Getting Started

Time and Frequency Responses

Time responses investigate the time-domain transient behavior of linear models for particular classes of inputs and disturbances. You can determine such system characteristics as rise time, settling time, overshoot, and steady-state error from the time response. The Control System Toolbox provides functions for step response, impulse response, initial condition response, and general linear simulations. For example, you can simulate the response to white noise inputs using lsim and the MATLAB function randn.

In addition to time-domain analysis, the Control System Toolbox provides functions for frequency-domain analysis using the following standard plots:

• Bode
• Nichols
• Nyquist
• Singular value

This table lists available time and frequency response functions and their use.

Table 3-1: Functions for Frequency and Time Response 

Functions	Description
bode	Bode plot
evalfr	Computes the frequency response at a single complex frequency (not for FRD models)
freqresp	Computes the frequency response for a set of frequencies
gensig	Input signal generator (for lsim)
impulse	Impulse response plot
initial	Initial condition response plot
iopzmap	Pole-zero map for each I/O pair of an LTI model
lsim	Simulation of response to arbitrary inputs
margin	Computes and plots gain and phase margins
nichols	Nichols plot
nyquist	Nyquist plot
pzmap	Pole-zero map
step	Step response plot

These functions can be applied to single linear models or LTI arrays.

The functions step, impulse, and initial automatically generate an appropriate simulation horizon for the time response plots. Their syntax is

• step(model_name) 
  impulse(model_name)
  initial(model_name,x0)    % x0 = initial state vector
  

where model_name is any continuous or discrete LTI model or LTI array.

Frequency-domain plots automatically generate an appropriate frequency range as well.

Functions for Time and Frequency Response

Plotting MIMO Model Responses