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Course Description

Title: Control Systems

Course Overview

This course introduces the analysis and design of feedback control systems used to regulate the behavior of dynamic systems. Students develop mathematical models of physical systems, analyze system behavior in the time and frequency domains, and design controllers to meet performance, stability, and robustness requirements.

The course emphasizes classical control theory using mathematically rigorous and conceptually stable techniques that remain relevant across technologies and application domains. Computational tools are used to support analysis and visualization, while laboratories and projects reinforce engineering judgment through simulation and data-driven validation.

Intended Audience

This course is intended for:

  • Upper-division undergraduate students in Electrical Engineering
  • Students in Mechanical Engineering, Computer Engineering, or Mechatronics programs with sufficient mathematical preparation
  • Engineering students preparing for advanced coursework in robotics, embedded systems, power systems, signal processing, and cyber-physical systems

Prerequisites

Here is a list of the specific mathematical and technical skills students are expected to have proficiency in before they take this course:

  • Calculus (differentiation, integration, basic multivariable concepts)
  • Differential equations (first- and second-order linear ODEs)
  • Linear algebra (vectors, matrices, eigenvalues and eigenvectors at a conceptual level)
  • Complex numbers (rectangular and polar forms, magnitude and phase)
  • Signals and systems concepts (LTI systems recommended)
  • Basic programming or scripting experience (Python or equivalent)

Detailed Topics Covered

Foundations of Control Systems

  • Purpose and applications of control systems
  • Open-loop versus closed-loop control
  • Feedback concepts and real-world examples

System Modeling

  • Differential equation models of dynamic systems
  • Electrical, mechanical, and electromechanical analogies
  • Linearization of nonlinear systems (introductory)
  • Transfer function representations

Laplace Transform Methods

  • Laplace transform review
  • Poles, zeros, and system behavior
  • Initial and final value theorems

Block Diagrams and Signal Flow

  • Block diagram representation of systems
  • Block diagram reduction techniques
  • Signal flow graphs and Mason’s gain formula (introductory)

Time-Domain Analysis

  • Step, ramp, and impulse responses
  • Transient response specifications
  • Steady-state error analysis

Stability Analysis

  • Concept of stability in feedback systems
  • Routh–Hurwitz stability criterion
  • Root locus analysis

Frequency-Domain Analysis

  • Sinusoidal steady-state response
  • Bode magnitude and phase plots
  • Gain margin and phase margin
  • Nyquist stability criterion (introductory)

Controller Design

  • Proportional, integral, and derivative control
  • PID controller tuning concepts
  • Lead and lag compensation
  • Performance–robustness tradeoffs

Computer-Aided Analysis

  • Time-domain simulation
  • Frequency-domain visualization
  • Validation of analytical results using computational tools

Concepts NOT covered in this course

The course scope is bounded to classical, continuous-time, SISO control using transfer function methods, with frequency and time-domain analysis. Any learning graph should exclude state-space methods, digital control, MIMO systems, and advanced nonlinear/optimal/robust control techniques.

  • State-space representation and state feedback design
  • Discrete-time/digital control (Z-transforms, sampling)
  • Multi-input multi-output (MIMO) systems
  • Lyapunov stability theory
  • Optimal control (LQR, LQG, MPC)
  • Robust control (H∞, μ-synthesis)
  • Adaptive control
  • Nonlinear control methods (beyond basic linearization)
  • Kalman filtering and state estimation
  • Hardware implementation (sensors, actuators, real-time systems)

Note that specific hardware used in labs might be found in an appendix to this book, but they are not mentioned in the main chapter content.

Bloom’s Taxonomy (2001) Learning Objectives

1. Remember

Students will be able to:

  • Recall fundamental control systems terminology
  • Identify standard control system block diagram symbols
  • List common performance specifications for control systems
  • Recognize standard test inputs used in system analysis
  • Recall definitions of stability and steady-state error
  • Identify typical controller structures (P, PI, PID)

2. Understand

Students will be able to:

  • Explain the purpose and benefits of feedback control
  • Describe how system poles and zeros affect response
  • Interpret time-domain response plots
  • Explain the meaning of Bode magnitude and phase plots
  • Summarize stability concepts using qualitative reasoning
  • Describe controller parameter effects on system behavior

3. Apply

Students will be able to:

  • Compute transfer functions from system models
  • Apply Laplace transforms to analyze dynamic systems
  • Calculate time-domain performance metrics
  • Use computational tools to simulate system response
  • Construct block diagrams for interconnected systems
  • Apply standard tuning rules to PID controllers

4. Analyze

Students will be able to:

  • Analyze system stability using root locus techniques
  • Compare open-loop and closed-loop system behavior
  • Analyze frequency response to assess robustness
  • Decompose complex systems into simpler subsystems
  • Evaluate the impact of controller parameters on performance
  • Analyze tradeoffs between speed, accuracy, and stability

5. Evaluate

Students will be able to:

  • Assess whether a control system meets design specifications
  • Judge system robustness using stability margins
  • Critique controller designs based on simulation results
  • Evaluate modeling assumptions and their limitations
  • Compare alternative controller strategies
  • Interpret experimental or simulated data to draw conclusions

6. Create

Students will be able to:

  • Design feedback controllers to meet given requirements
  • Develop mathematical models for new physical systems
  • Integrate modeling, analysis, and simulation into a design workflow
  • Create and document complete control system solutions
  • Implement and test controllers in simulation or laboratory settings
  • Propose design improvements based on performance evaluation

ABET Alignment

This course is designed to align with the student outcomes and curricular expectations of the Accreditation Board for Engineering and Technology (ABET) for undergraduate electrical engineering programs, emphasizing analytical rigor, design competence, and professional engineering practice.

See ABET CRITERIA FOR ACCREDITING ENGINEERING TECHNOLOGY PROGRAMS