JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Control Systems

Course Objectives:

• To explain the concepts of basics 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 nonlinear systems.
• To analyze the concept of stability for nonlinear systems and their categorization.

Course Outcomes

After completion of the course, students will be able to:

• Know various terms of basic and modern control system for the real time analysis and design of control systems.
• Perform state variables analysis for any real time system.
• Examine a system for its stability, controllability and observability.
• Implement basic principles and techniques in designing linear control systems.
• 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 diagonalization, 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 to 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.

TEXTBOOKS:

• 1. M.Gopal, “Modern Control System Theory”, New Age International, 1984.
• 2. Ogata. K, “Modern Control Engineering”, Prentice Hall, 1997.

REFERENCES:

• 1. N K Sinha, “Control Systems”, New Age International, 3rd Edition.
• 2. Donald E.Kirk, “Optimal Control Theory an Introduction”, Prentice Hall Network series, 1stEdition. M. Tech – I Semester L T P C 3 0 0 3