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MathGroup Archive 1997

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Wolfram Research Announces - Control Systems Professional

  • To: mathgroup at
  • Subject: [mg5739] Wolfram Research Announces - Control Systems Professional
  • From: Scott Brew <sbrew>
  • Date: Sat, 11 Jan 1997 14:29:24 -0500
  • Organization: Wolfram Research
  • Sender: owner-wri-mathgroup at

The First Comprehensive Environment with Integrated Symbolic Capability

Symbolic control algorithms are now available as a part of Control
System Professional, the newest addition to the Mathematica Applications
Library. The software package uses a unified object-oriented approach to
integrate the arbitrary-precision, machine-precision, symbolic, and
graphical operations commonly performed in the control and systems
areas, and covers all the steps from creating and manipulating symbolic
models to analysis, design, and simulation of control systems. The
package is oriented toward practitioners in the field as well as
researchers. It is also a complete tool for educators and students
studying topics ranging from the beginning to the advanced level. 
Written for an interdisciplinary audience, the package is readily
applicable to a wide range of problems in the mechanical, electrical,
chemical, and aerospace industries, as well as other fields including
biochemistry and economics.

With Control System Professional, the user gains access to a library of
more than 150 functions and options that are designed to solve the
typical control problems. To make the package easy to use, the same
functions handle the state-space and transfer-function representations
of SISO or MIMO dynamic systems, defined in either the continuous-time
or discrete-time domains. Internally, the systems are represented by
data structures that allow the user to pass all system information from
one function to another simply by referencing the system by name--the
package automatically chooses appropriate algorithms. Experts, on the
other hand, may easily access all the intermediate steps.

Supporting both the "classical" and "modern" approaches, Control System
Professional finds the transfer-function matrices in the expanded and
factored polynomial forms and computes the state-space realizations from
the input-output forms or state equations. A collection of
interconnecting functions is supplied to build arbitrary complex systems
from simple ones. Numerous algorithms are provided to find the
discrete-time approximations of the analog systems and the
continuous-time models of the sampled system. The package handles
systems with time delays and supports several linearization methods for
nonlinear systems, including Pade and minimax approximations.

Control System Professional's model operations include computing the
minimal realizations and finding the Jordan and Kalman canonical forms,
as well as selecting controllable and observable subspaces. The package
also finds the internally balanced realizations and performs the
corresponding model reductions. Controllability and observability
properties are determined either in a transparent fashion or by
computing and analyzing the controllability and observability matrices
and Gramians. A similarity transform function enables conversion between
equivalent realizations. The user also has access to the continuous and
discrete matrix Lyapunov equation solvers.

Drawing on Mathematica's computational engine, Control System
Professional allows the user to obtain the time-domain responses
analytically or to simulate them numerically. Impulse, step, ramp, or
arbitrary response functions are obtainable with the same ease. The
package generates the Bode, Nyquist, Nichols, and singular-value plots
for the frequency domain representations as well as the root-locus plots
and animations.

The feedback design tools are represented by the robust and Ackermann's
algorithms for the eigenvalue assignment problem and the
linear-quadratic optimal control design tools for the infinite-horizon
state and output regulator problems. Special functions are provided to
compute the Kalman estimator and filter, the discrete equivalents to the
continuous regulator and estimator, and the solutions to the continuous
and discrete algebraic Riccati equations.

The package comes with a 186-page manual that describes its functions
and provides hundreds of examples that make the package immediately
useful for practical applications. The case studies are presented for
the inverted pendulum and magnetic ball levitation systems, the
production and inventory control model, the depth control of a
submarine, the lateral dynamics of an aircraft, the roll attitude
control of a missile, the concentration control of a chemical mixture in
a mixing tank, as well as the PID controller, the minimum-time response
controller, and others.  Also included is comprehensive on-line help.

Control System Professional is available for all platforms that run
Mathematica 2.2 or later. These include Microsoft Windows, Macintosh,
Linux, SunOS, Solaris, OSF/1, HP-UX, AIX, IRIX, NEXTSTEP, OS/2, and

For more information, send email to info at or phone
800-441-6284. The CSP home page is at Examples from the manual
are freely downloadable from

CSP is an open platform for implementing control algorithms. If you are
working on methods that can make a useful extension to the package, we
would be happy to help. Please contact us at
control-developer at

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