lsiminfo

Compute linear response characteristics

Syntax

S = lsiminfo(y,t)

S = lsiminfo(y,t,yfinal)

S = lsiminfo(y,t,yfinal,yinit)

S = lsiminfo(___,'SettlingTimeThreshold',ST)

Description

lsiminfo lets you compute linear response characteristics from an array of response data [y,t]. For a linear response y(t), lsiminfo computes characteristics relative to y_init and y_final, where y_init is the initial offset, that is, the value before the input is applied, and y_final is the steady-state value of the response.

lsiminfo uses y_init = 0 and y_final = last sample value of y(t) unless you explicitly specify these values.

The function returns the characteristics in a structure containing the fields:

• TransientTime — The first time T such that the error |y(t) – y_final| ≤ SettlingTimeThreshold × e_max for t ≥ T, where e_max is the maximum error |y(t) – y_final| for t ≥ 0.

  By default, SettlingTimeThreshold = 0.02 (2% of the peak error). Transient time measures how quickly the transient dynamics die off.

• SettlingTime — The first time T such that |y(t) – y_final| ≤ SettlingTimeThreshold × |y_final – y_init| for t ≥ T.

  By default, settling time measures the time it takes for the error to stay below 2% of |y_final – y_init|.

• Min — Minimum value of y(t).

• MinTime — Time the response takes to reach the minimum value.

• Max — Maximum value of y(t).

• MaxTime — Time the response takes to reach the maximum value.

S = lsiminfo(y,t) computes linear response characteristics from an array of response data y and corresponding time vector t. This syntax uses y_init = 0 and the last value in y (or the last value in each channel's corresponding response data) as y_final to compute characteristics that depend on these values.

For SISO system responses, y is a vector with the same number of entries as t. For MIMO response data, y is an array containing the responses of each I/O channel.

S = lsiminfo(y,t,yfinal) computes linear response characteristics relative to the steady-state value yfinal. This syntax is useful when you know that the expected steady-state system response differs from the last value in y for reasons such as measurement noise. This syntax uses y_init = 0.

For SISO responses, t and y are vectors with the same length NS. For systems with NY outputs, you can specify y as an NS-by-NY array and yfinal as an NY-by-1 array. lsiminfo then returns a NY-by-1 structure array S of response characteristics corresponding to each output channel.

S = lsiminfo(y,t,yfinal,yinit) computes response characteristics relative to the response initial value yinit. This syntax is useful when your y data has an initial offset, that is, y is nonzero before the input is applied.

For SISO responses, t and y are vectors with the same length NS. For systems with NY outputs, you can specify y as an NS-by-NY array and yfinal and yinit as an NY-by-1 arrays. lsiminfo then returns a NY-by-1 structure array S of response characteristics corresponding to each output channel.

S = lsiminfo(___,'SettlingTimeThreshold',ST) lets you specify the threshold ST used in definition of settling and transient times. The default value is ST = 0.02 (2%). You can use this syntax with any of the previous input-argument combinations.

Examples

Compute Response Characteristics of Transfer Function

Create the following continuous-time transfer function:

$$H(s)=\frac{s-1}{s^3+2s^2+3s+4}$$

sys = tf([1 -1],[1 2 3 4]);

Calculate the impulse response.

[y,t] = impulse(sys);

impulse returns the output response y and the time vector t used for simulation.

Compute the response characteristics using a final response value of 0.

s = lsiminfo(y,t,0)

s = struct with fields:
    TransientTime: 22.8700
     SettlingTime: NaN
              Min: -0.4268
          MinTime: 2.0088
              Max: 0.2847
          MaxTime: 4.0733

You can plot the impulse response and verify these response characteristics. For example, the time at which the minimum response value (MinTime) is reached is approximately 2 seconds.

impulse(sys)

Input Arguments

y — Response data

vector | array

Response data, specified as one of the following:

• For SISO response data, a vector of length Ns, where Ns is the number of samples in the response data.

• For MIMO response data, an Ns-by-Ny array, where Ny is the number of system outputs.

t — Time vector

vector

Time vector corresponding to the response data in y, specified as a vector of length Ns.

yfinal — Steady-state value

scalar | array

Response steady-state value, specified as a scalar or an array.

• For SISO response data, specify a scalar value.

• For MIMO response data, specify an Ny-by-1 array, where each entry provides the steady-state response value for the corresponding system channel.

If you do not provide yfinal, then lsiminfo uses the last value in the corresponding channel of y as the steady-state response value.

yinit — Response initial value

scalar | array

Value of y before the input is applied, specified as a scalar or an array.

• For SISO response data, specify a scalar value.

• For MIMO response data, specify an Ny-by-1 array, where each entry provides the response initial value for the corresponding system channel.

If you do not provide yinit, then lsiminfo uses zero as the response initial value.

ST — Settling time threshold

0.02 (default) | scalar between 0 and 1

Threshold for defining settling and transient times, specified as a scalar value between 0 and 1. To change the default settling and transient time definitions (see Description), set ST to a different value. For instance, to measure when the error falls below 5%, set ST to 0.05.

Output Arguments

S — Response characteristics

structure

Linear response characteristics, returned as a structure containing the fields:

• TransientTime

• SettlingTime

• Min

• MinTime

• Max

• MaxTime

For more information on how lsiminfo defines these characteristics, see Description.

For MIMO models or responses data, S is a structure array in which each entry contains the step-response characteristics of the corresponding I/O channel. For instance, if you provide a 3-input, 3-output model or array of response data, then S(2,3) contains the characteristics of the response from the third input to the second output.

Version History

Introduced in R2006a

R2021b: Settling time computation changed

The settling time calculation is now based on the time it takes for the error to stay below 2% of |y_final – y_init|. The following table summarizes the changes to the fields of the structure returned by lsiminfo.

Before R2021b	R2021b
SettlingTime — The first time T such that the error |y(t) – yfinal| ≤ SettlingTimeThreshold × emax for t ≥ T, where emax is the maximum error |y(t) – yfinal| for t ≥ 0. By default, SettlingTimeThreshold = 0.02 (2% of the peak error). SettlingTime measures the time for the error to fall below 2% of the peak value of the error.	SettlingTime — The first time T such that the error |y(t) – yfinal| ≤ SettlingTimeThreshold × |yfinal – yinit| for t ≥ T. By default, SettlingTime measures the time it takes for the error to stay below 2% of |yfinal – yinit|.

Additionally, the output structure S now contains a TransientTime field. This characteristic contains the peak-error-based settling time calculation used in releases before R2021b. Transient time is used to measure how quickly the transient dynamics die off.