1. SylabUZ
2. Wydział Informatyki, Elektrotechniki i Automatyki
3. semestr zimowy 2020/2021
4. Automatyka i robotyka - Program Erasmus pierwszego stopnia
5. Signals and dynamic systems

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Signals and dynamic systems - opis przedmiotu

Cel przedmiotu

• Skills and competences in signal analysis, convolution of signals, Fourier transform, Laplace transform and Z transform.
• Skills in system analysis and mathematical representation of systems.
• Using stability criteria.

Wymagania wstępne

Zapisz zmiany

Mathematical analysis, Linear algebra, modeling and simulation.

Zakres tematyczny

1. Signals. Signal representation. Signal types: step function, binary pseudo-random sequence, auto-regressive sequence, moving average, sum of sinusoids. Persistently exciting signals. Practical aspects of selecting input signal.

2. Fourier transform. Fourier series and Fourier transform. Spectroanalysis. Fast Fourier Transform (FFT). Fourier analysis of systems.

3. Laplace transform. Linear differential equations. Laplace transform and its properties. Solving linear differential equations using Laplace transform. Inverse Laplace transform. Transfer function.. Basic operations on transfer functions.

4. Z transform. Linear difference equations. Properties of the Z transform. Z transform of the step function and exponential functions. Application of the Z transform to solving linear difference equations. Determining the original of a given Z transform.

5. System representation Dynamic system. System input, system output, system state, control signal. Representation of discrete-time and continuous-time dynamic systems. Differential equations, difference equations. Transfer functions. State-space representations.

6. Fundamental properties of systems. Causality. Stationarity. Linearity. Stability of dynamic systems. Definitions of stability. Controllability and observability of linear dynamic systems, both continuous and discrete. 

7. Stability of dynamic systems. Linear continuous systems stability criteria: Hurwitz criterion, Routh criterion, Nyquist criterion. The first and second Lyapunov methods. Discrete systems stability criteria. Transformation of the left half complex plane into unit circle.

8. Spectral transfer function. Frequency characteristics: Bode diagram, attenuation diagram, phase diagram. Transient response: step response and impulse response. Relationship between transient responses and spectral transfer function.

9. Characteristic of selected dynamic elements. Proportional element, inertial element of the first and second order, integrating element, differential element, oscillating element and delay element

Metody kształcenia

lecture: classical lecture

labs: laboratory exercises

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture - the passing condition is to obtain a positive mark from the final test.

Laboratory – the passing condition is to obtain positive marks from all laboratory exercises to be planned during the semester. as well as give back all reports from laboratory exercices.

Final grade = lecture: 50% + laboratory: 50%

Literatura podstawowa

1. Won Y. Yang et al., Signals and systems with MATLAB, Springer, Berlin, 2009.

2. Steven T. Karris, Signals and systems with Matlab computing and Simulink modeling, Orchard Publications, 2007.

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez prof. dr hab. inż. Krzysztof Patan (ostatnia modyfikacja: 27-04-2020 20:52)