JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Control Systems

Course Objectives:

• To explain the concepts of basic and modern control system for the real time analysis and design of control systems.
• To explain the concepts of state variables analysis.
• To study and analyze non linear systems.
• To analyze the concept of stability for nonlinear systems and their categorization.
• To apply the comprehensive knowledge of optimal theory for Control Systems.

Course Outcomes

Upon completion of this course, students should be able to:

• Various terms of basic and modern control system for the real time analysis and design of control systems.
• To perform state variables analysis for any real time system.
• Apply the concept of optimal control to any system.
• Able to examine a system for its stability, controllability, and observability.
• Implement basic principles and techniques in designing linear control systems.
• Formulate and solve deterministic optimal control problems in terms of performance indices.
• Apply knowledge of control theory for practical implementations in engineering and network analysis.

UNIT - I

Mathematical Preliminaries and State Variable Analysis: Fields, Vectors and Vector Spaces – Linear combinations and Bases – Linear Transformations and Matrices – Scalar Product and Norms – Eigen values, Eigen Vectors and a Canonical form representation of Linear systems – The concept of state – State space model of Dynamic systems – Time invariance and Linearity – Non uniqueness of state model – State diagrams for Continuous-Time State models - Existence and Uniqueness of Solutions to Continuous-Time State Equations – Solutions of Linear Time Invariant Continuous-Time State Equations – State transition matrix and it’s properties. Complete solution of state space model due to zero input and due to zero state.

UNIT - II

Controllability and Observability: General concept of controllability – Controllability tests, different state transformations such as diagnolization, Jordon canonical forms and Controllability canonical forms for Continuous-Time Invariant Systems – General concept of Observability – Observability tests for Continuous-Time Invariant Systems – Observability of different State transformation forms.

UNIT - III

State Feedback Controllers and Observers: State feedback controller design through Pole Assignment, using Ackkermans formula– State observers: Full order and Reduced order observers.

UNIT - IV

Non-Linear Systems: Introduction – Non Linear Systems - Types of Non-Linearities – Saturation – Dead-Zone - Backlash – Jump Phenomenon etc; Linearization of nonlinear systems, Singular Points and its types– Describing function–describing function of different types of nonlinear elements, – Stability analysis of Non-Linear systems through describing functions. Introduction to phase-plane

analysis, Method of Isoclines for Constructing Trajectories, Stability analysis of nonlinear systems based on phase-plane method.

UNIT - V

Stability Analysis: Stability in the sense of Lyapunov, Lyapunov’s stability, and Lypanov’s instability theorems - Stability Analysis of the Linear continuous time invariant systems by Lyapunov second method – Generation of Lyapunov functions – Variable gradient method – Krasooviski’s method.

TEXT BOOKS:

• 1. M. Gopal, Modern Control System Theory by – New Age International - 1984
• 2. Ogata. K, Modern Control Engineering by– Prentice Hall - 1997
• 3. N K Sinha, Control Systems– New Age International – 3rd edition.

REFERENCES:

• 1. Donald E. Kirk, Optimal Control Theory an Introduction, Prentice - Hall Network series - First edition.