User Guide

tdcpy provides an interface for modeling LTI time-delay systems, supporting systems of retarded type, neutral type and delay descriptor systems. Next to modeling, tdcpy offers functionalities for spectral analysis, and controller design.

tdcpy is based on the TDS-Control MATLAB toolbox, developed and published by Pieter Appeltans and Wim Michiels in KU Leuven [Appeltans and Michiels, 2023]. Users already familiar with TDS-Control will find the basic functionality similar. tdcpy additionally utilizes the Python libraries NumPy for arrays and array operations, Scipy for scientific computations and Matplotlib for plotting. The user is required to have some basic familiarity with these packages when using tdcpy.

Organization

tdcpy is organized in several subpackages, each providing a specific set of functionalities. The main subpackages are:

tdcpy.common	Core data structures and functions
tdcpy.stability	Functions for stability analysis
tdcpy.plot	Visualization tools
tdcpy.stabopt	Tools for stabilization and controller design

Besides these subpackages, several high-level modules are provided for direct usage:

tdcpy.base	Base classes and functions
tdcpy.closed_loop	Functions for modeling the closed-loop.
tdcpy.controller	Functions for controller design.
tdcpy.dae	Functions for modeling DAEs.
tdcpy.ddae	Functions for modeling DDAEs.
tdcpy.gamma	Functions for computing gamma_r.
tdcpy.ndde	Functions for modeling neutral TDS.
tdcpy.roots	Function for computing the characteristic roots.
tdcpy.spectral_abscissa	Functions for computing the spectral abscissa and strong spectral abscissa.
tdcpy.zeros	Functions for computing the transmission zeros.

Kindly refer to the individual sections for more details on each of these subpackages and modules.

Quick-start

The following sections will guide you through the basic functionalities of tdcpy.

• Introduction
  • Getting Started
  • High-level API vs Low-level API
• Creating TDS Objects
  • Retarded DDEs
  • Neutral DDEs
  • Delay-differential algebraic equations (DDAEs)
• Computing the characteristic roots
  • Spectrum of a retarded system
  • Spectrum of a neutral system
  • Spectrum of a DDAE
• Controller Design
  • Defining a controller structure
  • Design of a stabilizing controllers for a retarded time-delay system
• References