DEPARTMENT OF ELECTRONIC ENGINEERING

DEPARTMENT OF ELECTRONIC ENGINEERING STUDY GUIDE CONTROL SYSTEMS 2 CSYS202 Latest Revision: Jul 2016 Page 1

SUBJECT: Control Systems 2 SUBJECT CODE: CSYS202 SAPSE CODE: 0808253220 PURPOSE: This subject is intended to introduce students to the fundamentals of control systems engineering and to illustrate how this knowledge can be applied to other subjects in the field. The subject prepares students for more advanced studies in Control Systems 3 and Control Systems 4 where the emphasis shifts to the design of control systems. PRE-REQUISITES: Electronics 2, Mathematics 2 and Electrical Engineering 2 (or Electrotechnology 2). Mathematics 3 is a concurrent subject (this means that it must be done at the same time or earlier). PRIOR KNOWLEDGE: For a student to succeed in this subject s/he must be proficient in the following: Basic algebra: Changing the subject of an equation, solving simultaneous equations, relational operators and Boolean algebra. Matrix algebra: Determinant of a matrix; inverse of a matrix; matrix addition, subtraction and multiplication (up to a 3 by 3 matrix). Trigonometric functions and identities. Integration and differentiation. Graphical representation and analysis of numerical data. Basic ac and dc circuit theory: Resistors, inductors and capacitors in series and parallel; complex impedance, magnitude and phase; voltage, current and power relations in circuits; peak-to-peak, peak and rms values; relationship between frequency expressed in Hz and rad/s; angles expressed in the form 2πft, where f is a frequency in Hz and t is time. Circuit theorems: Ohms law, Kirchoff s voltage and current law, mesh current analysis and nodal analysis, principle of superposition, etc. Standard test and measurement equipment: The oscilloscope; function generator; dc power supply; multi-meter; the student must be able to verify that the equipment is functioning correctly. The use of a breadboard: The internal breadboard connection layout; the student must be able to build simple circuits on a breadboard; the student must be able to verify that the circuit is operating correctly and to trace and correct faults in the circuit. Basic electronic circuits such as: The use of an operational amplifier; RC low pass filter. Computer hardware and software: Qwerty keyboard layout; working knowledge of the windows operating system; word processing, including the equation editor. DURATION: This course extends over ONE semester and consists of 3 one hour lecture periods and 1 two hour practical or tutorial per week. Page 2

RULES FOR CLASSROOMS AND LABORATORIES: No eating or drinking in the laboratories (including the chewing of gum). Closed shoes are to be worn at all times (slip-slops, bare feet and open shoes are not allowed). No cell phones may be used while in the laboratories. No unsupervised access is allowed in any of the laboratories. Permission must be given before entering a laboratory. Students are required to bring their own tool kits including breadboards to their practical sessions. METHOD OF ASSESSMENT: The final mark for this subject is made up of a semester mark and an examination mark. The semester mark has a weighting of 40 % and the examination mark a weighting of 60 % (see departmental rule EL9 (1)), of the final mark. The semester mark will have a theory component (70 %) and a practical component (30%). These marks will be obtained from two tests, consisting of both theory and practical work. If a student obtains a theory mark between 30 % and 39 % (and has achieved at least 40 % for the practical mark) an optional theory makeup test may be written. If a mark of 50 % or more is obtained (for the makeup test) the overall theory mark will be increased to 40 %. For students who obtain between 40 % and 49 % for the practical mark (and at least 30 % for the theory mark), the practical assignment manual will be considered for makeup purposes. If a mark of 60 % or more is obtained (for the practical assignment manual assessment) the overall practical mark will be increased to 50 %. A student who misses a test for medical reasons, and provides the required medical certificate, will be required to write the Makeup test in place of the missed test. There is only one Make-up test at the end of the semester, irrespective of the number of tests missed. The Makeup test will cover all the work that was covered in this course. The Make-up test for the practical test missed will be the practical assignment manual assessment. The mark breakdown is as follows: Theory test 1 (35 %) Semester mark Theory test 2 (35 %) Practical mark (30 %) 40 % Examination mark 60 % Final mark 100 % Students with a practical mark of less than 50 % will not be allowed to write the final examination (see departmental rule EL11 (1)). Students with a semester mark of less than 40 % will not be allowed to write the final examination (see departmental rule EL11 (2)). A subject pass will be a final mark of 50 % or more and a distinction is 75 % or more. No notes or textbooks are allowed in the examination and class tests. The examination will be based on the theoretical as well as the practical components of the course. Page 3

PLAGIARISM: The University has taken a strong stance against any form of plagiarism. Students are expected to be familiar with the general university rules governing examinations. These rules apply to all assessments completed for this subject. If any work submitted (either assignments or practical work) is found to be similar to other submitted work in this semester or a previous semester, or work posted on the internet, it will be assumed that the work submitted has been copied and all students involved will get zero for that assessment. Any appeal process will follow the standard University rules, that is, a disciplinary hearing will take place. TEXT BOOKS: It is expected that all students obtain a textbook to use as a reference. While there are many very good text books available in the Allan Pittendrigh library, the following book closely follows the course material: Title: A Primer for Control Systems (2 nd edition) Author: Gary J van Vuuren ISBN: 978-0-62050-325-9 The following list of books is divided into two categories. Firstly, recommended books are books that must be read and used on an on-going basis. These books should be used to a varying degree depending on the topic being studied at the time. Secondly, additional reading books are books that are to be used for general interest purposes in the field of control and instrumentation engineering. Recommended: Title: Modern Control Engineering (4 th edition) Author: Katsuhiko Ogata ISBN: 0-13-227307-1 Title: Linear Control System Analysis and Design: Conventional and Modern (4 th edition) Author: John J D Azzo and Constantine H Houpis ISBN: 0-07-016321-9 Title: Modern Control System Analysis and Design Using MATLAB Author: Robert H Bishop ISBN: 0-201-59657-1 Additional reading: Title: A Funny Thing Happened on the way to the Control Room Author: Gregory K McMillan ISBN: 155617215X Title: How to Become an Instrument Engineer: The Making of a Prima Donna Author: Gregory K McMillan ISBN: 1556170076 Title: A Short History of Just About Everything Author: Bill Bryson ISBN: 9780385609616 Title: Popular Mechanics monthly magazine Page 4

COURSE CONTENT: W L SECTION TOPIC Comments/Homework 1 1 Introduction What is a control system? Natural control systems and man-made control systems, industrial control systems, simple examples. Basic elements of a control system. 2 Open loop control and closed loop control. What is meant by the design of control systems? Definitions of terms. 3 Dynamic models Introduction to modelling of physical systems. Example of different types of models and emphasis on the important ones. Electrical elements: Differential equations for RLC components and simple series and parallel circuits. Difference between using node voltages and mesh currents. Student to research and understand the definitions. State space system definitions. 2 4 Introduction to the concepts of state space representation. Advantages and disadvantages of state space representation over differential equation representation. Defining the state variables using the physical variable approach (energy storage elements). Tutorial 1 5 The redundancy of state variables. Systems with more than one input and output. Tutorial 1 6 7 Mechanical elements: Translational motion, mass/spring/damper components. Differential equations of translational systems. The mechanical circuit and the resulting differential equation. Friction in mechanical systems as another form of damping. State space representation of translational mechanical systems. Tutorial 2 Tutorial 2 3 8 Rotational motion, different symbols that are used, torque and inertia, angular momentum. Differential equations of rotational systems. Tutorial 2 4 9 State space representation of rotational systems. Tutorial 2 10 Tutorial 11 Transfer function models. Definition of a transfer function. Examples. Tutorial 4 12 5 13 Poles, zeros, and the s-plane. Block diagram models. Definition of a block diagram, standard symbols used. Block diagram reduction, including block diagram algebra, open loop transfer function, closed loop transfer function, error ratio. Page 5 Tutorial 4 Tutorial 4

14 General form of the state space representation and the state block diagram. The simulation diagram. Tutorial 4 15 Signal flow graph models and definitions. Tutorial 4 16 Mason s gain rule applied to signal flow graphs. Tutorial 4 6 17 Tutorial. 18 Models of physical systems: RL circuit, rotary potentiometer and tacho-generator. Tutorial 3 19 Armature controlled dc motor. Tutorial 3 7 8 9 10 11 20 Armature controlled dc motor. Tutorial 3 21 Tutorial 22 Control system inputs Impulse, step, ramp, parabolic and sine functions. Translation in time. Tutorial 5 23 Complex input functions. Tutorial 5 24 Tutorial 25 Model solutions 26 27 28 Tutorial. Transfer function models. Various forms of the TF. Tutorial 6 State space models, solution to the LTI state equation, solution to the output equation using the Laplace transform approach. Model conversions: State space to transfer function (ss2tf). Transfer function to state space (tf2ss). 29 System Steady state and transient response, system type number and system order. response 30 First order systems, time constant. Tutorial 6 Tutorial 6 31 Second order systems, derivation of damping ratio and undamped natural frequency. Tutorial 6 32 Circle diagram for the damping ratio and damped natural frequency in more detail. Definition of the damped natural frequency. Tutorial 6 33 Link between roots in the s-plane and the resultant time response. Tutorial 6 Page 6

34 Time domain specifications. Tutorial 6 12 35 Error constants. Tutorial 6 36 Tutorial 37 Stability Routh-Hurwitz stability criterion. Special cases, zero in the first column and a zero row. Tutorial 6 13 38 Use of the criterion as a design tool. Tutorial 6 39 Tutorial PRACTICALS/TUTORIALS: W P SECTION TOPIC 2 1 MATLAB Introduction to Matrix Laboratory, base program, toolboxes, Simulink, etc. Using Matlab, navigation arrows, help, assigning variables, use of semicolon, basic commands. Data types: matrices, vectors and scalars. Entering and working with arrays, indexing, matrix constructors, matrix manipulation, element-wise arithmetic. Simple two-dimensional plotting. 3 2 Using an external storage device, Matlab editor/debugger, writing, saving and running scripts. Program layout, header and comments. Multiple plots, subplots, labelling of plots, text on plots, grid, legend, etc. 4 Tutorial. 5 Tutorial. 6 3 Entering and working with polynomials, roots, poly, conv, polyval commands. Block diagrams and block diagram manipulation. Finding the step response. 7 Input command, pause, display. 8 4 Control structures: for, if, while loops. 9 Menu command. 10 Fourier series example. 11 Tutorial. 12 Tutorial. Page 7