1. SylabUZ
2. Faculty of Computer Science, Electrical Engineering and Automatics
3. winter term 2018/2019
4. WIEiA - oferta ERASMUS / Automatic Control and Robotics - First-cycle Erasmus programme
5. Signals and dynamic systems

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Signals and dynamic systems - course description

Aim of the course

• 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.

Prerequisites

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Mathematical analysis, Linear algebra, modeling and simulation.

Scope

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

Teaching methods

lecture: classical lecture

labs: laboratory exercises

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

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%

Recommended reading

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.

Further reading

Notes

Modified by dr hab. inż. Wojciech Paszke, prof. UZ (last modification: 29-04-2020 12:06)