The Wolfram Solution for

Control Systems

Build and analyze control systems, document design decisions, and interactively test controllers–all in one system.

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 new systems.

Building a control system for a Segway using Wolfram SystemModeler

The Wolfram Edge

How Wolfram Compares

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
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
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

Next: How Wolfram Compares

The Wolfram Edge

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 image processing, wavelets, statistics, 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
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

Improve the performance of systems using a broad selection of feedback design tools such as robust pole-assignment algorithms and linear-quadratic optimal control methods
Simulate open- and closed-loop systems to determine state and output responses
Analyze a control system interactively for different scenarios using the Manipulate command »
Solve Riccati and Lyapunov equations using built-in functions
Connect to databases instantly for easy access to specialized data

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