JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Control Systems

Course Objectives:

• To understand the fundamentals of digital control systems, z-transforms
• To understand state space representation of the control systems, concepts of controllability and observability
• To study the estimation of stability in different domains
• To understand the design of discrete time control systems, compensators, state feedback controllers, state observers through various transformations

Course Outcomes

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

• Carry map S-plane and Z-plane, do state-space analysis
• Carry stability analysis in S-domain and Z-domains
• Carry stability analysis through bilinear transformation and R-H criteria,
• design of discrete-time control systems, design of lag, lead, lead-lag compensators, design of PID controllers and design of state feedback controllers and observers,
• Apply the above concepts to real-world electrical and electronics problems and applications.

UNIT - I

Introduction To Digital Control Systems And Z-Transforms: Introduction - Merits and Demerits of Digital Control Systems - Practical aspects of the choice of sampling rate and Multirate sampling - Basic discrete time signals - Quantization – Sampling Theorem - Data Conversions and Quantization - Sampling process - Mathematical Modeling - Data Reconstruction and Filtering of sampled signals - Zero - Order Hold (ZOH). z- Transform and Inverse z-Transform, Relationship between s - plane and z - plane - Difference equation - Solution by recursion and z-Transform - Pulse Transfer Functions of the ZOH and relationship between G(s) and G(z) - Bilinear Transformation.

UNIT - II

Input/output Analysis of Digital Control Systems: Pulse transfer function - z transform analysis of open loop, closed loop systems - Modified z Transform - transfer function - Stability of linear digital control systems - Stability tests – Jury Stability test. Root loci - Frequency domain analysis - Bode plots - Gain margin and phase margin.

UNIT - III

Design of Controllers For I/O Model Digital Control Systems: Cascade and Feedback Compensation by continuous data controllers - Digital controllers - Design using Bilinear

R16 B.TECH EEE.

Transformation - Realization of Digital PID controllers, Design of Digital Control Systems based on Root Locus Technique.

UNIT - IV

State Space Analysis and State Feedback Control Design of Digital Control Systems: State Equations of discrete data systems, solution of discrete state equations, State Transition Matrix: Computation methods for State Transition Matrix: z - transform method - Relation between State Equations and Pulse Transfer Functions. Concepts on Controllability and Observability - Pole placement design by state feedback.

UNIT - V

Digital State Observer and Stability Analysis: Design of the full order and reduced order state observer, Design of Dead beat Controller - some case studies - Stability analysis of discrete time systems based on Lyapunov approach.

TEXT BOOKS:

• 1. K. Ogata, Discrete Time Control Systems, PHI/Addison - Wesley Longman Pte. Ltd., India, Delhi, 1995.
• 2. B. C Kuo, Digital Control Systems, 2nd Edition, Oxford University Press, Inc., 1992.

REFERENCE BOOKS:

• 1. F. Franklin, J.D. Powell, and M.L. Workman, Digital control of Dynamic Systems, Addison - Wesley Longman, Inc., Menlo Park, CA , 1998.
• 2. M. Gopal, Digital Control and State Variable Methods, Tata McGraw Hill, India, 1997.
• 3. C. H. Houpis and G.B. Lamont, Digital Control Systems, McGraw Hill, 1985.
• 4. John S. Baey, Fundamentals of Linear State Space Systems, McGraw Hill, 1st edition 1999
• 5. Bernard Fried Land, Control System Design, McGraw Hill, 1st edition 1986.
• 6. Dorsay, Continuous and Discrete Control Systems, McGraw Hill, 2001. R16 B.TECH EEE.