Online Education for Working Professionals
Develop a foundation of analytical mechanics and multiphysics modeling.

Dynamic Systems—Graduate Certificate

Dynamic Systems

Use individual and team exercises to build skills for a dynamic systems approach.

Engineered systems increasingly must exploit complex interactions between multiple domains—mechanical, electrical, chemical and biological. Numerical model prediction is a powerful tool for optimal design, vibration analysis, test plan development, and control system design. Through a combination of theory and practice, this certificate helps engineers model, analyze, and control multiphysics dynamic systems using MATLAB Simulink and Simscape.

3 courses in 3 semesters.

Department Mechanical Engineering-Engineering Mechanics
Admissions requirement Acceptance to the Graduate School.
Contact Jason Blough
Length 3 courses in 2-3 semesters
Effort 3 hours per credit per week
Each course 3 credits
Total credits 9
Course type Online or on-campus
Modality Watch class recordings on demand
Cost Based on credits and course type
Already enrolled? Speak with your advisor.

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Progress quickly with a compact curriculum.

Work with the program advisor to select courses that fit your interests and pre-requisite skills.

Check your preparation.

Here are some of the pre-requisite courses for this certificate.

EE 3261 - Control Systems

Mathematical formulation of control problems (both transfer function and state-variable descriptions); analysis of feedback control systems (stability, transient performance, steady-state error, sensitivity, etc.); analog and digital simulation; and experiments with physical systems.

  • Credits: 3.0
  • Lec-Rec-Lab: (2-0-2)
  • Semesters Offered: Fall, Spring
  • Pre-Requisite(s): EE 3160

MEEM 3400 - Mechanical System Design and Analysis

In this course, students learn mechanical synthesis and analysis methods. They use case studies to develop relationships between design and performance. They apply synthesis methods to the design of a new product.

  • Credits: 3.0
  • Lec-Rec-Lab: (0-3-0)
  • Semesters Offered: Fall, Spring, Summer
  • Restrictions: Must be enrolled in one of the following Major(s): Mechanical Engineering
  • Pre-Requisite(s): MEEM 2150 and MEEM 2700

MEEM 3750 - Dynamic Systems

This course deals with the modeling, analysis and control of mixed physics systems. It covers differential equation generation for mechanical, thermal, and electrical systems, their simulation, and methods for analyzing their performance operating in both open and closed loop.

  • Credits: 4.0
  • Lec-Rec-Lab: (0-4-0)
  • Semesters Offered: Fall, Spring, Summer
  • Restrictions: Must be enrolled in one of the following Major(s): Mechatronics, Mechanical Engineering
  • Pre-Requisite(s): MEEM 2700 and (MA 3520 or MA 3521 or MA 3530 or MA 3560)

Take 6 credits of required courses.

Take MEEM 5730 Dynamic System Simulation if it is offered, or take MEEM 5990 as Special Topics: Dynamic System Simulation.

MEEM 5701 - Intermediate Dynamics

Intermediate study of several topics in engineering dynamics, including three-dimensional kinematics and kinetics, generalized coordinates, Lagrange's equation, and Hamilton's principle. Uses computer-aided dynamic simulation tools for analyzing dynamic systems.

  • Credits: 3.0
  • Lec-Rec-Lab: (0-3-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Major(s): Mechanical Engineering, Mechanical Eng-Eng Mechanics, Engineering Mechanics
  • Pre-Requisite(s): MEEM 4901(C) or ENT 4950(C) or Graduate Status >= 1

MEEM 5990 - Special Topics

Study of selected subjects related to mechanical engineering or engineering mechanics.

  • Credits: variable to 3.0; May be repeated
  • Semesters Offered: Fall, Spring, Summer
  • Restrictions: Permission of department required; Must be enrolled in one of the following Level(s): Graduate

Take a 3 credit elective course.

MEEM 4450 - Vehicle Dynamics

This course will develop the models and techniques needed to predict the performance of a road vehicle during drive off, braking, ride, and steering maneuvers. Topics to be covered include: acceleration and braking performance, power train architecture, vehicle handling, suspension modeling, tire models, and steering control. Matlab, Adams Car, and Amesim, will be used as computational tools.

  • Credits: 3.0
  • Lec-Rec-Lab: (0-3-0)
  • Semesters Offered: Spring
  • Restrictions: Must be enrolled in one of the following College(s): College of Engineering; Must be enrolled in one of the following Class(es): Junior, Senior
  • Pre-Requisite(s): MEEM 3400 or EE 3261

MEEM 4775 - Analysis & Design of Feedback Control Systems

This course covers topics of control systems design. Course includes a review for modeling of dynamical systems, stability, and root locus design. Also covers control systems design in the frequency domain, fundamentals of digital control and nonlinear systems.

  • Credits: 4.0
  • Lec-Rec-Lab: (0-3-2)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Major(s): Mechanical Eng-Eng Mechanics, Mechatronics, Engineering Mechanics, Mechanical Engineering
  • Pre-Requisite(s): MEEM 3750

MEEM 5702 - Analytical Vibroacoustics

First in a series of two courses on vibro-acoustics to provide a unified approach to study noise and vibration. Emphasizes interaction between sound waves and structures. Presents advanced vibration concepts with computational tools. Discusses wave-modal duality.

  • Credits: 3.0
  • Lec-Rec-Lab: (0-3-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Major(s): Mechanical Engineering, Mechanical Eng-Eng Mechanics, Engineering Mechanics
  • Pre-Requisite(s): MEEM 4901(C) or ENT 4950(C) or Graduate Status >= 1

MEEM 5715 - Linear Systems Theory and Design

Overview of linear algebra, modern control; state-based design of linear systems, observability, controllability, pole placement, observer design, stability theory of linear time-varying systems, Lyapunov stability, optimal control, linear quadratic regulator, Kalman filter,

  • Credits: 3.0
  • Lec-Rec-Lab: (0-3-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate; Must be enrolled in one of the following Major(s): Mechanical Engineering, Mechanical Eng-Eng Mechanics, Engineering Mechanics
  • Pre-Requisite(s): MEEM 3750 or EE 3261

EE 5715 - Linear Systems Theory and Design

Overview of linear algebra, Modern Control: state-space based design of linear systems, observability, controllability, pole placement, observer design, stability theory of linear time-varying systems, Lyapunov stability, optimal control, Linear Quadratic regulator, Kalman filter, Introduction to robust control.

  • Credits: 3.0
  • Lec-Rec-Lab: (0-3-0)
  • Semesters Offered: Fall
  • Restrictions: Must be enrolled in one of the following Level(s): Graduate; Must be enrolled in one of the following Major(s): Electrical Engineering, Electrical & Computer Engineer
  • Pre-Requisite(s): EE 3261 or MEEM 3750

The minimum completion time is two semesters.

Here is a typical schedule.

Fall Spring
MEEM 5701
MEEM 4775
MEEM 5730

Interested in taking a single, online course? Enroll as a non-degree seeking student.

Upon completion of the Certificate the student should be able to:

  1. Develop differential equation models of multiphysics dynamic systems exploiting methods from analytical mechanics
  2. Create simulations of dynamic systems to achieve specified accuracy requirements using advanced MATLAB, Simulink, and Simscape techniques
  3. Develop and select integration schemes for both real-time (embedded) and batch simulations
  4. Design advanced control systems or conduct vibration analysis studies for complex dynamic systems
  5. Communicate the dynamic system analysis process through written project reports including: statement of assumptions, equation of motion derivation, listing of conserved quantities, numerical model architecture justification, and steps taken to verify numerical results

Michigan Tech was founded in 1885.

The University is accredited by the Higher Learning Commission and widely respected by fast-paced industries, including automotive development, infrastructure, manufacturing, and aerospace. Michigan Tech graduates deliver on rapid innovation and front-line research, leaning into any challenge with confidence.

The College of Engineering fosters excellence in education and research.

We set out as the Michigan Mining School in 1885 to train mining engineers to better operate copper mines. Today, more than 60 percent of Michigan Tech students are enrolled in our 17 undergraduate and 29 graduate engineering programs across nine departments. Our students and curriculum embrace the spirit of hard work and fortitude our founders once had. Our online graduate courses are the same, robust classes taken by our doctorate and masters candidates, taught directly by highly regarded faculty, with outstanding support from staff. We invite working professionals to join these courses, bring their own experience and challenges as part of the discussion. Leverage the national reputation of Michigan Tech to advance your career in tech leadership.

Meet the online certified instructors.

Students have the flexibility to review class recordings later.

Andrew Barnard

Andrew Barnard

Director, Great Lakes Research Center

Teaching Statement

Dr. Barnard has interests in acoustics, noise control, and vibration, as well as water resources and marine technology.

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Jason Blough

Jason Blough

Distinguished Professor, Mechanical Engineering—Engineering Mechanics

Teaching Statement

Dr. Blough teaches classroom and industry short course topics on dynamic measurement, signal analysis, and other experimental noise, vibration, and harshness techniques.

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Steven Ma

Steven Ma

Professor of Practice, Mechanical Engineering–Engineering Mechanics

Teaching Statement

Dr. Ma teaches courses in mechanical system design and analysis, advanced CAD and CAM methods, mechanism synthesis, dynamic modeling, and vehicle dynamics.

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Gordon Parker

Gordon Parker

John and Cathi Drake Endowed Chair in Mechanical Engineering

Teaching Statement

Dr. Parker teaches courses in dynamic systems, control, robotics, and mechatronics, as well as linear and nonlinear system theory.

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Wayne Weaver

Wayne Weaver

Associate Professor, Mechanical Engineering-Engineering Mechanics

Teaching Statement

Dr. Weaver teaches on propulsion systems for hybrid electric vehicles and linear systems theory and design.

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Yongchao Yang

Yongchao Yang

Assistant Professor, Mechanical Engineering-Engineering Mechanics

Teaching Statement

Dr. Yang teaches on topics of statics, shock, and vibration.

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