## Digital Control

(3-0-0-3)

**CMPE Degree:** This course is Not Applicable for the CMPE degree.

**EE Degree:** This course is Not Applicable for the EE degree.

**Lab Hours:** 0 supervised lab hours and 0 unsupervised lab hours.

**Technical Interest Group(s) / Course Type(s):** Systems and Controls

**Course Coordinator:** Yorai Wardi

**Prerequisites:** None.

**Corequisites:** None.

### Catalog Description

Techniques for analysis and synthesis of digital control systems. Sample-data systems, state-space systems, and linear feedback design.### Textbook(s)

Discrete-Time Control Systems### Course Outcomes

Not Applicable

### Student Outcomes

In the parentheses for each Student Outcome:"P" for primary indicates the outcome is a major focus of the entire course.

“M” for moderate indicates the outcome is the focus of at least one component of the course, but not majority of course material.

“LN” for “little to none” indicates that the course does not contribute significantly to this outcome.

1. ( Not Applicable ) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. ( Not Applicable ) An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors

3. ( Not Applicable ) An ability to communicate effectively with a range of audiences

4. ( Not Applicable ) An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts

5. ( Not Applicable ) An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives

6. ( Not Applicable ) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

7. ( Not Applicable ) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

### Strategic Performance Indicators (SPIs)

Outcome 1 (Students will demonstrate expertise in a subfield of study chosen from the fields of electrical engineering or computer engineering):

Upon successful completion of the course, the student should be able to:

1. Analyze discrete-time systems and sample-data systems.

2. Apply the principle of the argument to compute the inverse z-transform.

3. Analyze reachability and observability of state-space linear systems.

Outcome 2 (Students will demonstrate the ability to identify and formulate advanced problems and apply knowledge of mathematics and science to solve those problems):

Upon successful completion of the course, the student should be able to:

1. Design digital controllers for continuous plant-systems.

2. Design linear feedback laws for state-space linear systems.

Outcome 3 (Students will demonstrate the ability to utilize current knowledge, technology, or techniques within their chosen subfield):

Upon successful completion of the course, the student should be able to:

N/A

### Course Objectives

### Topical Outline

1. The z-transform

a. Definition and properties of the z transform

b. The inverse z transform by partial fraction expansions.

c. Solving difference equations by thye z transform

2. Introduction to complex-functions theory

a. Complex integration and Cauchy theorem

b. Contour integration and its applications to the inverse z transform

3. Z-plane analysis of discrete-time linear systems

a. Sampling and hold

b. The Nyquist sampling theorem

c. Deriving the transfer functions of sampling-and-hold systems

4. Design of discrete-time control systems

a. Mappings between the s plane and the z plane

b. Stability analysis of closed-loop systems

c. Design of digital controllers for sample-data systems

5. The State-space approach

a. State-space representations of discrete-time systems

b. Analysis os discrete-time state-space equations

6. Feedback Design for State-space Systems

a. Controllability and observability

b. Contrller design by pole placement

c. State observers

7. Introduction to Optimal Control

a. General principles of discrete-time optimal control

b. The linear-quadratic regulator