Linearization for Model Analysis and Control Design

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Linearize Simulink models

Linearization involves creating a linear approximation of a nonlinear system that is valid in a small region around the operating or trim point, a steady-state condition in which all model states are constant. Linearization is needed to design a control system using classical design techniques, such as Bode plot and root locus design. Linearization also lets you analyze system behavior, such as system stability, disturbance rejection, and reference tracking.

You can linearize a nonlinear Simulink® model to produce a linear state-space, transfer function, or pole-zero-gain model. You can use these models to:

  • Plot the Bode response
  • Evaluate loop stability margins
  • Analyze and compare system responses near different operating points
  • Design linear controllers with reduced sensitivity to parameter variations and modeling errors
  • Measure resonances in the frequency response of the closed-loop system

An alternative to linearization is feeding input signals through the model and calculating frequency response from the simulation output and input. You can use frequency response estimation when the model cannot be linearized because of event-based dynamics, such as those associated with pulse-width modulation and Stateflow® diagrams.

For more information on linearizing Simulink models, see Simulink Control Design™. It also provides functions for calculating frequency response without making changes to the model.

Examples and How To

Steady-State Operating Points and Linearization

Frequency Response Estimation

Software Reference

See also: control systems, PID control, parameter estimation, PID Tuning, Control Design Software, Bode Plot, root locus, linearization videos