Time and Frequency Domain Analysis
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. To get started with 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 response of dynamic system
|Rise time, settling time, and other step-response characteristics
|Impulse response plot of dynamic system; impulse response data
|System response to initial states of state-space model
|Plot simulated time response of dynamic system to arbitrary inputs; simulated response data
|Compute linear response characteristics
|Create periodic signals for simulating system response with
|Output and state covariance of system driven by white noise
|Options for step or impulse responses (Since R2023a)
|Bode plot of frequency response, or magnitude and phase data
|Magnitude-only Bode plot of frequency response
|Nyquist plot of frequency response
|Nichols chart of frequency response
|Superimpose Nichols chart on Nichols plot
|Singular value plot of dynamic system
|Evaluate system response over a grid of frequencies
|Evaluate system response at specific frequency
|Low-frequency (DC) gain of LTI system
|Frequency response bandwidth
|Peak gain of dynamic system frequency response
|Crossover frequencies for specified gain
|Pointwise peak gain of FRD model
|Norm of linear model
|Convert decibels (dB) to magnitude
|Convert magnitude to decibels (dB)
|Open-loop transfer function of control system represented by
|Closed-loop transfer function from generalized model of control system
|Sensitivity function from generalized model of control system
|Complementary sensitivity function from generalized model of control system
Live Editor Tasks
|Interactively create linear analysis response plots in the Live Editor (Since R2022b)
Analysis Plots Basics
- Plotting System Responses
This example shows an overview of generating time-domain and frequency-domain response plots.
- Time-Domain Responses
Generate and visualize time-response data such as step response and impulse response.
- 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
stepinfofunction 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.
- Import LTI Model Objects into Simulink
Use the LTI System block to import linear system model objects into Simulink®.
- Frequency-Domain Responses
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.
Linear System Analyzer
- 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.
- Analyzing MIMO Models
In analysis plots of multiple-input, multiple output LTI models, there are plot tools for selecting subsystems and grouping I/O pairs.
Systems with Time Delays
- 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.