metadata
license: gpl
Control Systems Analysis Dataset
This dataset contains analytical examples for both continuous and discrete closed-loop control systems and control objects.
🛠️ Core Analysis Methods
- Maxima CAS: Examples using the Maxima symbolic computing system (Computer Algebra System).
- Hybrid Workflows: Systems and objects analysis combining Maxima and Python.
📈 Continuous Objects & Control Systems
Circuit Analysis & Modeling
- Kirchhoff's Rules: Introduction to electrical circuit analysis.
- Equation Systems: Compiling systems for circuit voltages and node currents.
- Incidence Matrices: Using a netlist to compose structural matrices.
Transfer Function & Stability Analysis
- Step Response: Transfer function analysis and obtaining response to a given signal.
- Zero-Pole Analysis: Zeros and poles of the transfer function.
- Stability: Pole-based stability criteria.
- Root Locus: Constructing trajectories when varying object or system parameters.
Second-Order System Analysis
- Symbolic Evaluation: Symbolic analysis for second-order systems.
- System Types: Discriminant, oscillatory, aperiodic, and multiply aperiodic systems.
Frequency Domain Analysis
- Complex Response: Evaluation of complex frequency response (imaginary and real parts).
- Bode Elements: Frequency and phase response using the arctangent of complex arguments.
Integral Transforms
- Laplace Transform: Forward and inverse Laplace transforms.
- Numerical Methods: Numerical Inverse Laplace transform for higher-order systems.
🔢 Discrete Systems
Discretization Techniques
- Bilinear Transforms: Tustin substitution, bilinear transform, rectangle (left/right), and trapezoid methods.
- Zero-Pole Matching: Matching methods for continuous-to-discrete translation.
- Special Cases: Matching methods in the presence of single or multiple zeros equal to zero.
Digital Filter Implementation
- Reduction: Reducing discrete transfer functions to digital filters.
- DSP Optimization: Types of digital filters and optimization for digital signal processors.
🧮 Numerical & Nonlinear Computation
Function Calculation Methods
- Taylor Series: Function approximation and sine function calculations.
- Newton-Raphson Method: Root functions and division operations.
- Coefficient Approximation: Approximation methods for Taylor series coefficients.
- Fixed-Point Optimization: Adapting approximations for arithmetic right and left bit-shifts.
⚡ Advanced Power Control
Park Transform Systems
- Modulation Effects: Laplace transform of function-sine products and amplitude modulation.
- Dynamic Links: Links in $\alpha\beta$ or $dq$ channels.
- Symbolic Modeling: Analysis of symmetrical closed-loop systems with Park transforms.
- Harmonic Analysis: Evaluation of second harmonic effects.
Single-Phase Astatic Systems
- Transformations: Single-phase $dq$ transform.
- Filtering: Second-order notch filters and infinite Q band-pass filters.
- Resonant Controllers: Controller properties and closed-loop systems with resonant controllers.
- Astatic Control: Control based on a specific frequency component.
- AC Circuits: Symbolic analysis of AC circuits at a given frequency.
Symmetrical Components
- Extraction: Symmetrical components extraction and the rotation operator.
- Signal Orthogonalization: Phase filters and orthogonal signal generation.
Variable coefficients filters
- Variable Coefficients Phase filters with variable transfer function coefficients.
- Adaptive Filtering Notch filters with variable coefficients.
Phase-Locked Loops (PLL)
- Variable Coefficients: Phase, Notch filters, Integrators with variable transfer function coefficients.
- Feedback Systems Nonlinear frequency-dependent feedback loops.
- Phase filtering with unwrapping +- pi correction of atan2