**Systems and Robotics**

The interface between engineering systems and robotics is an area that demands sophisticated mathematical abilities. This area is characterized by the use of sophisticated control methods with electronic/digital implementations, active structural materials, and other topics from classical mechanical design. The Systems and Robotics option blends mathematics, electrical engineering, and mechanics into one cohesive program.

In addition to the common core of mathematics courses, students in Systems and Robotics take courses in electronics, microprocessor systems, and electric machines from the Electrical and Computer Engineering Department, dynamics and mechanics from Physics, and advanced systems engineering and control courses offered by the Mathematics and Statistics Department. Graduates of the program are exceptionally well-prepared for careers in systems engineering, mechatronics, and robotics, as well as careers in any field requiring strong analytical skills.

**Second Year Courses**

ELEC 221: Electric CircuitsThis course introduces the circuit analysis techniques which are used in subsequent courses in electronics, power, and signals and systems. Circuits containing resistance, capacitance, inductance, and independent and dependent voltage and current sources will be studied. Emphasis is placed on DC, AC, and transient analysis techniques.

ELEC 252: Electronics IThis course is an introduction to semiconductor electronics for students in the Electrical Engineering program and related programs. Topics studied include: operational amplifiers; dc and small signal models for diodes, basic principles of bipolar transistors and field effect transistors, dc analysis of electronic circuits and practical applications of the devices to the design of power supplies, amplifiers and digital logic circuits.

ELEC 271: Digital SystemsBoolean algebra applied to digital systems; logic gates; combinational logic design; electronic circuits for logic gates; arithmetic circuits; latches and flipflops, registers and counters; synchronous sequential logic and state machine design; implementation in programmable logic chips.

ELEC 274: Computer Architecture Number and data representation. Logical structure of computers. Instruction set architecture. Instruction execution sequencing. Assembly-language programming. Input/output interfaces and programming. Processor datapath and control unit design. Semiconductor memory technology and memory hierarchy design.

ENPH 225: MechanicsExtension of classical mechanics and engineering applications. Plane dynamics, relative motion and forces in moving and accelerated reference frames. Introduction to general three-dimensional motion of a rigid body, inertia tensor and steady-state precession. The laws of conservation of mass, momentum and energy.

**Third Year Courses**

ELEC 278: Fundamentals of Information StructuresFundamentals of Data Structures and Algorithms: arrays, linked lists, stacks, queues, deques, asymptotic notation, hash and scatter tables, recursion, trees and search trees, heaps and priority queues, sorting, and graphs. Advanced programming in the C language. Introduction to object oriented programming concepts in the context of data structures.

ELEC 371: Microprocessor Interfacing and Embedded SystemsMicroprocessor bus organization and memory interfaces; parallel input/output interface design; assembly-language and high-level-language programming; interrupts and exceptions; timers; embedded systems organization and design considerations; integration in microcontrollers and programmable logic chips; interfacing with sensors and actuators; embedded system case studies.

ENPH 239: Electricity and MagnetismThe experimental basis and mathematical description of electrostatics, magnetostatics and electromagnetic induction, together with a discussion of the properties of dielectrics and ferromagnetics, are presented. Both the integral and vector forms of Maxwell’s equations are deduced.

MTHE 351: Probabilty IProbability theory: probability models; random variables; jointly distributed random variables; transformations and generating functions. Inequalities and limit laws. Distributions: binomial, Poisson, exponential, gamma, normal. Applications: elementary stochastic processes, time-to-failure models, binary communication channels with Gaussian noise.

MTHE 353: Probability IIIntermediate probability theory as a basis for further study in mathematical statistics and stochastic processes; probability measures, expectations; modes of convergence of sequences of random variables; conditional expectations; independent systems of random variables; Gaussian systems; characteristic functions; Law of large numbers, Central limit theory; some notions of dependence.

**Fourth Year Courses**

MTHE 430: Modern Control TheoryThis course covers core topics in modern control theory: Linearization, existence and uniqueness of trajectories for nonlinear and linear systems, the transition matrix, controllability, observabiity, minimal realizations, feedback stabilization, linear state observers, optimal control theory, the linear quadratic regulator, dynamic programming.

MTHE 474: Information TheoryTopics include: information measures, entropy, mutual information, modeling of information sources, lossless data compression, block encoding, variable-length encoding, Kraft inequality, fundamentals of channel coding, channel capacity, rate-distortion theory, lossy data compression, rate-distortion theorem.

MTHE 472: Control of Stochastic SystemsThis course concerns the optimization, control, and stabilization of dynamical systems under probabilistic uncertainty with applications in engineering systems and applied mathematics. Topics include: controlled and control-free Markov chains and stochastic stability; martingale methods for stability and stochastic learning; dynamic programming and optimal control for finite horizons, infinite horizons, and average cost problems; partially observed models, non-linear filtering and Kalman Filtering; linear programming and numerical methods; reinforcement learning and stochastic approximation methods; decentralized stochastic control, and continuous-time stochastic control.

**Technical Electives**

In the fourth year of the program, students choose four technical electives to compliment the core courses and explore their individual interests. At least one must be chosen from List I and the remaining from List I or List II so that they satisfy certain engineering design and engineering science criteria. Course offerings change year to year.

See the current Academic Calendar for a complete list of offered technical electives.

### List I

MTHE 439: Lagrangian Mechanics, Dynamics, and ControlGeometric modelling, including configuration space, tangent bundle, kinetic energy, inertia, and force. Euler-Lagrange equations using affine connections. The last part of the course develops one of the following three applications: mechanical systems with nonholonomic constraints; control theory for mechanical systems; equilibria and stability.

MTHE 477: Data Compression and Source CodingTopics include: arithmetic coding, universal lossless coding, Lempel-Ziv and related dictionary based methods, rate-distortion theory, scalar and vector quantization, predictive and transform coding, applications to speech and image coding.

MTHE 455: Stochastic Processes and ApplicationsMarkov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Brownian motion and Poisson processes, queuing theory, branching processes.

### List II

ELEC 353: Electronics IITransistor-level modeling and design of analog and digital electronic circuits. Differential amplifiers, Gilbert Cell multipliers, multi-stage amplifiers, amplifier frequency response, negative feedback amplifiers, LC-tank and crystal oscillators, two-port networks. Advanced concepts in logic design. Students learn the basics of computer aided design (CAD) of integrated circuits including schematic simulation, layout, design rules, layout versus schematic verification and extracted circuit simulation. Laboratory work is design-oriented and students are introduced to advanced test and measurement techniques using vector network analyzers.

ELEC 431: Power ElectronicsThis course introduces the basic concepts of power electronics, which include power semiconductor devices and switching power converters. Emphasis is placed on the analysis and design of various power electronics circuits. Their industrial application, such as in telecommunications and computing, will also be discussed. More specifically, the course will cover the characteristics of switching devices, especially that of MOSFET. The course will also cover the operation of various switching converters such as phase controlled ACto- DC converters, AC voltage controllers, DC-to-DC switching converters, DC-to-AC inverters and switching power supplies. The requirements and configurations of power systems for telecommunications will be introduced. The techniques to analyze and design these power systems using available components will also be discussed. Computer simulation will be used to analyze the detailed operation of switching converters.

ELEC 448: Introduction to Robotics - Mechanics and ControlRobotics is an interdisciplinary subject concerning areas of mechanics, electronics, information theory, control systems and automation. This course provides an introduction to robotics and covers fundamental aspects of modeling and control of robot manipulators. Topics include history and application of robotics in industry, rigid body kinematics, manipulator forward, inverse and differential kinematics, workspace, singularity, redundancy, manipulator dynamics, trajectory generation, actuators, sensors, and manipulator position and contact force control strategies. Applications studied using MATLAB/Simulink software simulation and laboratory experiments.

MINE 472: Mining Systems, Automation, and RoboticsIn order to address issues related to safety, productivity, and remote operations, the world’s mineral resources industry has been gradually shifting towards the increased use of automated systems and roboticallyenhanced machines. It is important, therefore, that graduate engineers understand how these new technologies work so as to improve and make best use of them. This online course introduces senior students to the fundamental tools and techniques of automation and robotics as applied to modern mining practice. Enrolment is open to students from a range of engineering disciplines. This course provides an introduction to the basics of systems control, examples of how methods of automatic control can be applied to mining equipment and associated industrial vehicles, as well as to the fundamentals of sensing and navigation as applied to the design of robotic mobile equipment.