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מבוא למערכות לינאריות
Introduction to Linear Systems |
0512-2531-08 | ||||||||||||||||||||||||
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| הנדסה | תואר ראשון - חשמל ואלקטרוניקה | |||||||||||||||||||||||||
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סילבוס מקוצר
שעות: 3 ש"ס
משקל: 2.5
דרישות קדם: משוואות דיפרנציאליות רגילות, מבוא להנדסת חשמל
סווג מערכות: מודלים מתמטיים למערכות לינאריות ודיאגרמות אקויולנטיות. ניתוח מערכות רציפות בתחום הזמן: תגובה לתנאי התחלה, תגובה לאילוץ תגובה להלם, קונבולוציה כתגובה לערור שרירותי, יציבות. התמרת לפלס החד צדדית ושימושיה: פונקצית התמסורת, קטבים ואפסים במישור התדר המורכב. תיאור מערכת במרחב המצב, הצגת משוואות מצב ופתרונן בתחום הזמן ובתחום התדר. תגובת תדר לערור סינוסואידלי, עקומות בודה. מערכות בדידות: קבלת משוואות הפרש ופתרונן בתחום הזמן, תגובה לתנאי התחלה, תגובה לאילוץ, הקונבולוציה הבדידה, יציבות. התמרת z החד צדדית ושימושיה, פונקצית התמסורת הבדידה. תיאור מערכת בדידה במרחב המצבים, פתרון משוואות מצב בדידות.
Course description
Credit Points: 2.5
Prerequisites: Ordinary Differential Equations; Introduction to Electrical Engineering
Classification of linear systems: mechanical, electrical, thermal, hydraulic and hybrid systems with constant lumped elements. Construction of electrical analogue circuits, formulation of mathematical models. Analysis of continuous linear systems in the time domain: response to initial conditions, impulse response, convolution as a response to arbitrary excitation. Fundamental analysis of first and second order systems. The one-sided Laplace Transform and its uses; transfer functions, poles and zeros in the complex frequency plane. System description in the state-space, presentation of state equations and their solution in the time and frequency domains. System description with the aid of block diagrams. Frequency response to sinusoidal excitation, Bode plots. Linear discrete-time systems: obtaining the difference equations and their solution in the time-domain, response to initial conditions and the discrete convolution theorem. The one-sided Z transform and its uses, the discrete transfer function. A description of a discrete-time system in state-space, solution of the discrete state equations. Polynomial stability criteria for continuous and discrete time systems.
1. Analyzing a linear system in the time domain; Solution of differential equations in the time domain and with the Laplace transform. Response to initial conditions and to an impulse (2 weeks).
2. Mathematical models to various linear systems; Presentation of electrical mechanical translation and rotational and hybrid systems by equivalent electrical analog diagrams (2 weeks).
3. State-space presentation for continuous-time systems. The solution of the state equations in the time and the frequency domains.
4. Frequency domain analysis of continuous-time systems. The system transfers function, its poles and zeros. Frequency response curves, Bode plots (2 weeks).
5. Discrete-time systems; Difference equations and their solution. Response to initial conditions, the discrete impulse response, discrete convolution. (2 weeks)
6. Frequency domain analysis of discrete-time systems. The Z-transform its properties and its applications. (2 weeks)
7. State-space presentation to discrete-time systems; The solution of the discrete state equations in the time and the frequency domains. (1 week)
8. Stability and stability criteria for continuous and discrete systems and their application. (1 week)
Prerequisites: Ordinary Differential Equations; Introduction to Electrical Engineering
Classification of linear systems: mechanical, electrical, thermal, hydraulic and hybrid systems with constant lumped elements. Construction of electrical analogue circuits, formulation of mathematical models. Analysis of continuous linear systems in the time domain: response to initial conditions, impulse response, convolution as a response to arbitrary excitation. Fundamental analysis of first and second order systems. The one-sided Laplace Transform and its uses; transfer functions, poles and zeros in the complex frequency plane. System description in the state-space, presentation of state equations and their solution in the time and frequency domains. System description with the aid of block diagrams. Frequency response to sinusoidal excitation, Bode plots. Linear discrete-time systems: obtaining the difference equations and their solution in the time-domain, response to initial conditions and the discrete convolution theorem. The one-sided Z transform and its uses, the discrete transfer function. A description of a discrete-time system in state-space, solution of the discrete state equations. Polynomial stability criteria for continuous and discrete time systems.
1. Analyzing a linear system in the time domain; Solution of differential equations in the time domain and with the Laplace transform. Response to initial conditions and to an impulse (2 weeks).
2. Mathematical models to various linear systems; Presentation of electrical mechanical translation and rotational and hybrid systems by equivalent electrical analog diagrams (2 weeks).
3. State-space presentation for continuous-time systems. The solution of the state equations in the time and the frequency domains.
4. Frequency domain analysis of continuous-time systems. The system transfers function, its poles and zeros. Frequency response curves, Bode plots (2 weeks).
5. Discrete-time systems; Difference equations and their solution. Response to initial conditions, the discrete impulse response, discrete convolution. (2 weeks)
6. Frequency domain analysis of discrete-time systems. The Z-transform its properties and its applications. (2 weeks)
7. State-space presentation to discrete-time systems; The solution of the discrete state equations in the time and the frequency domains. (1 week)
8. Stability and stability criteria for continuous and discrete systems and their application. (1 week)