Linear Control Systems

Course Description

Linear Control Systems explores the fundamental principles of control systems. Students model physical systems and analyze linear systems to assess stability and steady-state tracking, and the course covers the design of various controllers using root locus techniques and introduces state space methods for controller and observer design.

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 EEL4657C offer it at approximately 4 Florida institutions.

Control theory is the most portable subject in the electrical engineering curriculum, and that is worth saying plainly. The same mathematics governs an aircraft autopilot, a chemical reactor's temperature, a hard drive's head position, a power system's frequency, and a robot's joint. The discipline abstracts away what the plant is and reasons only about its transfer function — which is why control engineers move between industries more freely than almost any other specialism.

The central idea is feedback, and its power is that it makes a system's behaviour depend on the controller rather than on the plant. A high-gain feedback loop delivers accurate output even when the plant is poorly known, nonlinear, or drifting. The catch is that feedback can also make a stable plant unstable, and the entire apparatus of root locus, margins, and pole placement exists to manage that trade.

⚠ 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

• Model physical systems and derive transfer functions from governing equations.
• Model electrical, mechanical, and electromechanical systems in a common framework.
• Linearise a nonlinear model about an operating point.
• Construct and reduce block diagrams and signal flow graphs.
• Analyse first- and second-order system time response.
• Relate damping ratio and natural frequency to transient specifications.
• Compute rise time, peak time, overshoot, and settling time.
• Determine system type and compute steady-state error constants.
• Assess stability using the Routh-Hurwitz criterion.
• Construct root locus plots and interpret them.
• Design proportional, PI, PD, and PID controllers using root locus.
• Design lead and lag compensators.
• Construct and interpret Bode plots for open-loop systems.
• Determine gain margin and phase margin and relate them to transient response.
• Apply the Nyquist stability criterion.
• Describe the effect of pole and zero locations on closed-loop behaviour.
• Represent systems in state space form.
• Convert between transfer function and state space representations.
• Assess controllability and observability.
• Design state feedback controllers by pole placement.
• Design state observers and describe the separation principle.
• Use software to analyse and design control systems.

Optional Outcomes

• Describe robustness and sensitivity to model uncertainty.
• Describe disturbance rejection design.
• Describe optimal control at an introductory level.
• Describe the effects of actuator saturation and anti-windup.
• Describe system identification from measured data.
• Describe digital implementation and the effect of sampling.

Major Topics

Required Topics

• System modelling and transfer functions
• Electrical, mechanical, and electromechanical analogies
• Linearisation
• Block diagrams and signal flow graphs
• First- and second-order time response
• Damping ratio and natural frequency
• Transient performance specifications
• System type and steady-state error
• Routh-Hurwitz stability
• Root locus construction and interpretation
• PID design via root locus
• Lead and lag compensation
• Bode plots and frequency response
• Gain and phase margin
• The Nyquist criterion
• State space representation
• Controllability and observability
• Pole placement by state feedback
• Observer design and the separation principle
• Control system software

Optional Topics

• Robustness and sensitivity
• Disturbance rejection
• Introductory optimal control
• Saturation and anti-windup
• System identification
• Digital implementation and sampling

Resources & Tools

• Nise, Control Systems Engineering — the most widely adopted undergraduate text, and strong on worked design examples.
• Ogata, Modern Control Engineering — the classic and more mathematical alternative.
• Dorf and Bishop, Modern Control Systems — another standard.
• MATLAB with the Control System Toolbox — the standard tool; check UWF's campus licence before purchasing. rlocus, bode, margin and step are used constantly.
• Python with the control package — free; python-control mirrors the MATLAB toolbox interface closely and is a genuine substitute.
• GNU Octave with the control package — free.
• Brian Douglas control lectures — free; widely regarded as the clearest intuitive explanations of control concepts available anywhere, and an excellent complement to a formal text.
• MIT OpenCourseWare 2.004 and 16.06 — free.
• An inexpensive microcontroller board — implementing a PID loop on real hardware makes sampling, saturation, and windup concrete in a way no simulation does.
• IEEE Control Systems Society — inexpensive student membership.

Career Pathways

• Electrical engineers — SOC 17-2071; mechanical engineers — SOC 17-2141; control genuinely spans both.
• Controls and automation engineering — consistently in demand across manufacturing, process, aerospace, energy, and marine.
• Industrial automation and PLC programming — Florida's manufacturing base and its utilities both hire for this, and it is an accessible entry point.
• Aerospace guidance, navigation and control — Lockheed Martin (Orlando), Northrop Grumman (Melbourne, St. Augustine), and the Space Coast launch sector.
• Autonomous systems and unmanned vehicles — a significant Northwest Florida sector tied to Eglin Air Force Base and NSA Panama City.
• Robotics — see EEL4663.
• Power system control — Florida Power & Light, Duke Energy Florida, Gulf Power.
• Process control in chemical and water treatment — Florida's municipal water and wastewater systems run on this.
• Medical device control systems.

Special Information

⚠⚠ 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 EEL3112, and it is load-bearing

• UWF publishes EEL3112 Circuits II as the sole prerequisite, not asterisked, so it must be complete.
• ⚠⚠ The prerequisite is about transforms, not circuits. This course runs entirely on Laplace-domain reasoning, and students who treated Laplace as a lookup procedure in Circuits II rather than understanding the pole-zero picture struggle badly here — because in this course the pole-zero picture is the reasoning.
• Refresh partial fractions, poles and zeros, and Bode construction before the term.
• ⚠ The companion laboratory is EEL4657L, which lists this course with the concurrent asterisk — take them together. This course is also the prerequisite for EEL4635 Digital Control Systems.

⚠⚠ The concepts students most often misunderstand

• Root locus is a design tool, not a plotting exercise. The sketching rules matter because they let an engineer see how closed-loop poles move as gain changes — and students who only learn to produce the plot cannot use it to choose a controller.
• ⚠ Higher gain is not better. Increasing gain reduces steady-state error and typically reduces stability margin. Every control design is a position on that trade-off, and there is no setting that wins on both.
• ⚠⚠ Gain and phase margin measure distance from instability, not quality. A system with adequate margins can still respond badly, and margins say nothing about disturbance rejection. Marginal stability is not a safe design point; real plants drift and real models are wrong.
• Steady-state error depends on system type and on the input. A type 0 system tracks a step with finite error and a ramp not at all — students routinely quote error constants without reference to the input.
• ⚠ Right-half-plane zeros produce initial response in the wrong direction and fundamentally limit achievable bandwidth. This is the clearest example of a limit that no controller can design away.
• State space is a different representation, not a different subject. The same system appears in both forms, and controllability and observability are structural properties that determine whether a design problem is solvable at all.

⚠ The model is not the plant

• Every design in this course starts from a transfer function that is an approximation — linearised, with unmodelled dynamics and neglected delay.
• ⚠⚠ A controller designed with no margin for model error will fail on hardware, and this is the lesson EEL4657L delivers directly. Friction, backlash, saturation and sensor noise are all absent from the model and present in the plant.
• Time delay is the most destabilising unmodelled effect, because it consumes phase margin directly.
• Design for robustness rather than for nominal performance. A controller that performs adequately across a range of plant parameters beats one that is optimal for a plant you do not actually have.

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 software-based analysis.
• Typically taken in the fourth year, after Circuits II, with EEL4657L alongside.
• ⚠ It gates EEL4635 Digital Control Systems, so a delay here closes off that course.
• Graphical construction by hand is still examined at most institutions even though software does it instantly — because the hand method is what builds the design intuition.
• 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.

EEL4657 is 3 semester hours at the University of West Florida, paired with the 1-semester-hour EEL4657L. Institutions carrying the integrated EEL4657C cover both in one course.