As mentioned in our introductory part in our basic discussion of the methods, the validity of this reduced and parameterized model has to be checked. Of course, this what's done here also. Namely different parameter modifications of system parameters have been carried out. You see these parameter modifications were between zero and 40 percent depending on the different type of parameters. What's given in the main graph are so different frequencies and modes, starting from frequency in mode number one up to frequency in mode number 20. The lower curve shows the behavior, the frequencies without parameter modifications. The two upper curve is which practically match each other, shows the behavior of the results of full model simulation and parameter modification, and reduce model simulation parameter modification. You sees well matches with each other. So this gave us sufficient confidence that at least in this variation range which showed at the upper part and left upper part of this graph, this could use model and parameterize that use model can be reasonably applied. As always in development of aerospace systems, we should correlate once hardware's available. You should correlate the simulation results with the test results, and this is shown here. This is the transfer function of such a sandwich panels versus frequency, where the response is shown with uncontrolled vibration behavior, these as a large peaks. Blue and red curve shows the behavior under vibration control, and then become correlate this with tests on such a panel. You see that this behavior from simulation from test correlates very well. These are nearly quite identical curve, but, of course, it can apply different mathematical criteria for correlation, but also this qualitative correlation tells it's quite good. By the way, this is control and vibration control in that case, was stand by applying control actuation via attention piezo-ceramic plates on the sandwich and properly clicker, which is a control loop. Our final example is taken from high precision Cloud telescopes and their active optics. What do we mean by this? There's just a large Cloud telescopes under development in Europe, which is called the Extra Large Telescope, ELT. This Extra Large Telescope has a main mirror diameter of close to 40 meters, which is quite large and a big step in astronomical telescopes. This large mirrors have to keep their shape very accurately even under very different disturbances. In order to guarantee this, one is sectioning this large mirror of 40 meter diameters into many small sections. We see here a single panel or a single section of these large mirror, a few from the rear side. First of all, if you have a closer look, you'll see it's a finite element modeling in this case. We also see some structure on the rear side. We also see actuators are integrated in order to control and counteract the deformation of such a panel due to external excitations. So it means that one has to deal with very large models, and one has to deal with control structure interaction problems, which in the end require many thousand, even more than 10,000 actuators. This is very large models have to be properly condensed in this overall simulation on structural contour and optics behavior. The overall integrated model structure contour optics end-to-end model of this telescope is shown as u-curve. Take first instructional model, the optical model, but also we need to properly model the actuators, which are attached to the rear side of this main mirror. We have the controllers and so forth. We have to take the disturbances, which are wind load seismic disturbances, even solar pressure and thermal behavior, temperature changes. But it's also interesting to consider this disturbance shown on top, which is the so-called atmospheric turbulence. The atmosphere always is turbulent, which means the air has different densities and optical rays going sources areas different densities are disturbed. Since it's also to be compensated via active control technique. As mentioned, we have now to assess the validity of this reduced model and the validity also with respect to parameter variations. See validity can be valid checked via transfer functions. We have seen this graph already. It comes from this large content scope. Remember, the original model had, with respect to finite element degrees of freedom, 500,000 degrees of freedom. So its used model only in quotation mark now has 200 degrees of freedom. Or from a control point of view, in the original model might be determined, 1,400 states. While in the reduced model, we only determined and had to be determined only 26 states. This transfer function shows us that it really works for frequencies and eigenfrequencies, which are relevant here from structural optics point of view for up to 10, 50, 20 hertz.