Course Outline (W2024)

BME639: Control Systems and Bio-Robotics

Instructor(s)Dr. Owais Khan [Coordinator]
Office: ENG328
Phone: (416) 979-5000 x 556096
Office Hours:
Calendar DescriptionIntroductory course for Biomedical Engineers: system modeling, simulation, analysis and classical-controller designs of linear, time-invariant, continuous time systems. System dynamic properties in time and frequency domains, performance specifications and basic properties of feedback are investigated. Stability analysis is reinforced through Routh-Hurwitz criterion, Root-Locus method, Bode plots, and Nyquist criteria. Concept of Bio-Robotics is introduced, and exposure to basics of state-space representation and feedback. Key control concepts are experienced through laboratory experiments using modular servo-system with open architecture, fully integrated with MATLab and Simulink; use of simulation tools; and solving design problems.
PrerequisitesBME 532, CEN 199
AntirequisitesELE 639


Compulsory Text(s):
  1. Automatic Control Systems, 10th Edition, Benjamin C. Kuo and Farid Golnaraghi, 2017, McGraw Hill Education
  2. BME639: Lecture Notes, The lecture notes are available from the secure course website as PDF downloadable files.
  3. MATLAB User Manual (including Control Systems Toolbox and Simulink) the Mathworks, Inc., Copyright 1995-2018, available for download on the Departmental Network as Matlab help files.
Reference Text(s):
  1. Control Systems Engineering, Norman S. Nise, 7th edition, 2016, Wiley Inc.
  2. Modern Control Systems, Katsuhiko Ogata, 5th Edition, 2011, Prentice Hall
  3. Feedback Control of Dynamic Systems, 7th Edition, Gene F. Franklin, J. Da Powell, Abbas Emami-Naeini, 2014, Pearson
Learning Objectives (Indicators)  

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

  1. Demonstrates understanding of control system representations, such as block diagrams, signal flow graphs, methods to analyze transient response. (1c)
  2. Demonstrate understanding of stability analysis, such as root locus, Routh-Hurwitz criteria, Nyquist criterion, controller design (PD, PI, and PID) a, and state-space analysis. (1d)
  3. Demonstrate competency in modeling and analysis of a SISO, continuous, LTI control system in a single feedback loop configuration, including specific tasks of defining a system analytical description, its stability and its dynamic response. (2b)
  4. Determine transfer function model of the DC servo motor by applying two methods. First, the theoretical method, by applying the mathematical and scientific principles. Second, the experimental method, by using the real-time experimental data. Then compare the results of the theory and the experiment and explain the behaviour of the process. This includes obtaining and verifying experimental data, assessing the accuracy of the results and explaining sources of possible discrepancies. (3a)
  5. Implement a PI controller on the obtained model by simulation and on the real-time actual DC servo motor. Compare the control system results. Determine the existing constraints in the real-time control and explain their effects on the control systems. (3b)
  6. Identify and then carry out steps required in designing a single loop controller (PID, Lead, Lag and State-feedback) for a low order LTI system to meet a set of specifications and then evaluate the controller design by verifying its performance against a set of criteria. (4a)
  7. Identify and then carry out steps required in designing a simple in-the- loop controller (PID, Lead, Lag and State-feedback) for a low order LTI system to meet a set of specifications and then evaluate the controller design by verifying its performance against a set of criteria. (4b)
  8. Demonstrate proficiency in the use of high-performance engineering modeling and analysis software (Matlab and Simulink) for control system analysis and design in this course, and for subsequent engineering practice. (5a)
  9. Work effectively as a member of a team in the laboratory, manage the time to complete the lab projects appropriately in the given time schedule and submit the lab report according to the submission due date. Produce a lab summary individually and submit it with along the lab report to explain the teamwork has been done to achieve the goals of the lab project. (6a)
  10. Produce a technical report using appropriate format, grammar, and citation styles, with figures and tables are carefully chosen to illustrate points made, with appropriate size, labels, and references in the body of the report, and respond appropriately to verbal questions from instructors - lab interviews. (7a), (7b), (7c)
  11. Involve and play an active role in the lab projects, take a responsibility to complete the part of the lab project that has been assigned to do and produce a technical lab report for the assignment. (8b)

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
1.5 hours of lab per week for 12 weeks
0.0 hours of tutorial per week for 12 weeks

Teaching AssistantsTBA
Course Evaluation
Midterm Exam 34 %
Final Exam 45 %
Labs 1-3 (3 x 7% in pairs) 21 %
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).

ExaminationsMidterm exam in Week 7  during the Lecture time, two hours, problem solving, closed book (covers Week 1-6).
 Final exam during exam period, closed-book (covers Weeks 1-13).
Other Evaluation InformationThere are assignment problems for each chapter posted on the course D2L. The assignment will not be collected. However, students are expected to solve the assignment problems.
Other InformationLab marks are based on attendance, successful completion of pre-lab problems, participation, completion of experiment steps, lab reports and successful reply to your TA questions during submission. Students will have the responsibility to achieve a working knowledge of the software packages that will be used in the lab. Students will work in groups of two.

Course Content



Chapters /

Topic, description

Week 1


Chapter 1, 3

Introduction: Information session, General concepts of feedback and control systems, Closed-loop control versus Open-loop control, Differential Equations and Laplace Transform Review.

Week 2


Chapter 2.2, 4.1-4.2

System Modeling and Representation: Modeling of Electrical Networks, Transfer function representation, Block diagram rules and simplifications, Signal flow graphs Mason's Gain Formula.

Week 3


Chapter 7.1-7.5,7.8

Linear System Time Response: Transient response analysis, First-order systems, Second-order systems, Higher-order systems and dominant poles.

Week 4


Chapter 5, 7.6

Stability Analysis: BIBO stability definition, Characteristic polynomials, Poles and stability conditions of LTI systems, Routh-Hurwitz stability criterion, Steady-State error analysis of feedback systems.

Week 5


Chapter 9

Root Locus Analysis: Closed-loop pole relation to the loop gain, Root locus graphical method of pole representation, Magnitude and angle laws, Root-locus plotting rules.

Week 6


Chapter 7.7, 11.5

Root Locus Design: Static feedback design, Gain selection from root-locus, Dynamic compensation design, Effect of adding pole/zeros to root-locus, Lead/Lag networks Lead/Lag compensator design in time-domain.

Winter Study Week

Week 7


Practice Problems

Midterm Test.

Week 8


Chapter 10.1-10.2

Frequency Response Analysis: Frequency response, Frequency-domain representation, Bode Diagram, Relation between magnitude and phase, Cross over frequency Bandwidth.

Week 9


Chapter 10.4-10.11

Frequency Response Analysis: Polar Plots Nyquist Diagram Nyquist stability criteria Relative stability, Stability margins, Gain margin and phase margins

Week 10


Chapter 11.1-11.5

Frequency Response Design: Lead/Lag compensator and P PI PD and PID controller design in frequency-domain

Week 11


Chapter 8.1-8.11

State-Space Analysis: State-space representation of systems, State diagrams and state variables, State-space equations from high-order differential equations, State transition matrix, Characteristic equation and eigenvalues.

Week 12


Chapter 8.12-8.19

State-Space Design: Controllability and Observability of Linear Systems, State feedback control, Tracking objectives, Pole placement method, State feedback with integral control

Week 13


Practice Problems

Course Review: Review of Controller Design in Frequency Domain: Lead/Lag and PID Examples. Wrap up.

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





Lab 1.1

Lab # 1.1: Introduction to Simulink, Open-Loop Control vs. Closed-Loop Control


Lab 1.2

Lab # 1.2: Transient Response Analysis and Stability of 2nd and 3rd Order Systems.


Lab 2.1

Lab # 2.1: Transfer Function Modeling of Physical Systems and Control.


Lab 2.2

Lab # 2.2: Introduction to Lead and Lag Compensators


Lab 3.1

Lab # 3.1: Introduction to PI PD and PID Controllers


Lab 3.2

Lab # 3.2: State Space Modeling of Physical Systems and Control.

University Policies & Important Information

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Refer to the Departmental FAQ page for furhter information on common questions.

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