JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Control Systems

Course Objectives:

• To provide a basic knowledge of the theoretical foundations of optimal control
• To develop skills needed to design controllers using available optimal control theory and software
• To implement optimization methods for optimal control.

Course Outcomes

After the completion of this course, the student will be able to

• Understand the design and implement system identification experiments
• Apply input-output experimental data for identification of mathematical dynamical models.
• Apply singular value techniques to analyze the robustness of control systems.
• Incorporate frequency-domain-based specifications into multivariable control system designs.
• Apply H-infinity methods to design controllers

UNIT - I

Static optimization: An overview of optimization problem - concepts and terms related to optimization - constrained and unconstrained problems and their solutions using different techniques; such as Gradient method, steepest and decent method, conjugate gradient method and Newton’s method

UNIT - II

Convex optimization: Convex set and convex function - convex optimization problem - quadratic optimization problem - Karush - Kuhn - Tucker (KKT) necessary and sufficient conditions for quadratic optimization problem.

UNIT - III

Primal and dual optimization problem: Interior point method for convex optimization - linear programming - primal and dual problems and basic concept of multi– objective optimization problem.

UNIT - IV

Dynamic Optimization: Concept of functional, different types of performance indices, Calculus of variation to optimal control problem - Fundamental concepts of functional involving a single and multiple independent functions, necessary and sufficient conditions for optimal solution of problem

UNIT - V

Formulation of optimal regulator control problem: State the linear quadratic regulator problem and derive the solution of optimal regulator control problem; remarks on weighting matrices, solution of Riccati equation by iterative method and eigen-value and eigen vector methods.

TEXT BOOKS:

• 1. Jasbir S. Arora, Introduction to optimum design, Elesevier, 2005.
• 2. D.S. Naidu, Optimal control systems, CRC Press, First edition, 2002.
• 3. Ravindran, K. M. Ragsdell, and G. V. Reklaitis, Engineering optimization: Methods and applications, Wiley India Edition.

REFERENCES:

• 1. Donald E. Kirk, Optimal Control Theory an Introduction, Prentice - Hall Network series - First edition, 1970.
• 2. Arturo Locatelli, Optimal control: An Introduction, Birkhauser Verlag, 2001.
• 3. S. H. Zak, Systems and Control, Indian Edition, Oxford University, 2003.
• 4. Niclas Anreasson, Anton Evgrafov and Michael Patriksson, An introduction to continuous optimization, Overseas Press (India) Pvt. Ltd. M. Tech – I Year – II Sem. (Control Engg. / Control Sys.)