MECH 412 - System Dynamics and Control

Modelling of physical linear time-invariant systems using transfer functions. Transient and steady-state response specifications. State space representation of systems. Frequency-response characterization. Stability. Feedback control systems. PID controller design. Frequency response design methods. Lead, lag and PID compensators.

Instructor: Prof. James Richard Forbes

Course Overview

MECH 412 introduces modelling, analysis, and design methods for feedback control systems. Students develop mathematical models of engineering systems, study their dynamic behaviour, and design controllers that meet performance and robustness requirements.

Topics include:

  • Transfer functions and state-space models
  • Dynamic modelling of physical systems
  • System identification
  • Time-domain and frequency-domain response
  • Feedback control
  • PID, lead, and lag compensator design
  • Loop shaping and robustness

Prerequisite and Corequisite Courses

Students are expected to be comfortable with:

  • Calculus
  • Differential equations
  • Linear algebra
  • Python programming

Prerequiste Courses

  • MECH 309
  • MECH 315

Corequisite Courses

  • MECH 331

Python Resources

The course makes extensive use of Python and the python-control package.

Useful resources:

Learning Outcomes

By the end of the course, students will be able to:

  • Derive dynamic models suitable for control-system analysis.
  • Analyze system behaviour in both the time and frequency domains.
  • Design controllers that satisfy performance and robustness specifications.
  • Apply mathematics, simulation, and engineering tools to solve control problems.
  • Use modern computational tools to support engineering decision making.

Textbooks

There is no required textbook. However, lectures are based on the following references.

  • L. Qiu and K. Zhou, Introduction to Feedback Control. Upper Saddle River, NJ: Prentice-Hall, Inc., 2010.
  • L. Guzzella, Analysis and Synthesis of Single-Input Single-Output Control Systems, 4th ed. ETH Zurich: vdf Hochschulverlag AG, 2019.
  • P. Seiler and J. Theis, An Introduction to Classical Control and Loopshaping. Ann Arbor, MI: University of Michigan, 2022.
  • W. J. Palm, System Dynamics, 3rd ed. Toronto, ON: McGraw Hill, 2013.
  • K. A. Seeler, System Dynamics. New York, NY: Springer, 2014.

Additional Resources

Schedule

Week Date Topic Materials
1 Sep/Jan Mathematical Review

ODEs, state-space models, linearization.
2 Sep/Jan Applications of Laplace Transforms

Laplace Transforms, transfer functions, block diagrams.
3 Sep/Jan Physical System Models

Mechanical, electrical, hydraulic, and thermal systems.
4 Sep/Jan System Identification

Building mathematical models from experimental data.
5 Oct/Feb Open-Loop System Properties

Stability concepts and the Routh-Hurwitz criterion.
6 Oct/Feb Time-Domain Analysis

First- and second-order transient response specifications.
7 Oct/Feb Frequency Response

Bode plots and frequency-domain signal analysis.
8 Oct/Feb The Control Problem

Feedback systems, well-posedness, and internal stability.
9 Nov/Mar Classical Controllers

P, PI, PD, PID, lead, lag, and lead-lag compensators.
10 Nov/Mar Nyquist Analysis

Nyquist stability criterion and robustness analysis.
11 Nov/Mar Design Margins

Gain margin, phase margin, and vector margin.
12 Nov/Mar Loop Shaping

Frequency-domain controller design techniques.
13 Dec/Apr Robust Control

Model uncertainty and robust control methods.