Build and analyze control systems, document design decisions, and interactively test controllers—all in one system.
Underlying the Mathematica 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 efficiently. The Mathematica solution is ideal for testing ideas and designing new systems efficiently.
Simulating the response of state-space or transfer-function models
The step responses of a second-order system for different values of damping
Interactively analyzing system behavior
Determining critical points of system behavior, such as break-away, break-in, and imaginary-axis crossings, using an interactive root-locus plot
Determining system stability using built-in functions
Analyzing a system's stability from its Nyquist plot
Building regulators and observers for systems
The LQG regulator of a stochastic system
Constructing observers to estimate the states of a system
The trajectories of the states and a Luenberger-observer's state estimates
Specify models of linear, time-invariant systems in natural form
The linearized state-space model of an inverted pendulum is generated from the underlying equations of motion and typeset in a natural traditional form
Specify state-space and transfer-function models in natural form, and easily convert from one form to another
Obtain linearized state-space models of systems described by differential or difference equations
Freely convert between continuous-time and discrete-time models using a wide selection of algorithms
Perform system manipulations, such as selecting or deleting subparts, cascading a set of systems, constructing interconnections of subsystems, and more
Analyze and design systems using frequency-response tools centered around Bode plot, Nyquist plot, Nichols plot, and singular-value plot
Analyze state-space models and convert between different realizations, including Kalman, Jordan, balanced, and other forms
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
Simulate open- and closed-loop systems to determine state and output responses
Connect to databases instantly for easy access of specialized data
Next:
Why Choose Mathematica
Key Capabilities
Why Choose Mathematica
Ways to Use
Compare Mathematica to your current tools. Do they have these advantages?
Directly input both transfer-function and state-space models in natural form Competitor note: Matlab allows you to specify transfer-function models only as a matrix of row vectors
Analyze symbolic and numeric systems Competitor note: Matlab handles numeric systems only
Well integrated with the core Mathematica system and more than 20 built-in application areas, such as image processing, wavelets, statistics, linear algebra, and more
Next:
Ways to Use
Key Capabilities
Why Choose Mathematica
Ways to Use
Compute the state-space model of a system described by difference or differential equations
Analyze the stability of a system using built-in frequency-response tools, computing the poles, or solving a Lyapunov equation
Simplify models of systems with interconnected components using block-diagram reduction
Manipulate linear models as transfer-function or state-space data objects
Interactively analyze the system behavior as parameters are varied
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
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
Develop feedback laws to enhance the performance of dynamic systems
Estimate unmeasured states or noisy measurements
Directly obtain models of controllers and estimators that can be easily assembled to form a closed-loop system for further simulations
Discretize continuous-time feedback algorithms for real-time implementation
"I think software in engineering and math should not be done like it is usually done in other programming languages. Mathematica is much richer, and there are more possibilities."
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