Wolfram Mathematica

Enhanced Control Systems

Mathematica 9 adds several extensions and improvements to the control system functionality. PID controllers are the most widely used in industry, and Mathematica now provides PID tuning with automated workflows. Time delays are common in systems with communication lags or sensing delays and can create instabilities. Mathematica's control system suite now supports modeling and design of time-delay systems. Descriptor systems allow for explicit representation of algebraic constraints and are naturally generated from modern modeling systems. Descriptor systems are now fully supported throughout the control system framework.

Support for automatic tuning of PID controllers.
Automatic computation of design quantities including closed-loop transfer functions, PID parametrizations, etc.
Support for more than a dozen tuning algorithms including Ziegler-Nichols.
Support for stability analysis using Nyquist plots and circle criterion.
Full support for delay systems, transfer function or state space, discrete time or continuous time. »
Delay systems can be connected, simulated, and analyzed using frequency plots.

Use any control design method on delay-free system and implement stable controller using a Smith compensator.
Automatically computed delay-free approximation.
Full support for descriptor state-space models allowing for mixtures of differential or difference and algebraic equations. »
Descriptor systems can be connected, simulated, and analyzed like standard state-space models.
Full support for control design (pole placement, linear quadratic) for descriptor systems.