Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

    címtáras azonosítással

    vissza a tantárgylistához   nyomtatható verzió    

    Control Engineering

    A tantárgy neve magyarul / Name of the subject in Hungarian: Szabályozástechnika

    Last updated: 2023. február 24.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Electrical Engineering BSc program
    BSc degree program
    Mandatory subject
    Course ID Semester Assessment Credit Tantárgyfélév
    VIIIAB05 4 2/1/1/v 5  
    3. Course coordinator and department Dr. Kiss Bálint,
    Web page of the course
    4. Instructors

    Name postion department

    Dr.habil. István Harmati associate professor Control Engineering and Information Technology

    Dr. Bálint Kiss associate professor Control Engineering and Information Technology 

    5. Required knowledge
    Mathematics: linear algebra, matrix calculus, complex algebra, differential and integral calculus, first order linear differential equations. Signals and systems: description of linear, continuous time systems in time, frequency and complex frequency domains, description of discrete time linear systems in time and Z domains.
    6. Pre-requisites
    ((TárgyEredmény( "BMEVIHVAB01" , "aláírás" , _ ) = -1
    VAGY TárgyEredmény( "BMEVIHVA200" , "aláírás" , _ ) = -1)

    ÉS NEM ( TárgyEredmény( "BMEVIIIA303" , "jegy" , _ ) >= 2
    TárgyEredmény("BMEVIIIA303", "FELVETEL", AktualisFelev()) > 0)

    ÉS (Training.Code=("5N-A7") VAGY Training.Code=("5N-A7H") VAGY Training.Code=("5NAA7")) )


    ((TárgyEredmény( ahol a TárgyKód = "BMEVIHVA214", ahol a Típus = "JEGY", ahol a Ciklus = tetszőleges, ahol a KépzésKód = tetszőleges) >= 2
    TargyEredmeny( "BMEVIHVAB00" , "jegy" , _ ) >= 2 )

    ÉS Training.Code=("5N-A8") )

    A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

    A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

    Mathematics A1 and A2, Signals and systems 1 and 2
    7. Objectives, learning outcomes and obtained knowledge

    The control of technological, economical, and environmental processes belongs to the electrical engineers’ most important professional activities that require both abstract and applied knowledge and competences. Besides its contribution to form an engineering approach of problem solving, the course teaches the fundamentals of control engineering, the main principles of analysis and synthesis of control loops, and the use of the related computational tools. Students successfully satisfying the course requirements will be able

    • (K2) explain the fundamental notions of control engineering, enumerate the standard elements and signals of a control loop, identify these elements and signals for a real control system and to describe the quality measures of a closed-loop control systems;
    • (K3) apply methods to check the stability of single variable, continuous or sampled time, linear and time-invariant control loops;
    • (K2) present the elements of the specification to controller design and the practical constraints to be taken into consideration;
    • (K3) apply model based controller design methods for single variable, continuous or sampled time, linear and time-invariant systems using different representation of the plant model;
    • (K3) utilize the services of the Matlab/Simulink development environment supporting the controller design procedure;
    • (K2) explain the goal and steps of some model identification methods;
    • (K2) have the general knowledge in control engineering to enroll to advanced courses in control theory (optimal and robust control, nonlinear control systems, etc.) and to enroll courses of specialization tracks such as (control systems, embedded systems, intelligent robots and vehicles); 
    • (K2) have the background knowledge in control engineering to enroll to the Laboratory 1 and 2 courses.
    8. Synopsis

    1. Basic notions of control theory (2 hours of lectures): The principle of control and description of control structures. Principles and differences of open and closed loop control. Functional diagrams, dataflow diagrams, conventions and standard signals and their nomenclature in a control loop. Static and dynamic characteristics of control loops, integrals of the error function. Classification of control systems. 

    2. Modeling of dynamical systems (2 hours of lectures): Dynamical systems. State, and state space. Solution of the state equation of a continuous time, linear, time invariant (LTI) system, the exponential matrix, the transfer function, poles, and zeros. The consequences of a (invertible linear) coordinate transformation in the state space. Linearization around a setpoint. Models of some classes of physical systems including mechanical and thermal processes using energy preservation laws of physics.  

    3. Analysis of continuous time linear control systems (4 hours of lectures): Description of single variable (SISO) linear transfers: ordinary differential equation, transfer function, Bode-plot, impulse response, step response, state equation. Transformations between descriptions. Fundamental interconnections of elements, open and closed loops. Elementary transfers; first and second order prototype systems: characteristics in the time and frequency domains. Relation between the dominant pole(s) and the dynamical characteristics of a transfer. Properties of the amplitude and phase plots of a general open loop transfer function, the calculation of the crossover frequency. Steady-state in linear control loops steady-state properties of reference tracking and disturbance rejection. Stability of control loops: BIBO stability definition, Hurwitz criterion, Nyquist criterion, Bode criterion, phase margin and crossover frequency. 

    4. Synthesis of continuous time linear control systems in frequency domain (4 hours of lectures): The class of PID compensators, the filtered D term, Bode plots and pole-zero distribution of the compensators. Properties of the compensators. Setting the compensator parameters for a desired phase margin and steady-state behavior. Prototype examples of compensation with P, PD, PI, and PID controllers. Feedback compensation. Controller design for minimal error square integral. Root locus methods. Compensation of plants with time lag: compensation of an ideal time lag with an integrator. 

    5. Analysis of discrete time linear control systems (2 hours of lectures): The Shannon law of sampling. Properties of hold elements. Signal propagation in a discrete time system in frequency domain and using state space description. Discrete time equivalent of a continuous time plant using a zero-order-hold circuit and an ideal sampler. Discrete time implementation of continuous time compensators: discrete time realization of integral and differential operators (approximations), step response equivalence.  

    6. Synthesis of discrete time linear control systems (4 hours of lectures)Hardware and software realization of a PID controller using integrator anti-windup techniques. Dead-beat controller design to get finite impulse response in closed loop. The correction polynomial and the calculation of its coefficient. Design of two-degree-of-freedom controllers: the choice of the observer polynomial and the transfer function of the reference model, the steps of the design procedure to arrive to a Diophantine equation. Illustration with an example. Robustness of the two-degree-of-freedom controller scheme against parameter uncertainties.  

    7. Continuous time control loop analysis and synthesis in state space (2 hours of lectures): Controllability and observability in continuous time linear systems. Conditions of full state controllability and observability. Pole placement using state feedback, the Ackermann formula. Design of full state observers, algebraic equivalence to the pole placement problem. Integral control and load estimator design. 
    8. Discrete time control loop analysis and synthesis in state space (2 hours of lectures): Controllability, reachability, detectability and observability in discrete time linear systems and their conditions. Pole placement using state feedback, the Ackermann formula. Design of full state, actual observers, algebraic equivalence to the pole placement problem. Integral control and load estimator design. 
    9. Discrete time system models and parameter identification methods (4 hours of lectures): Autoregressive (AR) and moving average (MA) processes, ARX and ARMAX models. Parameter identification of ARX models using LS methods. Parameter identification of the ARMAX model using numerical optimization and the quasi-Newton method. The services of the Identification toolbox of Matlab.  
    Practice sessions
    Classroom and computer room practices are paired together. Students use Matlab and Simulink during computer room practices. Topics of the practice session pairs (a classroom and a computer room practice):
    1.Introduction to Matlab, Control Systems Toolbox and Simulink. Features of the LTI view tool. 
    2. Analysis of control loops: simulation, stability, stability criteria, frequency and time domain features, their relations
    3. Serial compensators: design with Matlab, features of the SISO design tool. Solution of the parameter equations using fsolve.
    4. Discrete time controller design: discrete realization of a PID controller, two degrees of freedom controller design
    5. State space controller design in continuous time, state feedback, state observer, load estimation and integral control 
    6. State space controller design in discrete time 
    7. identification from measured data using the services of the system identification toolbox
    9. Method of instruction

    Two hours of lectures and alternating, weekly practice sessions of two hours of classroom and computer room practices. Since the knowledge elements presented during the semester are highly interconnected, regular preparation to classes and to practice sessions is highly suggested.

    10. Assessment

    During the period of classes, each of the following conditions must be met to obtain signature:

    1. Presence: students must visit both classroom and computer room practice, prepared. The number of the missed practice sessions cannot be higher than three.
    2. Partial evaluation (quizzes): preparedness is checked at the beginning of five computer room practices (starting with the second computer room practice) using a written quiz. The result of at least three quizzes out of five must be at least pass. No quiz can be repeated. Missed quiz is recorded in the average as a quiz with result 0. The average of all five quizzes is the basis of bonus points for the exam.
    3. Summary evaluation: one midterm is scheduled, its result must be at least pass. The duration of the midterm is 90 minutes and its questions may refer to the 50% of the course material. The result of the midterm makes up 10% of the exam result.
    During the exam period a comprehensive exam must be successfully taken:
    1. Signature is required to participate at exams.
    2. The exam result is based on the evaluation of written answers and on results obtained during the period of classes. The modification (e.g. improvement) of the results obtained during the period classes is not possible during exams.
    3. The written exam has two parts. The first part is a test for a maximum amount of 40 points. During the second part, students are expected to solve control system analysis and synthesis problems with computers for a maximum amount of 50 points. The exam is failed if the number of point obtained for the first part is less than 16 (sixteen) or the number of points obtained for the second part is less than 20. The result of the midterm is taken into consideration with up to 10 points, proportionally to its grade.
    4. At least 40 points is required to pass the exam.
    5. If the exam is passed, twice the average of the quizzes is added to the number of points and the resulting amount of points is used to determine the final grade of the exam.
    There is no pre-exam.
    11. Recaps

    The mid-term can be repeated once during the period of classes. The mid-term cannot be repeated during the repeat week. Missed practices (classroom or computer room) cannot be repeated. 

    12. Consultations Available on request.
    13. References, textbooks and resources
    A. D. Lewis, A Mathematical Introduction to Feedback Control, 2002
    Karl Johan Aström, Richard M. Murray. Feedback systems: an introduction for scientists and engineers. Princeton University Press, 2008
    B. C. Kuo, Farid Golnaraghi. Automatic Control Systems, 8th edition. Wiley, 2001
    Classroom and computer room practices (downloadable from Educational Portal –
    14. Required learning hours and assignment
    Contact hours56
    Preparation for contact hours42
    Preparation for the midterm12
    Preparation for the exam40
    Total workload150
    15. Syllabus prepared by
    Name Position Department 
    Dr. habil. Béla Lantos professor emeritus Control Engineering and Information Technology 
    Dr. habil. István Harmati associate professor Control Engineering and Information Technology 
    Dr. Bálint Kiss associate professor Control Engineering and Information Technology