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| license: gpl |
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| # Control Systems Analysis Dataset |
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| This dataset contains analytical examples for both continuous and discrete closed-loop control systems and control objects. |
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| ## 🛠️ 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 |
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| ### 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. |
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| ### 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. |
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| ### Second-Order System Analysis |
| * **Symbolic Evaluation:** Symbolic analysis for second-order systems. |
| * **System Types:** Discriminant, oscillatory, aperiodic, and multiply aperiodic systems. |
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| ### 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. |
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| ### 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 |
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| ### 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. |
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| ### 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 |
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| ### 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 |
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| ### 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. |
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| ### 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. |
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| ### Symmetrical Components |
| * **Extraction:** Symmetrical components extraction and the rotation operator. |
| * **Signal Orthogonalization:** Phase filters and orthogonal signal generation. |
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| ### Variable coefficients filters |
| * **Variable Coefficients** Phase filters with variable transfer function coefficients. |
| * **Adaptive Filtering** Notch filters with variable coefficients. |
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| ### 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 |
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