Control Design Module
The Xmath Control Design Module takes advantage of the Xmath included system data structure by adding a library of functions for advanced control design synthesis and analysis. Synthesis functions include focus on system construction, conversion, and interaction. The module contains the added analysis functionality of classical tools such as SISO root locus calculation, Nyquist and Nichols plot computation, and modern control design tools, including a Ricatti equation and a pole place solver. Time-response computation functions and steady-state analysis tools are also included.
Robust Control Module
The Xmath Robust Control Module provides a library of advanced tools for analyzing and developing control solutions for systems with model uncertainties. The added library of functions includes a number of commands for performing robustness analysis on closed-loop systems and evaluating the performance of those systems. It also includes functions for synthesizing controllers based on the three most commonly used techniques for robust control - H∞ control synthesis, LQG (H2) control synthesis, and the loop transfer recovery method.
The Xmath Optimization Module provides the ability to perform linear and nonlinear optimization on any linear, quadratic, or nonlinear Xmath or SystemBuild performance index. All values of the optimization process are user-defined, including cost, constraints, initial values and bounds, optimization and penalty parameters, and maximum and minimum iteration numbers. Optimization of linear and quadratic performance indexes features Karmarkar-style algorithms.
Model Reduction Module
The Xmath Model Reduction Module features tools for producing reduced-order, lower complexity controllers for high-order plant models. These tools are based on a number of different reduction techniques, which can be applied individually or in any combination depending on the specifications of the model. Additional utility functions are also included for computing the Hankel singular values, decomposing a system into stable and unstable parts, and performing a graphical comparison of full-order and reduced-order models.
The Xmath Xμ Module includes a library of functions for designing, analyzing, and refining linear robust systems. The module begins with a library of functions that use the overloading features of Xmath to build, manipulate, and interconnect complex systems. It also includes a collection of model reduction functions to reduce high controller order -- which often results from μ-synthesis -- with little degradation in closed-loop performance. Finally, you can use controller synthesis functions, focusing on H∞ and H2 methods and refine them with a collection of D-K iteration commands.
Signal Analysis Module
The Xmath Signal Analysis Module uses the object-oriented nature of the MathScript language to help you simulate complex communication systems by chaining together series of lower-level generation functions. The library includes commands to represent function, signal, and noise generators. Analysis functions include linear and nonlinear operators, modulators, demodulators, spread spectrum, transforms, and special complex operators for efficient machine analysis and simulation. Finally, additional smart plotting utilities are added for refined signal display and analysis.
Interactive System Identification Module
The Xmath Interactive System Identification (ISID) Module provides a library of functions for identifying complex MIMO systems accessible graphically or from the Xmath command line. The ISID features many identification methodologies, including nonparametric, least squares, and recursive weighted error. Additional tools are included for state-space and polynomial model transformations and model validation. The graphical user interface of the ISID features an intuitive block chaining approach for organizing the steps of the identification process.
Interactive Control Design Module
The Xmath Interactive Control Design Module (ICDM) provides an interactive environment for synthesizing and refining controllers for SISO and MIMO systems. After loading a plant from Xmath, quickly develop a controller using PID, root locus, pole place, LQG, H∞, or multiloop synthesis techniques. You can visually evaluate controller behavior with the included plotting capabilities, analyze the robustness of one or more controllers as a result of the plant transfer function, and load the final controller directly into the Xmath environment for simulation against the original plant.