RespConfig

Options for step or impulse responses

Since R2023a

Description

Use a RespConfig object to specify options for plotting step responses (step, stepplot), impulse responses (impulse, impulseplot), and initial responses (initial and initialplot).

Step responses apply configuration as follows.

• In the SISO case

  $$u(t)=\{\begin{array}{cc}U,& t<T_0+T_d\\ U+dU,& t\ge T_0+T_d.\end{array}$$

• In the MIMO case, the step response of the jth input channel is obtained by setting

  $$u(t)=\{\begin{array}{cc}U,& t<T_0+T_d\\ U+d{U}_j*e_j,& t\ge T_0+T_d\end{array},$$

  where e_j is the jth basis vector.

Impulse responses apply configuration as follows.

$$u(t)=U+dU*\delta (t-(T_0+T_d))$$

Here:

• U is the baseline input value.

• dU is the input level change relative to U.

• T₀ is the start time.

• T_d is the time at which the change occurs relative to T₀.

Creation

Syntax

respOpt = RespConfig

respOpt = RespConfig(Name=Value)

Description

respOpt = RespConfig creates a response configuration object with default property values.

respOpt = RespConfig(Name=Value) creates a response configuration object and sets its properties using one or more name-value arguments.

Properties

Bias — Baseline input signal value

0 (default) | scalar | vector | 'u0'

Baseline input signal value, specified as a scalar or vector.

• For single-input systems, Bias is a scalar value.

• For multi-input systems, Bias is a vector of length N_u, where N_u is the number of input channels. Each vector value corresponds to the signal value in that input channel. The functions compute the responses one input channel at a time.

• For state-space models with offsets, set Bias = 'u0' to apply the step or impulse change relative to the model offsets u₀, u₀(t) of the LTV model, or u₀(t,p) of the LPV model. For LTV and LPV models, this is the u0 output of the data function. The total input signal is then u₀ + u(t).

Amplitude — Input level change

1 (default) | scalar | vector

Input level change relative to the input signal bias, specified as a scalar or vector.

• For single-input systems, Amplitude is a scalar value.

• For multi-input systems, Amplitude is a vector of length N_u, where N_u is the number of input channels. Each vector value corresponds to the level change amplitude in that input channel. The functions compute the responses one input channel at a time.

Delay — Step or impulse delay

0 (default) | nonnegative scalar

Input signal delay, specified as a nonnegative scalar value. This value specifies when the change occurs relative to the simulation start time T₀.

InitialState — Initial state values

[] (default) | vector | 'x0' | initialCondition object

Initial state values, specified as a vector or initialCondition object.

By default, the simulation starts from the steady-state condition obtained for a constant input level equal to the input bias U. For state-space models without internal delays, the initial state x_init is obtained by solving:

• Continuous time — 0 = Ax_init + BU

• Discrete time — x_init = Ax_init + BU

To start the simulation from a different initial state, use one of the following.

• For state-space models, InitialState is a vector of length N_x, where N_x is the number of states.

• For state-space models with offsets, you can also set InitialState to 'x0'. This uses the state offset value x₀ for state-space models, x₀(T₀) for LTV models, or x₀(T₀,p(T₀)) for LPV models. For LTV and LPV models, the state offset value is the x0 output of the data function evaluated at t = T₀.

• For identified LTI models, such as idtf (System Identification Toolbox), idss (System Identification Toolbox), idproc (System Identification Toolbox), idpoly (System Identification Toolbox), and idgrey (System Identification Toolbox) models, you can use an initialCondition (System Identification Toolbox) object to specify the initial state. Using identified models requires System Identification Toolbox™ software.

InitialParameter — Initial parameter values for LPV models

[] (default) | scalar | vector

Initial parameter values for LPV models, specified as a scalar or vector.

This property is required only when you specify Bias = 'u0' or InitialState = [] or 'x0'. Otherwise, this value is ignored.

Object Functions

impulse	Impulse response plot of dynamic system; impulse response data
impulseplot	Plot impulse response of dynamic system
step	Step response of dynamic system
stepplot	Plot step response of dynamic system

Examples

Configure Options for Step Response

Create a transfer function model.

sys = tf([1 5],[1 10 50]);

Create an option set to specify step input bias, amplitude, and delay.

Config = RespConfig(Bias=-2,Amplitude=5,Delay=2);

Calculate the step response using the specified options.

step(sys,Config)

Configure Options for Impulse Response

Create a state-space model.

A = [-0.8429,-0.2134;-0.5162,-1.2139];
B = [0.7254,0.7147;0,-0.2050];
C = [-0.1241,1.4090;1.4897,1.4172];
D = [0.6715,0.7172;-1.2075,0];
sys = ss(A,B,C,D);

Create a default option set and use the dot notation to specify values.

respOpt = RespConfig;
respOpt.Bias = [-2,3];
respOpt.Amplitude = [2,-0.5];
respOpt.InitialState = [0.1,-0.1];
respOpt.Delay = 5;

Compute the impulse response.

t = 0:0.1:20;
impulse(sys,t,respOpt)

Simulate State-Space Model Relative to Model Offsets

This example shows how to apply a step change to a state-space model relative to its model offsets.

Create a random state-space model with offsets.

rng(0)
sys = rss(3,1,1); 
xoff = randn(3,1);
sys.Offsets = struct("x",xoff,"u",2,"y",-1);

Create a response configuration object. For state-space models with offsets, specify "u0" for the Bias argument and "x0" for the InitialState argument.

Config = RespConfig(Bias="u0",InitialState="x0");

Simulate the model.

t = 0:0.01:15;
y = step(sys,t,Config);

Simulate without response configuration.

y2 = step(sys,t);

Compare the responses.

plot(t,y,t,y2,"r--")
legend("With offsets","Without offsets",Location="best")

The responses do not match. Therefore, it is important to initialize models with offsets correctly for accurate responses.

Version History

Introduced in R2023a

R2024b: Set baseline input value using Bias property, renamed from InputOffset

The InputOffset property is now called Bias. The behavior of this property remains the same. There are no plans to remove support for existing references to InputOffset.

R2023a: Recommended over stepDataOptions

RespConfig replaces stepDataOptions for creating a response configuration for the step command. RespConfig has better support for providing initial conditions and baseline input signal values for linear time-varying and linear parameter-varying models.