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System responses such as Bode plots and step responses;
system characteristics such as response time and overshoot; simulation

Time-domain and frequency-domain analysis commands let you compute and visualize SISO and MIMO system responses such as Bode plots, Nichols plots, step responses, and impulse responses. You can also extract system characteristics such as rise time and settling time, overshoot, and stability margins. Most linear analysis commands can either return response data or generate response plots. For an overview of plotting commands, see Plotting System Responses. To create plots whose properties are customizable at the command line, see Plot Customization.

Linear System Analyzer | Analyze time and frequency responses of linear time-invariant (LTI) systems |

`step` |
Step response plot of dynamic system; step response data |

`stepinfo` |
Rise time, settling time, and other step response characteristics |

`impulse` |
Impulse response plot of dynamic system; impulse response data |

`initial` |
Initial condition response of state-space model |

`lsim` |
Simulate time response of dynamic system to arbitrary inputs |

`lsiminfo` |
Compute linear response characteristics |

`gensig` |
Generate test input signals for lsim |

`covar` |
Output and state covariance of system driven by white noise |

`stepDataOptions` |
Options set for step |

`bode` |
Bode plot of frequency response, magnitude and phase of frequency response |

`bodemag` |
Bode magnitude response of LTI models |

`nyquist` |
Nyquist plot of frequency response |

`nichols` |
Nichols chart of frequency response |

`ngrid` |
Superimpose Nichols chart on Nichols plot |

`sigma` |
Singular values plot of dynamic system |

`freqresp` |
Frequency response over grid |

`evalfr` |
Evaluate frequency response at given frequency |

`dcgain` |
Low-frequency (DC) gain of LTI system |

`bandwidth` |
Frequency response bandwidth |

`getPeakGain` |
Peak gain of dynamic system frequency response |

`getGainCrossover` |
Crossover frequencies for specified gain |

`fnorm` |
Pointwise peak gain of FRD model |

`norm` |
Norm of linear model |

`db2mag` |
Convert decibels (dB) to magnitude |

`mag2db` |
Convert magnitude to decibels (dB) |

LTI System | Use linear system model object in Simulink |

LPV System | Simulate Linear Parameter-Varying (LPV) systems |

Generate and visualize time-response data such as step response and impulse response.

**Time-Domain Response Data and Plots****Time-Domain Responses of Discrete-Time Model****Time-Domain Responses of MIMO Model****Time-Domain Responses of Multiple Models**

**Time-Domain Characteristics on Response Plots**

Visualize time-domain system characteristics such as settling time and overshoot on response plots.

**Numeric Values of Time-Domain System Characteristics**

Use the `stepinfo`

function to obtain
numeric values of step response characteristics such as rise time,
settling time, and overshoot.

**Response from Initial Conditions**

Compute and plot the response of a state-space (`ss`

) model to specified initial state values.

**Simulate Models with Arbitrary Inputs and Initial Conditions**

Use the Linear Simulation Tool to simulate system responses to arbitrary input signals and initial conditions.

Generate and visualize frequency-response data such as Bode plots and Nichols plots.

**Frequency-Domain Characteristics on Response Plots**

Visualize frequency-domain system characteristics such as peak response on plots.

**Numeric Values of Frequency-Domain Characteristics of SISO Model**

Obtain numeric values of frequency-domain characteristics such as peak gain, dc gain, and system bandwidth.

**Joint Time-Domain and Frequency-Domain Analysis**

Compare multiple types of responses side by side, including both time-domain and frequency-domain responses, using the Linear System Analyzer app.

**Linear Analysis Using the Linear System Analyzer**

Analyze the time-domain and frequency-domain responses of one or more linear models using the Linear System Analyzer app.

In analysis plots of multiple-input, multiple output LTI models, there are plot tools for selecting subsystems and grouping I/O pairs.

**Analysis of Systems with Time Delays**

The time and frequency responses of delay systems can have features that can look odd to those only familiar with delay-free LTI analysis.

**Analyzing Control Systems with Delays**

Many processes involve dead times, also referred to as transport delays or time lags. Controlling such processes is challenging because delays cause phase shifts that limit the control bandwidth and affect closed-loop stability.

**Analyzing the Response of an RLC Circuit**

Analyze the time and frequency responses of a second-order system.

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