# ECE 441A

## Automatic Control

### Course Level

### Units

### Instructor(s)

### Prerequisite(s)

### Course Texts

**Required Textbooks:**

- Control Systems Engineering, 8th Edition, Norman Nise, Wiley. We will use Zybooks in this course.
- (Reference; graduate). Feedback Control Theory, J. Doyle, B. Francis, A. Tannenbaum.
- fbswiki.org/wiki/index.php/Feedback_Systems:_An_Introduction_for_Scientists_and_Engineers

**Software**

- You will be required to use Matlab to work on assignments throughout the course. We will NOT cover "how to program in Matlab," rather, you are expected to know it or pick it up.

### Schedule

### Course Description

**Specific Course Information:
2021-2022 Catalog Data: **Linear control system representation in time and frequency domains, feedback control system characteristics, performance analysis and stability, and design of control.

### Learning Outcomes

**Specific Goals for the Course:
Outcomes of Instruction:** By the end of this course the student will be able to:

- Model, via differential equations or transfer functions, electrical, mechanical, and electromechanical dynamical systems. (Exam 1)
- Linearize a set of nonlinear dynamical equations. (Exam 1)
- Create a second-order model from a system's step response. (Exam 1)
- Construct all-integrator block diagrams from a transfer function, a set of differential equations, or a state-space representation and vice-versa. (Exam 1)
- Construct and interpret the Routh Array. (Exam 1)
- Sketch the root locrn, associated with a transfer function. (Exam 2)
- Determine the stability of a closed-loop system. (Exam 2)
- Calculate the phase margin and gain margin of a system from its frequency response (Bode plots). (Exam 2)
- Compute a state transition matrix from a system matrix. (Exam 2)
- Describe in terms of percent overshoot, settling time, steady-state error, rise-time, or peak time how the poles of a second-order continuous-time system influence the transient response. (Exam 2)
- Translate design specifications into allowable dominant pole locations in the s-plane (Exam2)
- Calculate a system's steady-state error and how the steady-state error can be influenced via system parameter changes. (Exam 2)
- Analyze stability using state-space techniques (Exam 3)
- Calculate a system's sensitivity with respect to different parameters.
- Design analog controllers using root locus techniques. (Exam 3)
- Design a system utilizing the observable canonical form. (Exam 3)
- Design an analog PID controller to meet design specifications. (Exam 3)
- Design analog controllers using Bode plot techniques. (Exam 3)
- Design full-state feedback gains to achieve acceptable closed-loop behavior.

### Course Topics

**Brief list of topics to be covered:**

- Course Description and Introduction
- System Modeling: Electrical & Mechanical Components, Electromechanical Systems;

Current-Force Analogy, Gears and Levers; Linearization - System Descriptions and Manipulation

Transfer Function Descriptions; Simulations of Systems; Block Diagram Algebra

System Identification and Frequency Response; State-Space Representation; State Transition Matrix; Mason's Gain Formula - Feedback System Characteristics

Sensitivity; Initial Value Theorem; Tracking; Steady-state Error - System Performance and Stability

Specifications (rise time, overshoot, steady-state error, and settling time); Pole locations and Time Response (2nd Order Systems); Routh-Hurwitz Test; Reative Stability; Time-domain Stability - Root Locus Analysis and Controller Design

Root Locus Construction Rules; Root Locus Phase Lead Design and Lag Design - Bode Analysis and Controller Design

Bode Plot Construction Rules; Frequency Response Measurements and Performance

Stability Margins; Phase Lead and Lag Bode Design - PID Controller Design
- State Feedback Design

Pull State Feedback Internal Model Design; Observer Design and Observer-based Compensator Design

### Relationship to Student Outcomes

ECE 414A contributes directly to the following specific electrical and computer engineering student outcomes of the ECE department:

1. An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.

5. 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. An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions