Simulink Control Design™ - MathWorks

Online Estimation of Frequency Responses of a

Nonlinear Plant

This example shows how to use the Frequency Response Estimator block to perform

online estimation of the plant frequency responses. For a nonlinear plant, estimation at

different nominal operating points produces different frequency responses.

Real Time Frequency Response Estimation

Frequency response describes the steady state response of a system to a sinusoidal input

signal. If the system is linear G(s), the output signal is a sine wave of the same frequency

with a different magnitude and a phase shift. A frequency response data (frd) model that

stores frequency response information at multiple frequencies is useful for tasks such as

analyzing plant dynamics, validating linearization results, designing a control system, and

estimating a parametric model.

There are different ways to obtain an frd model in the Simulink environment. The most

common approach is to linearize the Simulink model and calculate the frequency

responses directly from the obtained state-space system. When the Simulink model

cannot be linearized, you can use the frestimate command or use the Linear Analysis

Tool app to run simulation with some perturbation signals. Afterwards, the plant

frequency responses are estimated offline based on the collected experiment data. This

approach is called offline estimation.

This example shows an alternative online estimation approach using the Frequency

Response Estimator block is to conduct an experiment and estimate the frequency

response during simulation. Although this example uses a plant modeled in Simulink, if

you do not have a plant model in Simulink, you can deploy the block on your target

system and carry out frequency response estimation against a physical plant in real time.

For more information, see “Online Frequency Response Estimation Basics” on page 6-2.

Nonlinear Plant Model

This example uses a stable nonlinear SISO plant. The plant has two states. Trim the

model to find an initial steady-state operating point at which the plant output is zero.

plantMDL = 'scdfrePlant';

y0 = 0;

op = operspec(plantMDL);

op.Outputs.Known = true;

op.Outputs.y = y0;

Online Estimation of Frequency Responses of a Nonlinear Plant