The Wolfram Solution for

Control Systems

Build and analyze control systems, document design decisions, and interactively evaluate controllers–all in one system, with one integrated workflow.

Underlying the Wolfram control systems solution is a powerful hybrid symbolic-numeric computation engine with numerics of any precision, high-performance symbolics, advanced visualizations, and automated algorithm selection–everything to get accurate results efficiently. The Wolfram solution is ideal for testing ideas and designing efficient and reliable control systems.

Building a control system for a Segway using Wolfram SystemModeler
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Key Capabilities

Mathematica and SystemModeler include thousands of built-in functions that let you:

  • Compute the state-space model of a system described by difference or differential equations and any algebraic constraints
  • Analyze the stability of a system using built-in frequency-response tools, computing the poles, or solving a Lyapunov equation
  • Simplify models of systems with interconnected components using block-diagram reduction
  • Manipulate linear models as transfer-function or state-space data objects
  • Interactively analyze the system behavior as parameters are varied
  • Employ classical techniques such as Bode, Nyquist, Nichols, and root locus plots to analyze and design control systems
  • Evaluate the controllability and observability properties of a system
  • Compute state-space transformations to obtain decompositions that are controllable, observable, minimal, or balanced
  • Obtain continuous-time equivalents of discrete-time systems for analysis and design
  • Develop feedback laws to enhance the performance of dynamic systems
  • Design and analyze systems with time delays and algebraic equations
  • Automatically compute design quantities including closed-loop transfer functions, PID parametrizations, and more
  • Estimate unmeasured states or noisy measurements
  • Directly obtain models of controllers and estimators that can be easily assembled to form a closed-loop system for further simulations
  • Discretize continuous-time feedback algorithms for real-time implementation

Simulating the response of state-space or transfer-function models

Determining system stability using built-in functions

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How Wolfram Compares
Key Capabilities

Does your current tool set have these advantages?

  • Directly input both transfer-function and state-space models in natural form
    Matlab allows you to specify transfer-function models only as a matrix of row vectors
  • Analyze symbolic and numeric systems
    Matlab handles numeric systems only
  • Fully automated precision control and arbitrary precision arithmetic to ensure accurate results
    Matlab and other systems relying on machine arithmetic can show critical errors due to numerical accuracy failure
  • Instant interface construction to test a control system interactively for different scenarios
    Unique to Mathematica
  • Free-form linguistic input produces immediate results without the need for syntax
    Unique to Mathematica
  • Automated algorithm selection to get accurate results quickly—sometimes switching mid-calculation for further optimization
    Non-Mathematica computation systems like Matlab make you analyze your equations manually to determine which function to apply
  • Control systems functionality is well integrated with the core Mathematica system and more than 20 built-in application areas, such as signal processing, time series, image processing, wavelets, linear algebra, and more

Building a transfer function out of a collection of poles and zeros in the complex plane

Simulating a feedback control system with controller and second-order plant

Next: Key Capabilities
The Wolfram Edge
How Wolfram Compares
Key Capabilities

Mathematica includes thousands of built-in functions for computation, modeling, visualization, development, and deployment »

Control systems specific capabilities:

  • Specify state-space and transfer-function models in natural form, and easily convert from one form to another
  • Obtain linearized state-space models of systems described by differential or difference equations and any algebraic constraints
  • Freely convert between continuous-time and discrete-time models using a wide selection of algorithms
  • Perform system manipulations, such as selecting or deleting subparts, cascading a set of systems, constructing interconnections of subsystems, and more
  • Analyze and design systems using frequency-response tools centered around Bode plot, Nyquist plot, Nichols plot, and singular-value plot
  • Analyze state-space models and convert between different realizations, including Kalman, Jordan, balanced, and other forms

Wolfram SystemModeler is the most complete physical modeling and simulation tool for high-fidelity modeling. With SystemModeler, you can:

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