 Overview of the DynamicSystems Package - Maple Programming Help

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Overview of the DynamicSystems Package

 Calling Sequence DynamicSystems[command](arguments) command(arguments)

Description

 • The DynamicSystems package is a collection of procedures for creating, manipulating, simulating, and plotting linear systems models.
 • Continuous and discrete system objects may be created and defined in several ways, including differential equations, transfer functions, state-space matrices, and zero-pole-gain representations, and may be transformed from one form to another.
 • Input signals such as sine and step waveforms can be created by using the signal generation commands. These can be used to simulate a model using DynamicSystems simulation tools.
 • Standard plotting tools, such as Bode and root-locus plots, are available and can be used to plot both continuous and discrete system objects.
 • The system manipulation tools provide a mechanism for the advanced analysis of systems, including stability, observability, controllability, and sensitivity.
 • System objects may be simulated by using the simulation tools to obtain frequency, impulse, and transient response.
 • The Digits environment variable can be increased to accommodate systems which require greater numerical precision. See Digits for more details on how to change the number of number of digits that Maple uses when handling software floating-point numbers.
 • You can apply many of the commands from the DynamicSystems package in a clickable math way through context-sensitive options available in the Context Panel. For details, see Using the Context Panel with DynamicSystems.
 Note: The symbols used for the continuous time variable, complex frequency variable, discrete frequency variable, discrete time variable, input variable, output variable, and state variable must be unassigned or changed before using the DynamicSystems package. See SystemOptions for more details.

Plotting

 • DynamicSystems[BodePlot] : plot magnitude and phase versus frequency
 • DynamicSystems[DiscretePlot] : plot a vector of discrete points
 • DynamicSystems[ImpulseResponsePlot] : plot the impulse response of a system
 • DynamicSystems[MagnitudePlot] : plot log magnitude versus frequency
 • DynamicSystems[NicholsPlot] :  plot log magnitude versus phase
 • DynamicSystems[NyquistPlot] :  plot frequency response in complex plane
 • DynamicSystems[PhasePlot] : plot phase versus frequency
 • DynamicSystems[ResponsePlot] : plot response of a system to a given input
 • DynamicSystems[RootContourPlot] : generate a root-contour plot
 • DynamicSystems[RootLocusPlot] : generate a root-locus plot
 • DynamicSystems[ZeroPolePlot] : plot zeros and poles of a linear system

System Object Creation

 • DynamicSystems[AlgEquation] : create an algebraic equation system object
 • DynamicSystems[Coefficients] : create a coefficients system object
 • DynamicSystems[DiffEquation] : create a differential or difference equation system object
 • DynamicSystems[IsSystem] : verify the content of a system object
 • DynamicSystems[FrequencyResponseSystem] : create a frequency-response system object
 • DynamicSystems[NewSystem] : create a system object
 • DynamicSystems[PrintSystem] : print the content of a system object
 • DynamicSystems[StateSpace] : create a state-space system object
 • DynamicSystems[SystemOptions] : query and change system object options
 • DynamicSystems[TransferFunction] : create a transfer function system object
 • DynamicSystems[Verify] : verify the content of a system object
 • DynamicSystems[ZeroPoleGain] : create a zero-pole-gain system object

System Conversion

 • DynamicSystems[SSModelReduction] : reduce a state-space system
 • DynamicSystems[Resample] : resample discrete-time system object
 • DynamicSystems[ToDiscrete] : discretize a system object
 • DynamicSystems[ToContinuous] : discrete-time to continuous-time system object conversion

Signal Generation

 • DynamicSystems[Chirp] :  generate a chirp waveform
 • DynamicSystems[Ramp] :  generate a ramp waveform
 • DynamicSystems[Sinc] :  generate a sinc pulse
 • DynamicSystems[Sine] :  generate a sinusoidal waveform
 • DynamicSystems[Square] :  generate a periodic square-wave
 • DynamicSystems[Step] : generate a step waveform
 • DynamicSystems[Triangle] : generate a periodic triangular waveform

System Analysis

 • DynamicSystems[CharacteristicPolynomial] : compute the characteristic polynomial of a state-space system
 • DynamicSystems[ControllabilityMatrix] : compute the controllability matrix
 • DynamicSystems[Controllable] : determine controllability of a state-space system
 • DynamicSystems[Covariance] : compute output and state covariance matrices of system driven by white noise
 • DynamicSystems[GainMargin] : compute the gain-margin and phase-crossover frequency
 • DynamicSystems[Grammians] : compute the controllability and observability grammians
 • DynamicSystems[NormH2] : compute the H2 norm of a system
 • DynamicSystems[NormHinf : compute the ${H}_{\mathrm{\infty }}$ norm of a system
 • DynamicSystems[ObservabilityMatrix] : compute the observability matrix
 • DynamicSystems[Observable] : determine observability of a state-space system
 • DynamicSystems[PhaseMargin] : return the phase-margin and gain-crossover frequency
 • DynamicSystems[RouthTable] : generate the Routh table (stability) of a polynomial
 • DynamicSystems[SSTransformation] : perform similarity transformations on state-space matrices
 • DynamicSystems[StepProperties] : compute the properties of a step response

System Manipulation

 • DynamicSystems[AppendConnect] : append systems together
 • DynamicSystems[FeedbackConnect] : connect one or two systems in feedback
 • DynamicSystems[ParallelConnect] : connect systems in parallel
 • DynamicSystems[ScaleInputs] : scale inputs by constant coefficients
 • DynamicSystems[ScaleOutputs] : scale outputs by constant coefficients
 • DynamicSystems[SeriesConnect] : connect systems in series
 • DynamicSystems[SSModelReduction] : reduce a state-space system
 • DynamicSystems[Subsystem] : extract a subsystem from a system
 • DynamicSystems[SystemConnect] : connect systems

Linearization

 • DynamicSystems[EquilibriumPoint] : find the local equilibrium point of a system satisfying constraints
 • DynamicSystems[Linearize] : construct a linear model of a system at a point

Simulation Tools

 • DynamicSystems[FrequencyResponse] :  compute the frequency response of a system
 • DynamicSystems[ImpulseResponse] : compute the impulse response of a system
 • DynamicSystems[Simulate] : compute time-response of a system to an input

Reference

 • Using the Context Panel with DynamicSystems : details about the DynamicSystems context-sensitive menu
 • Description of the Model of a Linear System Object : details about linear system objects
 • DynamicSystems[System] : type check for a DynamicSystems object