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The purpose of adaptive inverse control is to create an inverse model of an unknown plant in a control system. You can control the unknown plant by using the inverse model of the plant. The following figure shows a diagram of an adaptive inverse control system.

In the previous figure, a stimulus signal *s*(*n*) excites the unknown plant. The plant generates a signal *x*(*n*), which is the input signal to the adaptive filter. The adaptive inverse control system also produces a delayed signal *d*(*n*) of the stimulus signal and compares *d*(*n*) with *y*(*n*), which is the output signal of the adaptive filter. *z*^{–Δ} is the delay function. *e*(*n*) is the error signal. The adaptive filter adjusts the coefficients iteratively to minimize the power of *e*(*n*). When the power of *e*(*n*) reaches the minimal value, the adaptive filter represents the inverse model of the unknown plant.

One example of adaptive inverse control is vibration testing, which tests the reliability of products that operate in an environment with a large amount of vibration. For example, you can use a road simulator to verify whether consumer products can survive highway transportation. Most road simulators are shakers that simulate vibration in the transportation environment by replicating a vibration waveform that you record in a real-world transportation environment. When you apply a waveform to a shaker, the shaker cannot produce the vibration that is identical to the waveform due to the dynamic properties of the shaker. In this case, you can use an adaptive filter to control the shaker to produce the vibration that is identical to the real-world vibration you record.

The following figure shows a diagram of vibration testing.

This diagram is a modified form of the diagram of adaptive inverse control. In the previous figure, the reference input signal is the waveform that you expect the shaker to produce and *H*(*z*) is the inverse transfer function of the shaker. If you send the reference input signal to *H*(*z*) and use the output signal from *H*(*z*) to stimulate the shaker, *x*(*n*) becomes identical to the reference input signal except for a delay of *Δ* taps.

Refer to the Waveform Replication (Simulated) VI in the examples\Adaptive Filters\Applications\Waveform Replication directory for an example that uses the LabVIEW Adaptive Filter Toolkit to perform adaptive inverse control.