System Theory

1.lecture

Basic concepts: the concept of signal, system, network; management, control and regulation idea. Classification of signals. discrete and continuous time or value signs. Operations on discrete-time and continuous-time signals. Classification of systems: SISO, MISO, SIMO, MIMO systems; linear and non-linear systems; time invariant and time invariant systems; causal and acausal systems; systems with and without memory; deterministic and stochastic systems.

2. lecture

Networks. Analysis in time domain. The concept of impulse response, stepresponse and relationship. Expressing the response of a linear system. Convolution. (CT and DT systems)

3. lecture

State variable description of the system, solution of the state equation in the time domain (matrix functions) (CT and DT systems). Decomposition of the system response into components, eigenvalues, excitation-response relationship

4. lecture

Description of sinusoidal signals. Steady state of stable systems under harmonic excitation. Determination of transmission coefficient.

5. lecture

Fourier series of periodic signals. Periodic response of linear systems

6. lecture

Spectrum of a general signal, the Fourier transform. Band-limited and time-limited signals. Windowing. Spectrum of the response signal. Undistorted signal transmission, bandwidth condition.

7. lecture

Description of signals in the complex frequency domain, the Laplace transform. Inverse Laplace transform. Transferfunction of CT systems.

8. lecture

Description of signals in the complex frequency domain, the z-transformation. Inverse z-transform. transfer function of DT systems.

9. lecture

Relations between continuous-time and discrete-time signals and systems. simulation, impulse response, transfer function. Shannon's sampling law. Sampling, holding in time and frequency range.

10. lecture

System state variable and signal flow network description, specifying the answer is complex in the frequency range. Bode, Nyquist diagram. Stability. Stability test methods.

11. lecture

Open and closed control circuits. Effect diagram operations, substitution transformations. Value-preserving, follow-up regulations. The role of negative feedback. Characteristics of ideal fundamental elements (proportional, integrating, doubly integrating, differentiating, dead-time element): their impulse response, jump response, Nyquist, Bode diagram. Basics of control systems: closed and open circuit, circuit amplification, model number. Amplification and phase reserve. PID controller.

12. lecture

Filters. FIR, IIR filter structures. Filter design.

13. lecture

Presentation and programming of software radio (SDR) hardware elements. Implementation of simple modulation and demodulation (AM, FM, 4QAM) with software radio.

Lab 1

Impulse response, stepresponse, convolution. Matlab basics. Convolution in one dimension - time domain - reverberation. Two-dimensional convolution as an image processing procedure - averaging, noise filtering, edge enhancement.

Lab 2

State variable description of systems. Calculating the impulse response and jump response of linear state variable systems in the Matlab environment. Determining the response of a linear system.

Lab 3

Identical models of different physical systems – analogies (mechanical, electrical network, economic, biological, biochemical models). Simulation in the Matlab - Simulink environment.

Lab 4

Modeling: physical, black-box system modeling, mixed models. Modeling and simulation. Mathematical models of engineering problems. Structural, operational and impact outline.

Lab 5

Model creation procedures. Steps and tasks of modeling and simulation. Model and its verification.

Lab 6

Modeling and simulation. Mathematical models of engineering problems. Intervening bodies, sensors.

Lab 7

Harmonic excitation. Steady state of the system. Transfer characteristic. Transfer characteristics of simple physics networks. Bode diagram.

Lab 8

 System analysis using periodic excitation signals. Realization of the transfer characteristic and transfer function. FIR, IIR systems, filters in signal processing.

Lab 9

Fourier transformation, testing systems in the frequency domain. FFT algorithm and its application in image and sound compression procedures. Wired and radio communication application examples, amplitude and frequency modulation, frequency and time domain multiple access systems.

Lab 10

Sampling, quantization testing in a Matlab simulation environment. Restore sampled signals.

Lab 11

Examination of a storage system. (Temperature measurement on a heated resistor) Test of a proportional regulator.

Lab 12

PID control of a storage system. (Temperature control for heated resistance)

Lab 13

 Design and simulation of FIR, IIR filters in Matlab environment.