TimurZhoraev/ControlSystemDesign

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