Ordinary Differential Equation

• Mathematical description of physical system
• $a_ny^{(n)} + ... + a_1\dot{y} + a_0y = b_qu^{(q)} + ... + b_1\dot{u} + b_0u$

State-space representation

• Matrix form ($A, B, C, D$)
• Used in Modern Control Engineering
• State-space representation

Transfer Function (Übertragungsfunktion)

• Describes the dynamic behavior of a system over time
• Provides a calculation oof the output signal from any input signal
• Laplace transform of the impulse response
• Denoted: $G(s)$

Impulse Response (Gewichtsfunktion, Impulsantwort)

• Output signal for a Dirac impulse at input
• Completely describes an LTI (Linear Time-Invariant) system
• Denoted: $g(t)$

Step Response (Sprungantwort, Übergangsfunktion)

• Technically easy to generate, used instead of impulse response
• Completely describes an LTI (Linear Time-Invariant) system
• Denoted: $h(t)$

Frequency Response (Frequenzgang)

• Relationship between input/output of an LTI system
• Amplitude and phase (Complex quantity)
• Fourier transform of the impulse response
  • Analysis tools: Bode plot and Nyquist plot
• Denoted: $G(j\omega)$

Block Diagrams

• Used to analyze and model systems
• Can be split into smaller subgroups
• Can be combined to form larger systems