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# MULTI SHAKER CONTROL FOR SINE AND RANDOM

This option enables the system to output two drive signals simultaneously, to control two shakers. The phase difference between each drive and the control signal is calculated and taken into account during real-time operation. This option supports two shaker systems mounted either in push-pull or parallel-drive configurations.

## Two Scenarios in Dual Shaker Control

Scenario 1: There are multiple measurement points on the test species. Each measurement point can be defined as one of the control channels, limiting channels of monitoring channels. All the control input channels will be averaged into one Control Signal. The control algorithm will try to make the Control Signal converge to the single profile, i.e., the target.

Figure 1. Single profile with One Control Signal

Scenario 2: There are multiple measurement points on the test species. Each measurement point can be defined as one of the control channels, limiting channels of monitoring channels. Two profiles will be defined. The control signals are grouped into two. The first group is averaged into a Control Signal 1, the second the Control Signal 2. The control algorithm will manage to make the Control Signal 1 converge to the profile 1 and Control Signal 2 to Profile 2.

Figure 2. Two profiles with Two Control Signals

The scenario 1 is a lot easier to implement and execute comparing with the scenario 2 which requires the control algorithm to solve a more complex mathematics problem. Many restrictions will apply in this case. The measurement points of the control 1 group and the control 2 group cannot be highly correlated. The profile 1 and profile 2 cannot be radically different.

## Implementation

### Estimate X1 and X2

We will consider case one only. Case two requires too much change in the user-interface and I don’t see the practical usage of it.

At the first glance, the linear control system for case one can be described as simple as:

Y = H1 X1 + H2 X2

The target profile is P, so the goal of control system is to estimate X1 and X2 based on:

- Target P
- H1 and H2

Is it possible? No. The condition is not sufficient. For example, if target is 1.0, H1 = 1, H2 = 1, the value of X1 and X2 can be 0.5/0.5, 0.1/0.9 or any other solutions (unlimited).

Therefore we might consider to apply an artificial constrains on X1 and X2. For example, the weighting. A weighting applied to overall RMS or a weighting curve function applied to different band.

The weighting function can be described as:

Weighting (X1, X2) = 0

In the other words, the X1 and X2 can be solved by using:

- Target P
- H1 and H2
- Weighting

Described as:

P = H1 X1 + H2 X2

Weighting(X1, X2) = 0

For example, if X1 = 0.8X2, H1 = 0.5, H2 = 0.5, then:

*P = 0.5 * 0.8X2 + 0.5 X2*

*X2 = P/0.9 and X1 = (P/0.9) * 0.8*

### Estimate H1 and H2

Now the problem becomes how to estimate the H1 and H2 function while the system is running with measurement Y, X1 and X2. The answer is that this is unsolvable. If X1 and X2 are un-correlated, we can use partial coherence function to estimate H1 and H2. If X1 and X2 are correlated, we are lacking of one constrain condition to solve the problem, which means there are no solutions for H1 and H2 given Y, X1 and X2.

There is an idea that H1 and H2 can be estimated in two stages: In pretest and during the testing. In pretest, let’s estimate H1 and H2 each other by using zero X2 and X1:

*H1= Y/X1 when X2 = 0*

*H2= Y/X2 when X1 = 0*

Assume:

*H1 = H1 + **D H1*

*H2 = H2 + **D H2*

Where

*D H1 *is the change between current H1 and pretest H1; *D H2 *the change between current H2 and pretest H2.

The goal is:

P = (*H1 + **D H1)* X1 + (*H2 + **D H2*) X2

There is no easy way to estimate the *D H1 *and* **D H2, *so we can let the integration control do the job. The concept is, X1 and X2 is generated as:

*X1 = P/H1 +**D X1 *

*X2 = P/H2 +**D X2 *

*D X1 and **D X2 *will be estimated based on comparing error between P and Y.

For example, we can have:

*D X1= 0.01* (P-Y) * H1 *

*D X2= 0.01* (P-Y) * H2*

where *P* and *Y* are the averaged spectra of profile and measurement. We must retain the H1 and H2 above so the phase information is used.

### Importance of Phase Information

The phase information between H1 and H2 are critical to provide a good control. Consider case described in the following picture:

Figure 3. Two Shakers in Opposite Direction

This figure shows that two shakers are placed in the opposite direction. They will generate out-phase excitation to the structure. If we do not consider the relative phase of H1 and H2, the excitation of two shakers will be most cancelled. With the scheme described above, the phase information is retained in the *H1 *and *H2*. This allows that the excitations have relative phase information.