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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.

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

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

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

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

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

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

DynamicSystems:-EquilibriumPoint : find the local equilibrium point of a system satisfying constraints

DynamicSystems:-Linearize : construct a linear model of a system at a point

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

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