Digital Control Systems

Course Description

Digital Control Systems provides a foundation in discrete-time linear control system theory. It is offered concurrently with EEL5630, with graduate students assigned additional work.

Within the SCNS taxonomy, EEL is the Electrical Engineering prefix. The University of West Florida publishes this at 3 semester hours through the Department of Electrical and Computer Engineering, College of Science and Engineering. Institutions carrying the integrated EEL4635C offer it at approximately 4 Florida institutions.

Essentially every controller built today is digital, which makes this the course that describes how control is actually practised. EEL4657 develops continuous-time theory, and that theory is correct and incomplete: a real controller is a program running on a processor, sampling at discrete instants and holding its output constant between them. Sampling is not a minor implementation detail — it changes stability properties, introduces delay, and can destabilise a design that was comfortably stable in continuous time.

The central technical move is the shift from the s-plane to the z-plane, where the stability boundary becomes the unit circle rather than the imaginary axis. The structure is closely parallel to what EEL3135 taught for signals, and students who have that course behind them find this one substantially easier — though UWF does not require it.

⚠ Why this guide exists under this number

Many Florida institutions carry this material as a single integrated course with a C suffix. UWF instead runs a separate lecture and a separate laboratory, each with its own SCNS number, and this guide documents the UWF lecture. Its laboratory partner is documented separately in this repository. ⚠ SCNS equivalency does not cross numbers, so a transfer between the integrated and split forms is evaluated by hand rather than automatically — carry a syllabus in either direction.

⚠ The contact-hour figure is derived — the University of West Florida publishes none

UWF's catalog publishes a credit value in semester hours, the college and department, prerequisites, and a description. It does not publish contact hours, a lecture and laboratory split, or terms of offering for any course. It does publish a material and supply fee notice on the minority of courses that carry one — and maintains a separate Material & Supply and Equipment Fees section of the catalog — so the absence of a fee notice on this entry is meaningful, while the fee amount is not published here. Every contact-hour value in a UWF guide in this repository is therefore derived. The figure here applies the standard lecture convention of 15 contact hours per credit, giving 45 hours for a 3-semester-hour course. Confirm the meeting schedule with the department.

Learning Outcomes

Required Outcomes

• Describe the structure of a digital control system and its components.
• Describe sampling, the zero-order hold, and reconstruction.
• Apply the z transform and inverse z transform.
• Determine the pulse transfer function of a sampled-data system.
• Relate s-plane and z-plane pole locations through the sampling map.
• Assess stability in the z-domain using the unit circle criterion.
• Apply Jury's stability test.
• Analyse discrete-time transient response and its specifications.
• Compute steady-state error for discrete-time systems.
• Construct root locus in the z-plane and interpret it.
• Select a sampling rate appropriate to a plant's dynamics.
• Explain the effect of sampling rate on stability and performance.
• Design digital controllers by emulation of a continuous design.
• Apply discretisation methods and compare their fidelity.
• Design digital controllers directly in the z-domain.
• Design deadbeat and finite-settling-time controllers.
• Represent discrete-time systems in state space.
• Design discrete state feedback by pole placement.
• Design discrete observers.
• Describe quantisation and finite word length effects.
• Implement a digital controller in software and verify it.

Optional Outcomes

• Describe optimal discrete control and the linear quadratic regulator.
• Describe state estimation using the Kalman filter.
• Describe multirate and asynchronous sampling.
• Describe networked control and the effect of communication delay.
• Describe system identification for discrete models.
• Describe embedded implementation constraints and real-time scheduling.

Major Topics

Required Topics

• Digital control system structure
• Sampling and the zero-order hold
• The z transform
• Pulse transfer functions
• The s-plane to z-plane map
• Stability and the unit circle
• Jury's stability test
• Discrete transient response
• Discrete steady-state error
• Root locus in the z-plane
• Sampling rate selection
• Design by emulation
• Discretisation methods and their fidelity
• Direct digital design
• Deadbeat control
• Discrete state space
• Discrete pole placement
• Discrete observers
• Quantisation and finite word length
• Software implementation

Optional Topics

• Linear quadratic regulator
• Kalman filtering
• Multirate sampling
• Networked control and delay
• Discrete system identification
• Embedded real-time constraints

Resources & Tools

• Franklin, Powell and Workman, Digital Control of Dynamic Systems — the standard text in the field, and unusually good on the practical implementation issues.
• Ogata, Discrete-Time Control Systems — the thorough and more mathematical alternative.
• Åström and Wittenmark, Computer-Controlled Systems — a classic, and strong on sampling theory.
• MATLAB Control System Toolbox — c2d, d2c, and the discrete analysis functions are used constantly; check UWF's campus licence.
• Python with python-control and SciPy — free; full discrete-time support and a genuine substitute.
• GNU Octave with the control package — free.
• Simulink or Python simulation — simulating the sampled loop, rather than the continuous approximation of it, is what makes the sampling effects visible.
• ⚠ A microcontroller board (STM32, Teensy, Arduino) — inexpensive, and implementing a discrete controller with a real timer interrupt teaches sampling jitter, computational delay and quantisation in an afternoon.
• Brian Douglas control lectures — free; the discrete-control segments are excellent.
• IEEE Control Systems Society — inexpensive student membership.

Career Pathways

• Electrical engineers — SOC 17-2071.
• Embedded control and firmware engineering — where most digital control is actually implemented, and a very large employment category.
• Controls and automation engineering — industrial, process, and manufacturing.
• Aerospace guidance, navigation and control — Lockheed Martin (Orlando), Northrop Grumman (Melbourne), and the Space Coast launch sector; flight control is digital control.
• Autonomous systems and unmanned vehicles — Eglin Air Force Base and NSA Panama City in UWF's region.
• Robotics — every joint controller is a discrete controller.
• Automotive and electric vehicle control — motor control and battery management.
• Power electronics control — converter control loops are digital; see EEL4241.
• ⚠ This course plus embedded programming is a strong and uncommon combination, and it is asked about directly in controls interviews.

Special Information

⚠ Offered concurrently with the graduate EEL5630

• UWF teaches this alongside EEL5630, with graduate students assigned additional work. The pattern is routine at UWF and, across the corpus so far, is confined to 4000-level courses.
• The effect on an undergraduate is a section with graduate students in it and reading pitched to work at both levels. Undergraduate requirements are lower by design — the differential is in the additional graduate work, not in the shared material.
• For a student considering graduate study it is a useful preview, and the instructor sees the student working next to the standard they would be held to.

⚠⚠ The asterisk in a UWF prerequisite means the course may be taken at the same time

• UWF's catalog marks a concurrent course with an asterisk, defined on the catalog's Course Information page as: "This course may be taken prior to or during the same term."
• ⚠ This is the single most useful piece of notation in the UWF engineering catalog, and it is easy to miss. A prerequisite written without an asterisk must be completed first; one written with an asterisk may be taken in the same term.
• The practical effect is on time to degree. Reading an asterisked prerequisite as a hard prerequisite adds a term to the sequence for no reason, and in a tightly chained major like electrical engineering that error compounds down the whole plan.
• Confirm with an advisor before relying on it, and note that the registration system, not the catalog text, is what actually enforces the rule.

⚠ The prerequisite is EEL4657 — and EEL3135 is the unlisted asset

• UWF publishes EEL4657 Linear Control Systems as the sole prerequisite, not asterisked, so it must be complete.
• ⚠⚠ EEL3135 Discrete-Time Signals and Systems is not required and is very nearly a prerequisite in substance. The z transform, sampling, aliasing and the unit circle are all developed there, and a student who has taken it will find this course a change of application rather than a change of subject. One who has not will be learning the z transform and control design simultaneously.
• Take EEL3135 first where the schedule allows, and if not, expect to work harder in the first month.
• ⚠ The chain into this course is long: EEL3111 → EEL3112 → EEL4657 → EEL4635. A delay anywhere reaches it directly, and it is normally a final-year course.

⚠⚠ Sampling rate is a design parameter, and both extremes fail

• Too slow destabilises. Sampling introduces an effective delay of roughly half a sample period, and that delay consumes phase margin — a continuous design with comfortable margins can be unstable when implemented at a low rate.
• ⚠ The common rule of thumb is a sampling rate well above the closed-loop bandwidth, considerably faster than the Nyquist minimum, because Nyquist is about reconstructing a signal rather than about controlling a loop.
• ⚠⚠ Too fast also fails, for different reasons. Very high rates push discrete poles toward the unit circle at z equal to one, where finite word length effects and numerical conditioning become significant, and computation may not finish within the period.
• Anti-aliasing filtering is required before the sampler, and the filter itself adds phase lag that must be accounted for in the design.
• Computational delay is real. The controller output is available only after the calculation completes, which adds a further delay that should be modelled rather than ignored.

⚠ Emulation versus direct design, and why the distinction matters

• Emulation designs in continuous time and then discretises, which is simple, intuitive, and only valid when the sampling rate is high relative to the dynamics.
• ⚠ Discretisation methods are not equivalent. Tustin's bilinear method preserves stability but warps frequencies; forward Euler can turn a stable continuous design into an unstable discrete one. The choice affects the result and should be deliberate.
• Direct z-domain design accounts for sampling from the start and is the correct approach when the sampling rate is not comfortably fast.
• ⚠⚠ Deadbeat control is a cautionary example. It achieves finite settling in a few samples and typically demands large control effort, saturates real actuators, and is fragile to model error — an elegant result that is rarely the right engineering answer.
• Quantisation introduces a nonlinearity that linear theory does not describe, and it can produce limit cycles in an otherwise stable loop.

FE exam relevance

The Fundamentals of Engineering (FE) exam is the first step toward Professional Engineer licensure, and in Florida it is administered under the Florida Board of Professional Engineers. Most students take the FE Electrical and Computer exam in their final year. Licensure matters less in electrical engineering than in civil — the industrial exemption means most electrical engineers in manufacturing and product work never need a PE — but it is required for consulting practice, for sealing designs, and for power and building-systems work, which is exactly where Florida's utility and infrastructure employment sits.

Course format and position in the curriculum

• Lecture with problem sets, design assignments, and simulation work.
• Typically taken in the fourth year, after EEL4657.
• Taught with graduate students in the room; expect the level to reflect that.
• ⚠ If the course includes an implementation component, treat it as the most valuable part — the gap between a controller that works in simulation and one that works on a processor is where the real learning is.
• UWF publishes no contact hours, lecture and laboratory split, or terms of offering for any course, and no material and supply fee is noted on this entry. Confirm the offering pattern with the department.

How Florida course levels affect transfer

The first digit of an SCNS number denotes the year of offering, not transferability. Courses at the 1000 and 2000 levels transfer transparently between Florida public institutions, and 3000 to 4000 is unproblematic since both are upper division. The boundary that actually matters is 2000 to 3000, where lower-division credit generally cannot satisfy an upper-division requirement. ⚠ For engineering specifically, ABET-accredited programmes commonly require that upper-division engineering coursework be taken in residence, so transferability of the credit and applicability to the degree are separate questions.

EEL4635 is 3 semester hours at the University of West Florida, offered concurrently with the graduate EEL5630. Institutions carrying the integrated EEL4635C combine this with laboratory work in one course.