## Linearization for Model Analysis and Control Design |

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.

- Trim, Linearization, and Control Design for an Aircraft 7:17 (Video)
- Trimming and Linearizing an Airframe (Example)
- Linearizing of an Engine Speed Model (Example)
- Linearization of a Pneumatic System at Simulation Snapshots (Example)
- Batch Mode Trimming and Linearization 5:20 (Video)
- Steady-State Operating Points from State Specifications (Example)
- Steady-State Operating Point to Meet Output Specification (Example)
- Linearize at Trimmed Operating Point (Example)
- Linearize at Simulation Snapshot (Example)
- Linearize at Triggered Simulation Events (Example)
- Linearize Simulink Model (Example)
- Plant Linearization (Example)
- Compute Open-Loop Response (Example)

- Frequency Response Estimation 6:15 (Video)
- Estimate Frequency Response Using Linear Analysis Tool (Example)
- Estimate Frequency Response with Linearization-Based Input Using Linear Analysis Tool (Example)
- Frequency Response Estimation Using Simulation-Based Techniques (Example)
- Frequency-Domain Validation of Linearization (Example)
- Estimating Frequency Response Models with Noise Using System Identification Toolbox (Example)

- Linearization (Documentation)
- Steady-State Operating Points (Documentation)
- Frequency Response Estimation (Documentation)

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