Graduate Certificate Programs

Control Systems

Department of Mechanical and Aerospace Engineering

Program Description:
The control systems graduate certificate program is designed for working engineers to enhance their knowledge and provide current information on technological changes in the area of control systems. Earning a graduate certificate not only provides students the opportunity to strengthen their academic background, but also offers the possibility of pursuing a master's degree in the aerospace engineering or mechanical engineering programs.

Students pursuing a graduate certificate in control systems through the aerospace engineering program will select two courses from Group I and two courses from Group II:

  • Group I: Aero Eng 5361, Mech Eng/Aero Eng 5481, Mech Eng/Aero Eng 5001, Mech Eng/Aero Eng 6479
  • Group II: Elec Eng 5300, Elec Eng 6300, Elec Eng 6310

Students wishing to pursue a master of science degree in aerospace engineering should consult with the technical coordinator in aerospace engineering when selecting their courses.

Students pursuing a graduate certificate in control systems through the mechanical engineering program will select two courses from Group I and two courses from Group II:

  • Group I: Mech Eng/Aero Eng 5481, Mech Eng/Aero Eng 5001, Mech Eng/Aero Eng 6479
  • Group II: Aero Eng 5361, Elec Eng 5300, Elec Eng 6300, Elec Eng 6310

Students wishing to pursue a master of science degree in mechanical engineering should consult with the technical coordinator in mechanical engineering when selecting their courses.

Please check the semester wise Schedule of Classes for a current listing of the courses available for distance students.

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Aero Eng 5361: Flight Dynamics: Stability and Control (LEC 3.0)
Review of static stability, dynamic equations of motion, linearized solutions, classical control design and analysis techniques, introduction to modern control. Prerequisite: Aero Eng Eng 3361

Elec Eng 5300: Digital Control (LEC 3.0)
Analysis and design of digital control systems. Review of z transforms; root locus and frequency response methods; state space analysis and design techniques; controllability, observability and estimation. Examination of digital control algorithms. Prerequisites: Elec Eng 3320

Elec Eng 6300: Linear Control Systems (LEC 3.0)
Review of linear algebra, state variable formulations, solutions of state equations; controllability and observability; multivariable systems, matrix fraction decompositions; design of state and output feedback controllers and observers; introduction to calculus of variations; linear quadratic regulators. Prerequisite: Elec Eng 3320

Elec Eng 6310: Optimal Control and Estimation (LEC 3.0)
Review of linear quadratic regulators (LQR), LQR extensions; constrained optimization (Pontragin's minimum principle); review of probability theory and random processes; optimal prediction and filters; frequency domain properties of LQR and Kalman filters; linear quadratic Gaussian (LQG) control; model uncertainties, frequency shaping, LQG/LTR design methodology. Prerequisite: Elec Eng 6300

Mech Eng/Aero Eng 5481: Mechanical and Aerospace Control Systems (LEC 3.0)
Synthesis of mechanical and aerospace systems to perform specific control functions. Response and stability are studied. Singular value analysis for stability margins is introduced. Prerequisite: Mc Eng 4479 or Aero Eng Eng 5361

Mech Eng/Aero Eng 5001: Linear and Nonlinear Estimation: Theory and Applications
This course deals with the development and applications of linear and nonlinear estimation methods. It will begin with discussions on random processes and probability density functions. Formulation and development of Kalman filter for linear systems will be presented. Extended Kalman filter (EKF) for nonlinear systems will be developed and discussed at length. Applications papers in aerospace, mechanical, chemical, manufacturing, design and other disciplines will be considered. Both discrete and continuous versions of the filters will be developed. Implementation considerations will be presented. This course also will look at other nonlinear filters and current developments. Projects will consist of one assignment in linear filters and another assignment in nonlinear estimation and tailored to the background and interests of the students. Reading assignments will consist of technical papers in applications areas.

Mech Eng/Aero Eng 6479: Analysis and Synthesis of Mechanical and Aerospace Systems (LEC 3.0)
A unified treatment of modern system theory for the mechanical and aerospace engineering controls analyst, including analysis and synthesis of linear and nonlinear systems, compensation and optimization of continuous and discrete systems, and theory of adaptivity. Prerequisite: Mc Eng 5481 or Aero Eng Eng 5481

 * Curriculum is subject to change. Please contact the department for up-to-date information on courses. Other courses approved by the department may be substituted for any of the above listed courses on a case-by-case basis. The administrative coordinators must approve the substitution prior to enrolling in the course.

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Bachelor's degree in appropriate engineering discipline with GPA of 2.75 or better; minimum of two years of professional experience. Additionally, students who are currently accepted into aerospace engineering or mechanical engineering programs may pursue the graduate certificate through the respective program.

Graduate Certificate Requirements:
In order to receive a graduate certificate, the student must have a cumulative grade point average of 3.0 or better in the certificate courses taken. Once admitted to the program, the student will be given three years to complete the program as long as a B average is maintained in the courses taken.

Students admitted to the certificate program will have non-degree graduate status but will earn graduate credit for the courses they complete. If the four-course sequence approved by the graduate adviser is completed with a grade of B or better in each of the courses taken, the student will be admitted to the MS degree program in which they pursued the graduate certificate, if they apply. The certificate courses taken by students admitted to the program will count toward their master’s degrees.

Click here for more information on admissions.

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Students applying for a business project management graduate certificate will need the following:

Complete the Online Application. When you start your application select "Graduate Online/Distance" and then select which certificate you are applying for. Don't forget to list your current employer and company location on the application.

More Details

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Gainful Employment Program Disclosure

Effective July 1, 2011, the Department of Education requires that all certificate programs must disclose particular Gainful Employment information to current and prospective students. The information that is provided in the disclosure includes the estimated cost of the certificate program as well as on-time graduation and job placement rates for this particular certificate program. The disclosure information is based on data from the 2016-17 school year (defined as the period between July 1, 2016, and June 30, 2017)

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Graduate certificates were designed as a gateway to a master’s degree. If a student earns a B or better in each certificate course they may continue for the graduate degree (in the corresponding department), without needing to submit GRE/GMAT scores, or letters of recommendation*. A student does not need to continue on for the graduate degree, however most do. Graduate certificates were designed for working professionals who have real life work experience and may not have time to take the GRE/GMAT. Admission requirements for the graduate certificate program are also more relaxed than the graduate degree. This graduate certificate may act as a gateway to the following master’s programs:

Aerospace Engineering (MS)
Mechanical Engineering (MS)

(Applicants must indicate which program they wish to use the certificate as a gateway for when initially applying for the certificate).

*Completion of a graduate certificate program does not automatically guarantee admission into a corresponding graduate degree program. To continue in a master’s degree program, you must apply. Click here for details and check with academic department for program specific details and requirements.

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All courses are offered through distance education in a short condensed format, typically 5-8 weeks in length, over the internet, via live streaming video; collaborative learning software includes WebEx and Blackboard; classes are archived online for review and easy access.

Course Management Software: Blackboard.

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Contact Us

Mechanical and Aerospace Engineering

Dr. Xiaodong Yang
Associate Professor

227 Toomey Hall
400 W. 13th St.
Rolla, MO 65409-0050

Phone: 573-341-6273

Global Learning - Distance Education
Student Support Services

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300 West 12th Street

Rolla, MO 65409-1560

Phone: 573-341-6591

Toll Free: 1-877-678-1870
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