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Lecturer(s)
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Cvejn Jan, doc. Ing. Ph.D.
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Course content
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Topics of lectures by weeks: 1. Introduction: process control, automatic control, logic control. Reasons for automation, role of a human in automated production. 2. Dynamic systems. Types of mathematical models. Output and state description. Steady state value. Static characteriristic. Linear time-invariant (LTI) systems. Perturbation model. 3. Anaylisis of linear stationary one-dimensional systems in time domain: the principle of superposition of inputs, the impulse and step responses, the dependence between input and output by using convolution. 4. Fourier and Laplace transforms. Basic statements about images. Simplified vocabulary of L-transform. 5. Using L-transform for obtaining time response of linear systems. 6. The system transfer function. Standard form of the transfer function - gain, time constants. Frequency transfer function. Frequency response in complex plane. Magnitude and phase responses (Bode's plots). 7. The transfer function algebra and block diagrams. Serial, parallel and anti-parallel block interconnection. Obtaining the trasfer function of a composed system by the method of succeeding simplifications. 8. Overview of the most common types of linear systems and their properties (static plant of the first and second order, plants with astatism, high-order static system with a dead time). Replacement of a high-order system by the first-order model with dead time. 9. Automatic regulation. Open and closed control loops. Electronical analog and digital control system. Discontinuous controllers - two-state and three-state ones. 10. The PID controller and its variants. Meaning of particular components. Steady-state regulation error. The derivative term implementation. The digital PID controller realization. 11. The closed loop stability of dynamic systems and of the closed-loop control system. Hurwitz and simplified Nyquist criterions of stability. The stability margin. Magnitude and phase margins. 12. Criteria for setting-up the PID controller. Rise time, settle time and the step response overshoot. Integral criteria in the time domain. The frequency-domain criteria. 13. Practical methods for setting up the PID controller parameters. The Ziegler-Nichols critical gain method and its variants (setting up using the step response and the feedback method using a relay). The design based on dominant poles compensation.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Work with text (with textbook, with book), Demonstration
- Contact teaching
- 16 hours per semester
- Home preparation for classes
- 84 hours per semester
- Preparation for an exam
- 60 hours per semester
- Preparation for a credit (assessment)
- 20 hours per semester
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Learning outcomes
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The goal of the subject is to build up a mathematical aparatus, based on Laplace transform, used in analysis and synthesis of control systems and describe elementaty tools for realization of feedback control. The graduate obtains knowledge necessary for analysis and design of simple control systems. The knowledge is necessary for studying subjects in consequence, especially Automation II and Instruments of Automatic Control.
The graduate obtains knowledge necessary for analysis and design of simple control systems. The graduate is able to: - obtain a one-dimensional linear dynamic plant model in the form of a transfer function from the equations obtained by mathematical-physical analysis or by using an approximate experimental identification. - obtain a time dependence of an output of a one-dimensional linear system for given input signal by using the Laplace transform. - estimate the shape of time and frequency response functions for static plants of 1st and 2nd order and plants with astatism in dependence on the transfer function parameters. - resolve about stability of the feedback control loop with the PID controller based on the transfer function parameters or open-loop frequency response. - choose a suitable variant of the PID controller for given process, to determine the parameter values and describe the discrete PID controller algorithm.
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Prerequisites
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Required knowledge from mathematics: differential and integral calculus, linear differential equations. Elementary physics required: machanics, electrical and heat systems.
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Assessment methods and criteria
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Oral examination, Written examination
Active participation in seminars, tests, oral examination.
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Recommended literature
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Balátě, Jaroslav. Automatické řízení. Praha: BEN - technická literatura, 2004. ISBN 80-7300-148-9.
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Cvejn, J. Automatizace 1. Elektronický studijní materiál.. Pardubice: Univerzita Pardubice, 2017.
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Hlava, J. Prostředky automatického řízení, Skriptum ČVUT v Praze, 2000..
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Kotek, Z., Vysoký, P., Zdráhal, Z. Kybernetika. SNTL, Praha 1990..
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Pírko, Z., Veit, J. Laplaceova transformace, SNTL, Praha, 1970..
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Vítečková M., Víteček A. Základy automatické regulace. Ostrava: VŠB - Technická univerzita, 2006. ISBN 80-248-1068-9.
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