Control System Professional Is 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 Wolfram Research Mathematica
Applications Library. The software package uses a unified object-oriented
approach to integrate arbitrary-precision, machine-precision, symbolic, and
graphical operations commonly performed in control and systems areas. It
covers all steps from creating and manipulating symbolic models to analysis, design, and simulation of control
systems. Written for an interdisciplinary audience, the package is oriented
toward practitioners as well as researchers and is readily applicable to a
wide range of problems in mechanical, electrical, chemical, and aerospace
industries, as well as in other fields including biochemistry and economics.
It is also a complete tool for educators and students studying beginning- to
Control System Professional provides users with access to a library of more
than 150 functions and options that are designed to solve typical control
problems. To make the package easy to use, the same functions handle
state-space and transfer-function representations of SISO or MIMO dynamic
systems, continuous-time and discrete-time domains. Internally, 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 intermediate steps.
Supporting both classical and modern approaches, Control System
Professional finds transfer-function matrices in expanded and factored
polynomial forms and computes state-space realizations from 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 discrete-time approximations of analog
systems and continuous-time models of the sampled system. The package
handles systems with time delays and supports several linearization methods
for nonlinear systems, including Padé and minimax approximations.
Control System Professional's model operations include computing minimal
realizations and finding Jordan and Kalman canonical forms, as well as
selecting controllable and observable subspaces.
The package also finds internally balanced realizations and performs
corresponding model reductions. Controllability and observability
properties are determined either in a transparent fashion or by computing
and analyzing controllability and observability matrices and Gramians. A
similarity transform function enables conversion between equivalent
realizations. Users also have access to continuous and discrete matrix
Lyapunov equation solvers.
Drawing on Mathematica's computational engine, Control System Professional allows users to obtain 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 Bode, Nyquist,
Nichols, and singular-value plots for frequency domain representations as
well as root-locus plots and animations.
Feedback design tools are represented by robust and Ackermann's algorithms
for eigenvalue assignment problems and linear-quadratic optimal control
design tools for infinite-horizon state and output regulator problems.
Special functions are provided to compute Kalman estimator and filter,
discrete equivalents to continuous regulator and estimator, and solutions
to continuous and discrete algebraic Riccati equations.
The package comes with a 186-page manual that describes its functions and
provides hundreds of examples, thus making it useful immediately for
practical applications. Case studies are presented for inverted pendulum
and magnetic ball levitation systems, production and inventory control
model, depth control of a submarine, lateral dynamics of an aircraft, roll
attitude control of a missile, concentration control of a chemical mixture
in a mixing tank, as well as PID controller, minimum-time response
controller, and others. Also included is comprehensive online help.
Control System Professional requires Mathematica 2.2 or 3.0 (also available
from Wolfram Research) and runs on over 20 platforms including Microsoft
Windows 95 and NT, Macintosh 68k and PowerPC, SPARC, DEC AXP, Silicon
Graphics, IBM RS/6000, Linux, and NEXTSTEP. Memory requirements parallel
those needed for the given type of machine and corresponding operating system.