Course Outline (F2023)

ELE829: System Models and Identification

Instructor(s)Md Waselul Haque Sadid [Coordinator]
Office: TBA
Phone: TBA
Office Hours: Wednesday 10:00 - 11:00
Calendar DescriptionIntroduction to modern methods of linear system identification. Different types of models. Review of classic time- and frequency-based approach to empirical, 'black-box' system modeling. Non-parametric identification: impulse and step weights, spectral analysis. Parametric, discrete transfer function models from I/O data using Least Squares. Data-collection procedures, model structure selection, use of auto- and cross-correlation functions for diagnostics and model validation, overview of different estimation algorithms.
PrerequisitesELE 639




Compulsory Text(s):
  1. ELE829: Course Notes, available from the secure course website (login at as PDF downloadable files.
  2. MATLAB System Identification Toolbox (Matlab R2020) and System Identification Toolbox, User Guide, L. Ljung, the MathWorks, Inc., Copyright 1995-2020, available on the Departmental Network as Matlab help files.
Reference Text(s):
  1. System Identification - Theory for the User, L. Ljung, Prentice Hall, 11th Edition, 2009.
  2. System Identification, T. Soderstrom, P. Stoica, Prentice Hall, 1994.
Learning Objectives (Indicators)  

At the end of this course, the successful student will be able to:

  1. Demonstrates competency in developing mathematical models for deterministic systems (dynamic processes) and for stochastic systems (noise). Uses relevant computer simulation software - MATLAB System Identification Toolbox. Identifies and carries out steps required in performing a successful model identification procedure. Evaluates the effect of uncertainty in model parameters. (2b)
  2. Applies the tools for system identification to a real-time servomotor system, including obtaining experimental data. Selects appropriate analytical model for the real-time servomotor system, and verifies the model by comparing to experimental results. (3a)
  3. Selects appropriate analytical model for the real-time servomotor system, and verifies the model by comparing to experimental results. Assesses accuracy of the results obtained from the real-time servomotor system, verifying experimental data and explaining sources of possible discrepancies (non-linearity). (3b)
  4. Designs data collection experiments for diagnostics and identification of the model, selects appropriate model structure (BJ model) and noise filter function, and appropriate Least Squares Algorithm. (4b), (4a)
  5. Evaluates the quality of the derived system and noise models by validating against a set criteria, then improves the design until the model is validated. (4c)
  6. Demonstrates proficiency in the use of high-performance engineering modeling and analysis software, including System Identification Toolbox, in this course, and for subsequent engineering practice by completing and demonstrating to the professor the required simulation and analyses to perform system and noise model diagnostics, identification and verification. (5a)
  7. Helps other team members, and accepts help, on technical and team issues. Demonstrates capacity for team leadership while respecting others roles. Evaluates team effectiveness and plans for improvements. (6b)
  8. Produces a professionally prepared technical report using appropriate format, grammar, and citation styles, with figures and tables chosen to illustrate points made, with appropriate size, labels and references in the body of the report. Reports are graded on correctness, completeness, grammar, quality of graphics and layout. (7a)
  9. Responds appropriately to verbal questions from instructors, formulating and expressing ideas, using appropriate technical terminology this is assessed through comprehensive lab interviews by instructors. (7b)
  10. Demonstrates an understanding of project management principles, applying them both to the individual final project and to group tutorials. These include: negotiating the project scope, managing the deadlines, decomposing projects into key tasks and allocating responsibilities and resources according to deadlines. (11b)

NOTE:Numbers in parentheses refer to the graduate attributes required by the Canadian Engineering Accreditation Board (CEAB).

Course Organization

3.0 hours of lecture per week for 13 weeks
1.0 hours of lab per week for 12 weeks
0.0 hours of tutorial per week for 12 weeks

Teaching AssistantsShayan Sepahvand,
Course Evaluation
Course Activities (Individual/Group) 20 %
Final Project Report (Individual) 40 %
Lab/Tutorial Project (Group) #1 9 %
Lab/Tutorial Project (Group) #2 9 %
Lab/Tutorial Project (Group) #3 9 %
Lab/Tutorial Project (Group) #4 13 %
TOTAL:100 %

Note: In order for a student to pass a course, a minimum overall course mark of 50% must be obtained. In addition, for courses that have both "Theory and Laboratory" components, the student must pass the Laboratory and Theory portions separately by achieving a minimum of 50% in the combined Laboratory components and 50% in the combined Theory components. Please refer to the "Course Evaluation" section above for details on the Theory and Laboratory components (if applicable).

ExaminationsCourse evaluation is ongoing and semester-long, and includes both group work (lab/tutorial reports) and individual effort (final project). All reports include simulations. The course professor verifies all individual codes submitted with the final report. If the execution of the code does not support claims in the report, the project will receive a non-negotiable and significant reduction in the grade.
Other Evaluation InformationCourse activities are part of the ongoing and semester-long evaluation: there are graded activities in every week of classes (on top of scheduled tutorial/lab reports). The graded activities include both individual assessments (D2L quizzes), homework assignments and computer simulations on the application of theory learned, which are then demonstrated to the professor in class.
Teaching MethodsLectures and Tutorials will be conducted in person. Students will have access to course materials on D2L. Students will be required to complete D2L Quizzes and Homework Assignments using upload features of D2L. All tutorials and final project reports have to be uploaded to D2L. Zoom teleconferencing software will be used for individual consultation, office hours, and individual student simulation presentations.
Other InformationStudents will learn to work MATLAB System Identification Toolbox in the tutorial session with the help of course TA.

Course Content



Chapters /

Topic, description

Week 1


Goals for the course and course logistics. Overview: terminology, objectives, introduction to modern identification procedures (diagnostics, identification, validation), types of models. Data Collection - PRBS signal. Introduction to Matlab System Identification Toolbox. Introduction to Tutorial # 1. Review - frequency response, Bode plots for conventional modeling.

Week 2


Modeling: Non-parametric models in frequency domain: SPA, ETFE. Review: Transfer function models, conversion between continuous and discrete representations, sampling. Modeling - simple Box-Jenkins model structures: OE Model (deterministic process, white noise). Diagnostic tools in frequency domain - summary. Activity # 1 due.

Week 3


Introduction to Tutorial # 2: Non-parametric models in time domain. Review - time domain response for conventional modeling (Step and Impulse response plots). Review of basic definitions of stochastic processes. Non-parametric models in time domain: impulse and step weights from de-convolution and from correlation analysis. The effect of noise on non-parametric models in time domain. Simple parametric, non-robust, discrete transfer function models from impulse weights. Hankel Test of system order. Activity # 2 due.

Week 4


Diagnostic tools in time domain summary. Review of matrix algebra. Introduction to Least Squares methods. Robustness of parametric models, The effect of noise on conventional parametric models (non-robust and robust).

Week 5


Introduction to time-series modeling. Combined dynamic-stochastic models - Box-Jenkins structures. Overview of different parameter estimation algorithms. Figures of Merit for Model selection: Akaike Index, Loss Function. Refining OE model: ACF, PACF and CCF checks. Activity # 3 (D2L Quiz) due.

Week 6


Validation for OE Model: Residue whiteness testing - Chi-Square tests, Confidence Intervals. Full examples of OE Model Identification and Validation. Hands-on simulations and group work.

Week 7


Hands-on simulations and group work - Activity # 4 due. Introduction to Tutorial # 3: Stochastic noise models. Noise models: AR, MA, ARMA, processes. Auto- and Partial Auto-Correlation Functions as diagnostic tools for stochastic noise models.

Week 8


Hands-on simulations and group work - Activity # 6 due. Summary of all diagnostic tools for all Box-Jenkins models: non-parametric time and frequency domain models, Auto- and Partial Auto-Correlation functions.

Week 9


Hands-on simulations and group work- Activity # 7 due. Refining BJ model: ACF, PACF and CCF checks. Complete Validation for BJ Model: Residue whiteness testing - Chi-Square tests, Confidence Intervals. Activity # 8 (D2L Quiz) due.

Week 10


Hands-on simulations and group work - Activity # 9 due. Review - designing data collection experiment, model structure selection, complete diagnostics, structure revisions and final model validation. Examples of a full system identification procedure.

Week 11


Hands-on simulations and group work - Activity # 10 due. Overview of the Final Project (individual): "Black Box" System Identification of two systems (OE and PEM structures). Questions and answers regarding the project.

Week 12


Hands-on simulations and group work. Questions and answers regarding the final project, active consultation on final project computer simulations. Activity # 11 (D2L Quiz) due.

Week 13


Questions and answers regarding the final project, active consultation on final project computer simulations. Final Project due on December 6.

Laboratory(L)/Tutorials(T)/Activity(A) Schedule






Tutorial 1: Diagnostic Tools in Frequency Domain and Simple Model identification - OE Model (2 sessions)
 Part 1 - Non-Parametric Models in Frequency Domain as Diagnostic Tools.
 Part 2 - Simple Model Identification using OE Model.
 Part 3 - Conventional Parametric Model from Frequency Response Data.



Tutorial 2: Diagnostic Tools in Time Domain and Simple Model identification - OE Model (2 sessions)
 Part 1 - Non-Parametric Models in Time Domain as Diagnostic Part 2 - Simple Model Identification using OE Model.
 Part 3 - Conventional Parametric Model from Frequency Response Data.     
 Week 4: Tutorial 1 Report due/Tutorial 1 Quiz online.



Tutorial 3 - Stochastic Noise Models - Identify structure of four different noise models (2 sessions)
 Week 6: Tutorial 2 Report due/Tutorial 2 Quiz online.



Tutorial 4 - Simple System Identification of a Real-Life System – Servomotor (3 sessions)
 Part 1: Obtaining Experimental Frequency and Time Domain Responses from the Servo-motor.
 Part 2: Model Identification and Comparisons with Nominal Values Model.                                                                         
 Week 8: Tutorial 3 Report due/Tutorial 3 Quiz online.
 Week 11: Tutorial 4 Report due/Tutorial 4 Quiz online.

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