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The Linearize command returns a DynamicSystems model that is a linearized form of a linked subsystem, one that can be represented in first-order form:
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represents the state variables;
represents the input variables specified by inputs;
represents the output variables specified by outputs;
and are functions to be linearized;
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The output of Linearize can also be represented in state-space form:
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where , , , and are the Jacobian matrices evaluated at the linearization point (), which is the equilibrium or initial point. At the equilibrium point and . At the initial point may not be zero but this offset value will be returned in the equations.
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The linearization algorithm uses an initial point of the system in order to compute its equilibrium point (where derivatives of states are set to zero). If no equilibrium point can be found then the user is invited to linearize the system around the initial point. The ics option can be used to affect the computation of the initial point.
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The system must have state variables or output equations in order for linearization to occur. If there are output equations but no states then the state-space matrices , , and will be empty and only the matrix representing the part of the linearized system will be populated.
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The Linearize command provides information about the linearized model that can be used for various purposes, including model analysis and control design. For example, a MapleSim model with no inputs or outputs will be represented by its system matrix after linearization and this information can be used for modal analysis as shown in the Examples section.
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The A := MapleSim:-LinkModel() statement needs to be run prior to successfully using any of the ModelObject A's export functions.
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