Subsea Engineering

Course — MECE 6397: Feedback Control Systems

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Usually offered in the Spring Semester.


Design and stability analysis in s-plane (root locus), frequency domain (loop shaping) and time domain (state space); state observers; Kalman-Bucy filter; linear quadratic regulator (LQR); servomechanisms; linear quadratic Gaussian (LQG) and loop transfer recovery (LTR); discrete and digital systems and use of z-plane design; nonlinear systems; phase plane; gain scheduling; feedback linearization; Lyapunov theorem; sliding mode and back-stepping control. Students will complete an extended design case.
Students who complete the course should be able to analyze the response of and design control systems for engineered systems. Specifically, students should be able to:

  • Analyze the time dynamic response of electromechanical, and mechatronic systems using systematic techniques.
  • Analyze the behavior of interconnected dynamic systems.
  • Analyze the stability and the transient and steady state response of feedback control systems.
  • Design feedback control systems using frequency domain design techniques.
  • Design feedback control systems using state space techniques.
  • State estimation and observation theories.
  • Design optimal control systems.
  • Design digital control systems.
  • Analyze stability of nonlinear systems.
  • Design robust control system for nonlinear system.

Topics Covered: 

This course contributes to the students' knowledge of engineering topics. Students learn how to model and analyze the responses of a variety of mechanical and electrical dynamic systems and how to design and implement controllers for these systems using frequency and time response domain input-output and state space design techniques.

Theoretical concepts and design techniques are reinforced through the simulation platforms. Students develop modest proficiency in computer-aided tools, specifically Matlab Control System Toolbox and Simulink, both of which are used ubiquitously in the industry. Issues related to the impact of engineering solutions in an economic, environmental, and societal context are also discussed in the course. For practical issues including the use of control systems for performance in many electromechanical and mechatronic systems, economical designs that are easier to build by relaxing manufacturing tolerances and improve system energy consumption efficiency. Some of the topics introduced during the course are:

  • Introduction to control systems and Laplace transform.
  • Mathematical modeling of mechanical and electrical systems and manipulation of block diagrams.
  • Open loop and closed loop transfer function and stability based on Routh-Hurwitz.
  • Root locus analysis and lead lag compensator based on root locus analysis.
  • Frequency response, Bode and Nyquist plots, performance specifications in the frequency domain, phase margin, gain margin and sensitivity analysis.
  • Nyquist stability criterion, performance evaluation in the frequency domain, non-minimum phase systems.
  • Lead and lag compensation and frequency domain design and loop shaping.
  • State-space coordinates transformations, canonical realizations, controllability, observability and state feedback control.
  • State estimation, reduced-order observer and Kalman-Bucy filter.
  • Linear Quadratic Regulator (LQR), servomechanisms.
  • Linear Quadratic Gaussian (LQG) and linear transfer recovery (LTR).
  • Digital control system, Z-transform, design and stability analysis.
  • Nonlinear control system, state portrait, limit cycles, local and global stability.
  • Gain-scheduling and feedback linearization, Lyapunov theory and stability analysis.
  • Sliding mode and back-stepping control systems.

Course Grading: 

The course grade will be based on homework assignments, quizzes, design project and final exam.


A final design problem will be assigned by the end of September. This problem will allow applying the topics covered in the course to a realistic design problem. Students must work individually on this problem; only course staff can be consulted with questions.