Spaces, Change of Basis, Similarity Transforms, Introduction: Linearity, Differential equations, Transfer functions, State Space representations, Evolution of State trajectories Time Invariant and Time Variant Systems, Controller Canonical Form, Transformation to Controller Canonical form SI,MI, State Feedback Design SI, MI, Discrete time systems representation, reachability and state feedback design, Observability: Grammian, Lyapunov Equation, Output Energy, Observabilty matrix Observer canonical form (SO, MO), Unobservable subspace, Leunberger Observer (SO, MO), State Feedback with Leunberger Observers, Minimum order observers, Stabilizability and Detectability, Output feedback and Output Stabilizability, Disturbance Decoupling Problem

Text Books:

- S. Lang,
*Introduction to Linear Algebra*, Springer-Verlag, 2/e, 1997. - L. A. Zadeh and C. A. Desoer,
*Linear System Theory: The State Space Approach*, Springer-Verlag, 2008. - C.T. Chen,
*Linear System Theory and Design*, Oxford University Press, 3/e, 1999. - W. Rugh,
*Linear System Theory*, Prentice Hall, 2/e, 1995.

Reference:

- W. M. Wonham,
*Linear Multivariable Control, A Geometric approach*, Springer-Verlag, 1985

EE 551 |
Estimation and Identification |
3-0-0-6 |

Course Contents:

Estimation and identification – overview and preliminaries, Introduction to linear least squares estimation, Estimator properties – error bounds and convergence, Maximum likelihood estimation, Maximum a posteriori estimation, Linear mean squared estimation, Unmeasured disturbances and Kalman filter, Extended Kalman filter and Unscented Kalman filter for nonlinear systems, Frequency Response Identification – ETFE, ARX and ARMAX models for linear system identification, Recursive approaches for linear systems – RLS, ELS, RML, Introduction to nonlinear system identification – NARX, NRMAX models, Conditions on experimental data, Convergence properties of the identified model

Textbooks / References:

- S. M. Kay,
*Fundamentals of Statistical Signal Processing: Estimation Theory*, Prentice Hall, 1993 - R. L. Eubank,
*Kalman filter primer*, Chapman & Hall, 2006. - L. Ljung,
*System identification: theory for the user*,. 2E, Prentice Hall, 1999 - R. Pintelon and J. Schoukens,
*System identification: a frequency domain approach*, Wiley & Sons, 2012 - S. A. Billings,
*Nonlinear system identification: narmax methods in the time frequency and spatio temporal domains*, Wiley , 2013

EE 552 |
Applied Control Lab |
0-0-3-3 |

Course Contents:

1. DC Motor Speed Control: Using PLC to control the speed of DC Motor to understand the principles of feedback control, PWM and PLC programming. The objective is to study the following:

- Open loop speed control
- Close loop speed control
- Use of PLC for the speed control
- Acceleration and deceleration ramps programming in PLC
- To Monitor the duty cycle of the motor

2. AC Machine Control: The objective will be to study:

- Open loop speed control
- Close loop speed control
- Frequency converter and its control
- Acceleration and deceleration ramps programming in the controller
- PWM programming

3. Process Measurement and Control: The objective of this experiment is to understand:

- Industrial measurements
- The control systems used in industry
- The programming techniques of the controller to achieve specific purpose
- Process supervision through PC
- Various transducers and sensors used in the industry

EE 553 |
Optimal Control |
3-0-0-6 |

Course Contents:

Mathematical preliminaries, Static optimization, Calculus of variations, Solution of general continuous time optimal control problem, Continuous time Linear Quadratic Regulator design - Riccati equation, Optimal tracking problem, Free final time problems, Minimum time problem, Constrained input control and Pontryagin’s maximum principle, Bang-Bang control, Principle of optimality, Dynamic Programming, Discrete LQR using Dynamic Programming, Continuous control and Hamilton-Bellman-Jacobi Equation.

Textbooks / References:

- D. E. Kirk,
*Optimal Control Theory: An Introduction*, Prentice-Hall, 2004. - B.D.O. Anderson and J.B. Moore,
*Optimal Control: Linear Quadratic Methods*, Dover Publications, 2014. - F.L. Lewis, D. Vrabie and V.L. Syrmos,
*Optimal Control*, 3rd edition, Wiley & Sons, 2012

EE 554 |
Nonlinear Systems and Control |
3-0-0-6 |

Course Contents:

Introduction: state-space representation of dynamic al systems, phase-portraits of second order systems, types of equilibrium points: stable/unstable node, stable/unstable focus, saddle; Existence and uniqueness of solutions: Lipschitz continuity, Picard's iteration method, proof of existence and uniqueness theorem, continuous dependence of solutions on initial conditions; Features of nonlinear dynamical systems: multiple disjoint equilibrium points, limit cycles, Bendixson criterion, Poincare-Bendixson criterion; Linearization: linearization around an equilibrium point, validity of linearization: hyperbolic equilibrium points, linearization around a solution; Stability analysis: Lyapunov stability of autonomous systems, Lyapunov theorem of stability, converse theorems of Lyapunov theorem, construction of Lyapunov functions: Krasovskii method and variable gradient method, LaSalle invariance principle, region of attraction, input/output stability of non-autonomous systems, L-stability; Control of nonlinear systems: describing functions method, passivity theorem, small gain theorem, Kalman-Yakubovich-Popov lemma, Aizermann conjecture, circle/Popov criteria, methods of integral quadratic constraints and quadratic differential forms for designing stabilizing linear controllers, multiplier techniques.

Textbooks / References:

- H. K. Khalil,
*Nonlinear systems*, Prentice Hall, 3rd Edn., 2002. - M. Vidyasagar,
*Nonlinear systems analysis*, 2nd Edn., Society of Industrial and Applied Mathematics, 2002. - H. Marquez,
*Nonlinear Control Systems: Analysis and Design*, Wiley, 2003. - A. Isidori,
*Nonlinear Control Systems*, Springer, 3rd Edn., 1995. - F. Verhulst,
*Nonlinear Differential Equations and Dynamical Systems*, Springer, 1990.

EE 555 |
Automation Lab |
0-0-3-3 |

Course Contents:

DC motor characteristics, modeling using transfer function and state variable methods, position control of DC motor using PID controller, speed control of DC motor using pulse width modulation; Kinematic modeling and assembling of a differential drive automated wheeled robot, various sensors and their use in mobile robot localization and obstacle detection; Robot motion control and navigation.

EE 590 |
Linear Algebra and Optimization |
3-0-0-6 |

Course Contents:

Linear Algebra - vector spaces, linear independence, bases and dimension, linear maps and matrices, eigenvalues, invariant subspaces, inner products, norms, orthonormal bases, spectral theorem, isometries, polar and singular value decomposition, operators on real and complex vector spaces, characteristic polynomial, minimal polynomial; optimization - sequences and limits, derivative matrix, level sets and gradients, Taylor series; unconstrained optimization - necessary and sufficient conditions for optima, convex sets, convex functions, optima of convex functions, steepest descent, Newton and quasi Newton methods, conjugate direction methods; constrained optimization - linear and non-linear constraints, equality and inequality constraints, optimality conditions, constrained convex optimization, projected gradient methods, penalty methods.

Textbooks / References:

- S. Axler,
*Linear Algebra Done Right*, 2nd Edn., Springer, 1997. - E. K. P. Chong and S. H. Zak,
*An Introduction to Optimization*, 2nd Edn., Wiley India Pvt. Ltd., 2010. - G. Strang,
*Linear Algebra and Its Applications*, Nelson Engineering, 2007. - D. C. Lay,
*Linear Algebra and Its Applications*, 3rd Edition, Pearson, 2002. - D. G. Luenberger and Y. Ye,
*Linear and Nonlinear Programming*, 3rd Edn., Springer, 2010.