JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Control Systems

Course Objectives:

• 1. To understand the fundamentals of digital control systems representations, z-transforms
• 2. To understand analysis of discrete complex domain: Z-Transforms
• 3. To understand the concepts of state variables analysis for discrete LTIV systems.
• 4. To understand the concepts of controllability and observability of discrete time systems
• 5. To get exposed the design aspects of controllers and for discrete time systems
• 6. To understand the concepts of the stability for discrete LTIV systems
• 7. To understand the design aspects of observers for discrete time systems.

Course Outcomes

At the end of this course, students will demonstrate the ability to

• 1. Obtain discrete representation of LTI systems.
• 2. Find the state space analysis of discrete time systems.
• 3. Test and analyze the controllability and observability for discrete time systems
• 4. Analyze stability of discrete time systems using various methods
• 5. Design and analyze digital controllers.
• 6. Design state feedback controllers and observers.

UNIT - I: REPRESENTATION OF DISCRETE TIME SYSTEMS

Basics of Digital Control Systems. Discrete representation of continuous systems. Sample and hold circuit. Mathematical Modeling of sample and hold circuit. Effects of Sampling and Quantization. Choice of sampling frequency. ZOH equivalent. Z-Transforms, Mapping from s-plane to z plane, Properties of Z-Transforms and Inverse Z Transforms. Pulse Transfer function: Pulse transfer function of closed loop systems. Solution of Discrete time systems. Time response of discrete time system, Steady State errors.

UNIT - II: DISCRETE TIME STATE SPACE ANALYSIS

State space representation of discrete time systems, Conversion of pulse transfer function to state space models and vice-versa, Solving discrete time state space equations, State Transition Matrix, Pulse Transfer Function Matrix. Discretization of continuous time state space equations. Concept of Controllability, stabilizability, observability, reachability – Controllability and observability tests. Effect of pole zero cancellation on the controllability & observability.

UNIT - III: STABILITY ANALYSIS OF DISCRETE TIME SYSTEM

Concept of stability in z-domain, Stability analysis discrete time system: by Jury test, using bilinear transformation. Stability Analysis of discrete time systems using Lyapunov methods.

UNIT - IV: DESIGN OF DIGITAL CONTROL SYSTEM BY CONVENTIONAL METHODS

Design and realization of digital PID Controller, Design of discrete time controllers with bilinear transformation, Design of digital control system with dead beat response, Practical issues with dead beat response design.

UNIT - V: DESIGN STATE FEEDBACK CONTROLLERS AND OBSERVERS

Design of discrete state feedback controllers through pole placement, Design of Discrete Observer for LTI System: Design of full order and reduced observers, Design of observer-based controllers.

TEXT BOOKS:

• 1. K. Ogata, “Digital Control Engineering”, Prentice Hall, Englewood Cliffs, 1995.
• 2. M. Gopal, “Digital Control Engineering”, Wiley Eastern, 1988.
• 3. V, I, George and C. P. Kurian, Digital Control Systems, CENGAGE Learning, 2012

REFERENCE BOOKS:

• 1. G. F. Franklin, J. D. Powell and M. L. Workman, “Digital Control of Dynamic Systems”, Addison-Wesley, 1998.
• 2. B.C. Kuo, “Digital Control System”, Holt, Rinehart and Winston, 1980. M.TECH.- I YEAR- II SEMESTER EMBEDDED SYSTEMS