README.md

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license: gpl
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# 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.

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## 📈 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.

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## 🔢 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.

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## 🧮 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.

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## ⚡ 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