Title: DIGITAL CONTROL
Catalog Description: Linear discrete dynamic systems and Z-transform theory. Design of digital filters. Numerical methods. Design of digital control systems using transform techniques and state-space methods. Microprocessor implementation of controllers. Sample-data systems. Quantization effects. Multivariable and optimal control. System identification algorithms.
Coordinator: Mehmet Akar, Associate Professor of Electrical Engineering
Goals: To introduce the concepts and methodologies of discrete-time control systems, to familiarize students with discretization techniques, and to develop digital control system design capabilities.
At the end of this course, students will be able to
1. Configure a discrete-time control system complete with Sample and Hold, A/D, digital processor, D/A, holder and if necessary transducer element.
2. Analyze a digital control system in the complex frequency domain using z-transforms.
3. Perform discretization of continuous time signals and systems using various discretization techniques.
4. Obtain the z-transfer function of the digital control system and relate it with time domain performance characteristics.
5. Perform the stability analysis of a digital control system.
6. Design a digital controller based on root-locus.
7. Design a digital controller based on frequency response method.
8. Design a deadbeat controller.
9. Perform state-space analysis of discrete time systems; and apply Lyapunov stability analysis, and check for controllability and observability.
10. Design state feedback controller based on pole placement and Ackerman’s formula.
Textbook: Discrete-Time Control Systems by K. Ogata, Prentice-Hall
1. Digital Control of Dynamics Systems by G.F. Franklin, J.D. Powell and M.L. Workman
2. Applied Digital Control by J.R. Leigh
Prerequisites by Topic:
1. Introductory course on control systems.
2. Basics of ordinary differential and difference equations.
3. Complex variables.
4. Laplace transformation.
5. Fourier transformation and frequency domain techniques.
6. Matrix algebra.
1. Introduction to digital control and related system architecture. (2 class hours)
2. Sampling, quantizing, coding. A/D and D/A converters. Reconstruction of original signals from sampled signals. (2 class hours)
3. The z-transform; properties and theorems; the inverse z-transformation. The pulse transfer function. (6 class hours)
4. Realization of digital controllers and digital filters. Stability analysis. (3 class hours)
5. Discrete-time equivalents of continuous-time filters. Numerical integration and approximation techniques. (4 class hours)
6. Mapping between the s-plane and z-pla ne. (2 class hours)
7. Design based on discrete-time equivalent of analog controllers. Transient and steady-state response analysis. (4 class hours)
8. Design based on root-locus methods. (5 class hours)
9. Design based on frequency response methods. (3 class hours)
10. Analytical design method. (2 class hours)
11. State-space representation of discrete-time systems. (4 class hours)
12. Discrete-time controller design via pole placement. (2 class hours)
13. (Time permitting) An introduction to quadratic optimal control. (2 class hours)
14. One mid-term exam. (2 class hours)
Course Structure: The class meets for three lectures a week, each consisting of a 50-minute session. There is an in-class quiz, a mid-term exam and a final exam. A two-part term project on digital control of a DC-motor is also assigned. The first part of the project is on controller design and the simulation of the DC motor feedback system in MATLAB -Simulink. For the second part of the project, the students are asked to experiment their designs on the DC motor setup in the laboratory.
Computer Resources: Students are encouraged to use MATLAB to solve their homework problems, and do their term project.
Laboratory Resources: As part of the term project, the students are expected to try their digital controller designs on the DC motor setup in the laboratory.
1. Quiz (15%)
2. Midterm 1 (30%)
3. Final exam (40%)
4. Project (15%)
a) Apply math, science and engineering knowledge. The course deals with discrete-time control systems described by ARMA type difference equations. Different tools from mathematics like complex variables, z-transforms and discrete-time Fourier transforms are used in the presentation of the lectures dealing with conventional control system analysis, while matrix algebra is used in the state space analysis of digital control systems.
b) Design a system, component or process to meet desired needs. Emphasis is placed on design issues with specifications expressed both in time domain and frequency domain.
Design of digital control systems in the z-domain is based on root-locus analysis.
Design of digital filters in the z-domain is specified by gain requirements and bandwidth requirements.
Design of control systems in the frequency domain is also performed based on gain margin and phase margin requirements.
Design in state space is done with state feedback and pole placement to meet time domain requirements.
c) Identify, formulate and solve engineering problems. These topics are extensively covered through the truly rich problems listed at the end of the each chapter of the text used in the course.
d) Recognize the need for, and have the ability to engage in life-long learning. This basic course will provide ability for life-long training and education. In the field of digital control system design both by conventional techniques and state-space approaches, the need for such life-long and continuous search of related literature was clearly and openly communicated to the students.
e) Use of modern engineering students. The analysis and design of tools taught in this course can be readily used by the students in their engineering practice. Modern engineering tools like MATLAB, which they use for homework and the term project, will also be employed in their future engineering practice.
f) Knowledge of contemporary issues : Contemporary issues concerning digital control applications, economic advantages, and technological issues related with digital control are emphasized.
Prepared By: Yorgo Istefanopulos and Mehmet Akar