# Digital Controls System

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 Course Number: ENGRG 7340 Course Name: Digital Control Systems (Online) Course Description: Digital Controller Design in time and frequency domain. State space modeling, controllability, observability, stability, minimal realization, pole placement and observer design. P: A BS degree in Engineering, with some background in Automatic Control Area. Prerequisites: ENGRG 7310 and ENGRG 7320 Level: Graduate Credits: 3 Format: Online Program: MS in Engineering

NOTE: The information below is representative of the course and is subject to change.  The specific details of the course will be available in the Desire2Learn course instance for the course in which a student registers.

Learning Outcomes

The student upon completion of the course should be familiar and be able to discuss the following topics that lean toward control theory and relevant to the analysis and design of discrete-time control systems:

• Signal conversion, A/D, D/A, and hold devices
• Z-transform, difference equation
• Sampling, block diagram reduction, time domain response, realization of controllers
• Analysis of discrete-time systems, transient and steady state response, stability, root locus construction in the z-plane, frequency response of systems (Bode and Nyquist diagrams)
• Design of digital controllers using root locus and Bode plot methods, design of dead beat controllers
• State space description of discrete-time systems, solution of state equations, controllability, observability, and stability of discrete-time systems, controller design using state feedback and design of observers

Unit Descriptions

Unit 1

• Discuss Unit Ramp, Unit Step and Exponential functions for Z-Transform Functions
• Use different theorems to discuss Z-Transform Solutions
• Understand Inverse Z-Transforms and use different methods to evaluate: Partial Fractions Method and Inversion Integral Method
• Use Difference Equations for evaluations of Discrete time systems
• Use MATLAB for Z-Transforms

Unit 2

• Be able to use mathematical models of a sampling process
• Use sampling theorem
• Use Ideal Sampler
• Use of data reconstruction to change signals into usable form
• Be able to use the Pulse Transfer Function
• Evaluate Transfer Functions of systems with cascaded elements
• Evaluate Transfer Function of closed loop digital control system
• Use Standard, Series, Parallel and Ladder Structures for realization of a controller
• Use MATLAB for sampling theorem evaluation and Transfer Functions

Unit 3

• Understand mapping from s-plane to z-plane
• Understand Constant Damping, Frequency and Damping Ratio Locus
• Use Stability for Scalar Systems
• Use Jury and Routh Tests for stability
• Evaluate Transient Response for closed loop poles. Use MATLAB for reinforcing methods
• Use Root Locus in Z-plane
• Use various methods of conversion from s-Domain to z-Domain
• Discuss Frequency response of Discrete Time Systems
• Understand Nyquist Plot and Stability Criterion
• Use MATLAB to reinforce above outcomes

Unit 4

• Understand Frequency Domain Design Method
• Design a Phase Lag Compensator
• Understand Analytic Design Method

Unit 5

• Understand State Space Description of Discrete Time Systems
• Learn about Common State Space Representations
• Understand Transfer Function Matrix from State Space Equations
• Understand the different solutions of State Space Equations

Unit 6

• Use different methods to determine system controllability
• Use different tests for system observability
• Notice pole placement and observer design methods
• Understand Observable Canonical form
• Use the Liapunov Stability Analysis
• Use MATLAB to determine if system is controllable, observable

Unit 7

• Be able to use Pole Placement in Design Practice
• Understand the term Deadbeat Response
• Learn to use the Observer Design Theory
• Use MATLAB for pole placement and observer design

Homework:   50%
Two Midterms:   25%
Final Exam:   25%