# ECE 442

## Digital Control Systems

**Usually offered:**Spring

**Required course:** No

### Course Level

### Units

### Instructor(s)

### Prerequisite(s)

### Course Texts

“Digital Control Engineering: Analysis and Design,” by M. Fadali and A. Visioli, Second Edition, Academic Press, Waltham, MA, 2013. ISBN: 978-0-12-394391-0. Available as an e-Book or Download through the University of Arizona Library.

### Schedule

### Course Description

**Specific Course Information:****2021-2022 Catalog Data: **Modeling, analysis, and design of digital control systems; A/D and D/A conversions, Z-transforms, time and frequency domain representations, stability, microprocessor-based designs.

### Learning Outcomes

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

- Design a pure, two-pole system that satisfies specified performance specifications like percent overshoot, peak time, settling time, and DC gain.
- Calculate the z-plane location of a pair of dominant poles given time-domain performance information like percent overshoot, settling time, and peak time.
- Create discrete equivalents from given continuous-time systems, e.g., a. create a zero-order hold equivalent discrete-time state space representation from continuous-time, state space representation, b. create a discrete-time transfer function from a continuous-time transfer function using a numerical integration strategy (Numerical Integration Strategies: Forward Rectangular, Backward Rectangular, and Tustin/Trapezoidal) or using a pole-zero mapping technique, c. create a zero-order hold equivalent discrete-time transfer function of a system given a continuous-time transfer function preceded by a zero-order hold.
- Construct a discrete-time difference equation containing input variables and output variables at particular time instances from a system’s discrete-time transfer function.
- Produce a closed-form expression for the output of a system given a system description and an applied input waveform. The system description could be in the form of a block diagram, transfer function, difference equation, or state-space representation.
- Numerically compute the value of any system variable (e.g., state variable or output variable) at any discrete, time instant given initial conditions and input waveforms.
- Compute the settling time, peak time, and percent overshoot for a discrete-time system. The discrete-time system could be represented in the form of a difference equation, a state-space representation, a block diagram, or a transfer function.
- Compute the z-Transform of a given discrete-time waveform.
- Compute the transfer function of a given system given a system representation in difference equation form, state-space form, or block diagram form.
- Compute the Inverse z-Transform given a rational expression in the frequency domain and the Region of Convergence (ROC).
- Correlate the different Region of Convergence (ROC) shapes with when the time domain waveform is defined, e.g., as a right-sided time sequence (one-sided), a left-sided time sequence (one-sided), or when the sequence is defined for all time indices (two-sided).
- Find the steady-state error in a given system.
- Determine if a discrete-time system is Bounded-Input, Bounded-Output (BIBO) stable. The system could be described in the form of a difference equation, a block diagram, a transfer function, or a state-space representation.
- Create a state-space representation of a system from a given system description. The system description could be in the form of a difference equation, a block diagram, or a transfer function.
- Apply the Final Value Theorem for discrete-time systems to find the limiting values of given system variables, i.e., errors, state variables, or output variables.
- Design stabilizing controllers for unstable systems using classical control design strategies, i.e., design strategies based on root locus design techniques.
- Sketch (by hand) a root locus diagram corresponding to a given system model that is interconnected in a negative, unity output-feedback configuration.
- Perform each step in the root locus diagram construction process.
- Design controllers based on the Ragazzini controller design approach.
- Identify a range of gain values that would provide a stable, closed-loop system if such a range of gain values exists.
- Design full-state feedback controllers to locate closed-loop poles at particular locations in the complex z-plane.
- Utilize the phase-angle condition in the root locus design approach to locate pole and zero locations in 1st-order or 2nd-order controllers.
- Design full-state feedback controllers with non-zero reference inputs to produce desired closed-loop pole locations and the desired DC gain in the closed-loop system

### Course Topics

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

This course provides an introduction to the fundamental concepts and mathematics of control systems engineering. Throughout the semester we will cover linear control system representation in time and frequency domains, feedback control system characteristics, performance analysis and stability, and design of control.

### Relationship to Student Outcomes

ECE 442 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.

2. 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