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 advanced-level topics.
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.