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

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

• Obtain discrete representation of LTI systems.
• Analyze stability of open loop and closed loop discrete-time systems.
• Design and analyze digital controllers.
• Design state feedback and output feedback controllers.

UNIT - I

Discrete Representation Of Continuous 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.

UNIT - II

Discrete System Analysis: Z-Transform and Inverse Z Transform for analyzing discrete time systems. Pulse Transfer function. Pulse transfer function of closed loop systems. Mapping from s-plane to z plane. Solution of Discrete time systems. Time response of discrete time system. Stability of Discrete Time System: Stability analysis by Jury test. Stability analysis using bilinear transformation. Design of digital control system with dead beat response. Practical issues with dead beat response design.

UNIT - III

State Space Approach for Discrete Time Systems: State space models of discrete systems, State space analysis. Lyapunov Stability. Controllability, reach-ability, Reconstructibility and observability analysis. Effect of pole zero cancellation on the controllability & observability.

UNIT - IV

Design of Digital Control System: Design of Discrete PID Controller, Design of discrete state feedback controller. Design of set point tracker. Design of Discrete Observer for LTI System. Design of Discrete compensator.

UNIT - V

Discrete Output Feedback Control: Design of discrete output feedback control. Fast output sampling (FOS) and periodic output feedback controller design for discrete time systems.

TEXT BOOKS:

• 1. K. Ogata, “Digital Control Engineering”, Prentice Hall, Englewood Cliffs, 1995.
• 2. M. Gopal, “Digital Control Engineering”, Wiley Eastern, 1988.

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.