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Trimming and Linearization

Find operating point and linearize model to explore system response and stability

Determining the response of a system to small perturbations at an operating point is a critical step in system and controller design. Once you find an operating point, you can linearize the model about that operating point to explore the response and stability of the system.

Functions

simscape.findNonlinearBlocks Check model for blocks with nonlinear equations

Topics

Finding an Operating Point
Describes how to find and manage operating points in Simscape™ models by trimming and other methods.
Linearizing at an Operating Point
Describes how to linearize Simscape models at specified operating points or times.
Linearize an Electronic Circuit
Example showing how to linearize a model and create a Bode plot for small-signal frequency-domain analysis. Depending on the software you have available, use the appropriate sections of this example to explore various linearization and analysis techniques.
Linearize a Plant Model for Use in Feedback Control Design
Example showing how to linearize a model to support control system stability analysis and design. Depending on the software you have available, use the appropriate sections of this example to explore various linearization and analysis techniques.

Featured Examples

Nonlinear Bipolar Transistor

An implementation of a nonlinear bipolar transistor based on the Ebers-Moll equivalent circuit. R1 and R2 set the nominal operating point, and the small signal gain is approximately set by the ratio R3/R4. The 1uF decoupling capacitors have been chosen to present negligible impedance at 1KHz. The model is configured for linearization so that a frequency response can be generated.

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Hydraulic Actuator with Digital Position Controller

A two-way valve acting in a closed-loop circuit together with a double-acting cylinder implemented in the isothermal liquid domain. The controller is represented as a continuous-time transfer function plus a transport delay. The delay allows for the computational time (one discrete time period) plus the zero-order hold (half a discrete time period) when implemented in discrete time. The model is configured for linearization so that a frequency response can be generated. To configure for faster desktop simulation, comment through the transport delay and increase the solver maximum step size.

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