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THE WOLFRAM SOLUTION FOR

CONTROL SYSTEMS

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• Agilent Technologies

• Air Force Research Laboratory

• Alcatel-Lucent

• Honeywell

• KLA-Tencor

• The Aerospace Corporation

ORGANIZATIONS USING WOLFRAM TECHNOLOGYMany of the world’s top companies and organizations rely on Wolfram products to maintain their competitive edge, including 100% of the Fortune 50 companies. Here are just a few:

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Visit our control systems page to find out how to incorporate Mathematica and

SystemModeler into your daily work and research.

– Mike UlreyAdvanced Air Traffi c Management, Boeing

▀ Specify transfer-function, state-space, affi ne, and nonlinear models in natural form, and easily convert from one form to another

▀ Obtain linear, affi ne, or nonlinear state-space models of systems described by differential or difference equations

▀ Perform system manipulations, such as selecting or deleting subparts, cascading a set of systems, constructing interconnections of subsystems, and more

▀ Freely convert between continuous-time and discrete-time models using a wide selection of algorithms

▀ Analyze state-space models and convert between different realizations, including Kalman, Jordan, balanced, and other forms

▀ Design and analyze control systems, including models with time delays and algebraic equations

▀ Use approximate linearization techniques, such as Taylor or Carleman, or exact linearization techniques to analyze and design controllers for nonlinear systems

▀ 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

▀ Build models of complex, multi-domain systems using simple drag-and-drop of ready-made components, derive the state-space representations, and evaluate the models with Wolfram SystemModeler

▀ Simulate open- and closed-loop systems to determine state and output responses

Build and analyze control systems, document design decisions, and interactively

evaluate controllers—all in one system, with one integrated workfl ow.

Underlying the Wolfram control systems solution is a powerful hybrid symbolic-

numeric computation engine with any-precision numerics, high-performance

symbolics, advanced visualizations, and automated algorithm selection—

everything to get accurate results effi ciently. The Wolfram solution is ideal

for testing ideas and designing effi cient and reliable control systems.

▀ Manipulate models as transfer-function, linear state-space, affi ne state-space, or nonlinear state-space objects

▀ Automatically select tuning rules and compute design quantities including closed-loop transfer functions, PID parameterizations, and more

▀ Design and analyze systems with time delays and algebraic equations

▀ Perform exact or approximate linearizations of nonlinear systems

▀ 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

▀ Analyze the stability of a system using built-in frequency-response tools, using the circle or Popov criterion, computing the poles, or solving a Lyapunov equation

▀ 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

▀ Design controllers for disturbance rejection, input tracking, regulation, and more

▀ Simplify models of systems with interconnected components using block-diagram reduction

▀ Discretize continuous-time feedback algorithms for real-time implementation

THE WOLFRAM EDGE

KEY CAPABILITIES

“Without Wolfram technologies, my

performance would suff er.”

– Bruce Colletti Defense Contractor Consultant

“I think software in engineering and math

should not be done like it is usually done in

other programming languages. Wolfram

technologies are richer, and there are

more possibilities.”

“It is my number one tool to move forward and

propose new ideas that will help us to develop

algorithms that are more adapted to our

customers’ needs.”

“Wolfram technology competes with all the tools

that exist and works ten times better. It was the

basis of technical development on which I built

my company.”

– Yves PapegayINRIA

– Fritz LebowskySenior Principal Engineer, STMicroelectronics

– Nicolas VenutiCEO, Virtual Dynamics

FOR MORE INFORMATION

Designing controllers for a nonlinear fl exible joint.

Designing PID controllers for industrial systems.

Building a control system for a Segway using Wolfram SystemModeler.