Application Areas

Integrated Control Systems Design

Mathematica 8 provides an extensive suite of built-in functionality to carry out analysis, design, and simulation of continuous- and discrete-time control systems with both classical and modern techniques. Mathematica's powerful symbolic-numeric computation engine facilitates the use of analytical solutions to study relationships between design elements and gives valuable insight into the behavior of complex control systems. With any-precision numerics, automatic algorithm selection, and advanced visualizations, Mathematica 8 is ideal for building and analyzing control systems, documenting design decisions, and interactively testing controllers—all from a single platform.

  • Functions to build state-space and transfer-function models in natural form and easy conversion from one form to another.
  • Construction of linearized state-space models of systems described by differential or difference equations.
  • Conversion between continuous-time and discrete-time models using a wide selection of algorithms.
  • Model connections and manipulations, such as selecting or deleting subparts, cascading a set of systems, constructing interconnections of subsystems, and more.
  • Collection of frequency response tools like Bode plot, Nyquist plot, Nichols plot, and singular-value plot to aid in system analysis and design.
  • Ability to analyze state-space models and convert between different realizations, including Kalman, Jordan, balanced, and other forms.
  • Broad selection of feedback design algorithms such as robust pole-assignment and linear-quadratic optimal control to improve system performance.
  • Simulation functions to determine state and output responses of open- and closed-loop systems.
  • Built-in capability to solve Riccati and Lyapunov equations.
Specify Models of Linear, Time-Invariant Systems in Natural Form »Connect Two Systems in Parallel »Interactively Analyze System Behavior  »
Determine System Stability Using Built-in Functions »Visualize the Relative Stability of Systems »Study the Frequency Response of Multivariable Systems »
Build Regulators and Observers for Systems »Simulate the Response of State-Space or Transfer-Function Models »Construct a Kalman Filter for a Stochastic System »
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