addResponse

Add dynamic system response to existing response plot

Since R2024b

Syntax

addResponse(rp,sys)

addResponse(rp, sys1,sys2,...,sysN)

addResponse(___,Name=Value)

Description

addResponse(rp,sys) adds the response for dynamic system model sys to the existing response plot associated with chart object rp.

• The time and frequency specifications for the added response are computed automatically.

• The line width and color for the response are assigned automatically.

addResponse(rp, sys1,sys2,...,sysN) add the responses for multiple dynamic system models.

addResponse(___,Name=Value) configures added responses using one or more name-value arguments.

Examples

Plot Multiple Step Responses

Create a second-order transfer function with a damping ratio of 0.5.

wn = 2;
zeta = 0.5;
sys = tf(wn^2,[1,2*zeta*wn,wn^2]);

Plot the step response of this system.

sp = stepplot(sys);

Create a transfer function with a lower damping ratio and add it to the step plot.

zetaL = 0.25;
sysL = tf(wn^2,[1,2*zetaL*wn,wn^2]);
addResponse(sp,sysL);

Create a transfer function with a higher damping ratio and add it to the step plot.

zetaH = 0.75;
sysH = tf(wn^2,[1,2*zetaH*wn,wn^2]);
addResponse(sp,sysH);

Add a legend to the plot.

legend("zeta = 0.5","zeta = 0.25","zeta = 0.75",...
    Location="southeast");

Input Arguments

rp — Response plot chart object

impulseplot object | initialplot object | stepplot object | lsimplot object | bodeplot object | nicholsplot object | nyquistplot object | sigmaplot object | pzplot object | iopzplot object | rlocusplot object

Response plot chart object, specified as one of the following objects:

• impulseplot (Control System Toolbox) — Impulse response

• initialplot (Control System Toolbox) — Initial condition response

• stepplot (Control System Toolbox) — Step response

• lsimplot (Control System Toolbox) — Simulated time response to arbitrary input

• bodeplot (Control System Toolbox) — Bode frequency response

• nicholsplot (Control System Toolbox) — Nichols frequency response

• nyquistplot (Control System Toolbox) — Nyquist response

• sigmaplot (Control System Toolbox) — Singular values for frequency response

• pzplot (Control System Toolbox) — Pole-zero map

• iopzplot (Control System Toolbox) — Plot pole-zero map for input-output pairs

• rlocusplot (Control System Toolbox) — Root locus plot

sys — Dynamic system

dynamic system model | model array

Dynamic system, specified as a SISO or MIMO dynamic system model or array of dynamic system models. Dynamic systems that you can use include:

• Continuous-time or discrete-time numeric LTI models, such as tf (Control System Toolbox), zpk (Control System Toolbox), or ss (Control System Toolbox) models.

• Sparse state-space models, such as sparss (Control System Toolbox) or mechss (Control System Toolbox) models.

• Generalized or uncertain LTI models such as genss (Control System Toolbox) or uss (Robust Control Toolbox) models. Using uncertain models requires Robust Control Toolbox™ software.

  • For tunable control design blocks, the function evaluates the model at its current value to plot the response.

  • For uncertain control design blocks, the function plots the nominal value and random samples of the model.

• Frequency-response data models such as frd models. For such models, the function plots the response at the frequencies defined in the model.

• Identified LTI models, such as idtf, idss, or idproc models.

• Linear time-varying (ltvss (Control System Toolbox)) and linear parameter-varying (lpvss (Control System Toolbox)) models.

Dependencies

The supported models depend on the type of chart object specified in rp.

• Frequency-response data models are supported only for bodeplot, nicholsplot, nyquistplot, and sigmaplot chart objects.

• Linear time-varying and linear parameter-varying models are supported only for stepplot, impulseplot, initialplot, and lsimplot chart objects.

• For rlocusplot chart objects, only SISO models are supported.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: Color="red" sets the plot color to red.

Plot Appearance

Color — Plot color

RGB triplet | hexadecimal color code | color name

Plot color, specified as an RGB triplet or a hexadecimal color code and stored as an RGB triplet.

Alternatively, you can specify some common colors by name. The following table lists these colors and their corresponding RGB triplets and hexadecimal color codes.

Color Name	RGB Triplet	Hexadecimal Color Code
"red" or "r"	[1 0 0]	#FF0000
"green" or "g"	[0 1 0]	#00FF00
"blue" or "b"	[0 0 1]	#0000FF
"cyan" or "c"	[0 1 1]	#00FFFF
"magenta" or "m"	[1 0 1]	#FF00FF
"yellow" or "y"	[1 1 0]	#FFFF00
"black" or "k"	[0 0 0]	#000000
"white" or "w"	[1 1 1]	#FFFFFF

LineStyle — Line style

"-" | "--" | ":" | "-."

Line style, specified as one of the following values.

Line Style	Description
"-"	Solid line
"--"	Dashed line
":"	Dotted line
"-."	Dash-dotted line

MarkerStyle — Marker style

"none" | "o" | "+" | "*" | "." | ...

Marker style, specified as one of the following values.

Marker	Description
"none"	No marker
"o"	Circle
"+"	Plus sign
"*"	Asterisk
"."	Point
"x"	Cross
"_"	Horizontal line
"|"	Vertical line
"s"	Square
"d"	Diamond
"^"	Upward-pointing triangle
"v"	Downward-pointing triangle
">"	Right-pointing triangle
"<"	Left-pointing triangle
"p"	Pentagram
"h"	Hexagram

Options — Plot options

timeoptions object | bodeoptions object | object | nicholsoptions object | nyquistoptions object | sigmaoptions object | pzoptions object

Plot options, specified as one of the following objects, depending on the type of chart object specified in rp.

Options Object	Chart Object rp
timeoptions (Control System Toolbox)	impulseplot, initialplot, stepplot, and lsimplot
bodeoptions (Control System Toolbox)	bodeplot
nicholsoptions (Control System Toolbox)	nicholsplot
nyquistoptions (Control System Toolbox)	nyquistplot
sigmaoptions (Control System Toolbox)	sigmapplot
pzoptions (Control System Toolbox)	pzplot, iopzplot, and rlocusplot

Step and Impulse Response

Time — Time steps

positive scalar | two-element vector | vector | []

Time steps at which to compute the response, specified as one of the following:

• Positive scalar tFinal— Compute the response from t = 0 to t = tFinal.

• Two-element vector [t0 tFinal] — Compute the response from t = t0 to t = tFinal. (since R2023b)

• Vector Ti:dt:Tf— Compute the response for the time points specified in t.

  • For continuous-time systems, dt is the sample time of a discrete approximation to the continuous system.

  • For discrete-time systems with a specified sample time, dt must match the sample time property Ts of sys.

  • For discrete-time systems with an unspecified sample time (Ts = -1), dt must be 1.

• [] — Automatically select time values based on system dynamics.

When you specify a time range using either tFinal or [t0 tFinal]:

• For continuous-time systems, the function automatically determines the size of the time step and number of points based on the system dynamics.

• For discrete-time systems with a specified sample time, the function uses the sample time of sys as the step size.

• For discrete-time systems with unspecified sample time (Ts = -1), the function interprets tFinal as the number of sampling periods to simulate with a sample time of 1 second.

Express t using the time units specified in the TimeUnit property of sys.

If you specified a step delay td using Config, the function applies the step at t = t0+td.

Dependencies

This argument is supported only when rp is a stepplot object or an impulse object.

Parameter — LPV model parameter trajectory

matrix | function handle

Parameter trajectory of the LPV model, specified as a matrix or a function handle.

• For exogenous or explicit trajectories, specify p as a matrix with dimensions N-by-Np, where N is the number of time samples and Np is the number of parameters.

  Thus, the row vector p(i,:) contains the parameter values at the ith time step.

• For endogenous or implicit trajectories, specify p as a function handle of the form p = F(t,x,u) in continuous time and p = F(k,x,u) in discrete time that gives parameters as a function of time t or time sample k, state x, and input u.

  This option is useful when you want to simulate quasi-LPV models. For an example, see Step Response of LPV Model.

Dependencies

This argument is supported only when sys is an LPV model and rp is a stepplot object or an impulse object.

Config — Response configuration

RespConfig object

Configuration of the applied signal, specified as a RespConfig object. By default, step applies an input that goes from 0 to 1 at time t = 0. Use this input argument to change the configuration of the step input. See Response to Custom Step Input for an example.

For lpvss (Control System Toolbox) and ltvss (Control System Toolbox) models with offsets (x₀(t),u₀(t)), you can use RespConfig to define the input relative to u₀(t,p) and initialize the simulation with the state x₀(t,p).

This argument is supported only when rp is a stepplot object or an impulse object.

Dependencies

This argument is supported only when rp is a stepplot object or an impulse object.

Frequency Response

Frequency — Frequencies

{wmin,wmax} | vector | []

Frequencies at which to compute the response, specified as one of the following:

• Cell array of the form {wmin,wmax} — Compute the response at frequencies in the range from wmin to wmax. If wmax is greater than the Nyquist frequency of sys, the response is computed only up to the Nyquist frequency.

• Vector of frequencies — Compute the response at each specified frequency. For example, use logspace to generate a row vector with logarithmically spaced frequency values. The vector w can contain both positive and negative frequencies.

• [] — Automatically select frequencies based on system dynamics.

For models with complex coefficients, if you specify a frequency range of [w_min,w_max] for your plot, then in:

• Log frequency scale, the plot frequency limits are set to [w_min,w_max] and the plot shows two branches, one for positive frequencies [w_min,w_max] and one for negative frequencies [–w_max,–w_min].

• Linear frequency scale, the plot frequency limits are set to [–w_max,w_max] and the plot shows a single branch with a symmetric frequency range centered at a frequency value of zero.

Specify frequencies in units of rad/TimeUnit, where TimeUnit is the TimeUnit property of the model.

Dependencies

This argument is supported only when rp is a bodeplot,nicholsplot, nyquistplot, or sigmaplot object.

Version History

Introduced in R2024b