**Chapter 9: Description of Siemens LMS Vibration Control Routines in Simulink environment**

**9.2 S IMULINK MODEL DESCRIPTION**

The Simulink model represents the real “heart” of the control system. It is a very complex system in term of logic and implemented functions. It is composed by different blockset drowned at each level as Mux, Demux, MatLab embedded functions, switch and transfer functions and it is written in order to be an HIL closed loop system, capable to reproduce the same characteristics and behaviours of the test facility control system.

The main control environment is endowed of appropriate “scopes” in order to see the output in real time. In Figure 51 and Figure 52 the Simulink environment at different levels is shown.

How is possible to see, the control system shows different masks. They shadow control logic, but, going deeper, there are some function impossible to analyse in order to better understand the logic.

In these terms, the Simulink model will be considered as a “black box” when the simulation run.

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**Figure 51: Main control environment **

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**Figure 52: Detailed sine control environment **

pag. 90 However, from a system point of view, is possible to describe the qualitative way in which the control system operates.

The code is able to perform the vibration control of a loaded system or device using up to 40 notchers (or DoFs) in order to monitoring their response.

It is written in order to guarantee always 4 pilot curves. In fact, the original version of the model considered provide just one output coming from DEMUX.

It is repeated considering 3 gain factors that amplifies the input signal. Subsequently, it becomes composed by 4 output. Then, is provided to the following MUX that recollect them with the other 40 signals coming from notchers in which some of them comes from the “C”

matrix of the state space system and the remaining part from the “ground”. Figure 53 (a)

**(a) ** **(b) **

**Figure 53: Modification to the Simulink model: before (a), after (b) **

This implemented modelling strategy were tested with the reduced models mass- spring- damper described in “Chapter 8: The Virtual Shaker Testing approach (VST)” but is not appropriate in order to perform the VST using a condensed model in which the pilots are extracted with the Craig- Bampton theory, according to the location of the physical accelerometers attached to the vibration platform.

For this reason, the Simulink model were modified in order to extract exactly 4 signals from DEMUX. Particularly, they refer to the pilots of the Craig- Bamption theory located into the first four position of the “C” matrix. Figure 53 (b).

After that, the signals come into the real “sine controller” which, for each time step, perform actions as notching level calculation, control amplitude, time delay or sinusoidal input means cola.

In Figure 54 is shown as is appear the mask of the sine control in which the input variables are recalled.

One of the key points of the sine control are the control and estimation strategy.

The first one represents the way in which the control takes place. It concerns the trend, and the values, of the pilots. Particularly, three possibilities are available:

• Maximum: the control signal generates a control profile characterized by the maximum value of the pilots

• Average: the control signal generates a control profile characterized by the sum of the pilot signals divided by the number of control channel, chosen in “Flow.m”

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• Minimum: the control signal generates a control profile characterized by the minimum value of the pilots

The second one gives the way in which all the signals are evaluated. Basically, there are four possibilities:

• Peak: it takes the greatest amplitude of the sample signal. If the system is characterized by noisy, this kind of evaluation could introduce some instabilities

• Average: if the signal is characterized by “N” sample time, it calculates the average of the absolute value of them. It takes the complete signal.

• RMS: it calculates the average of the squared values of “N” sample time during one period. As the average method, it evaluates the complete signal. It is able to produce a low drive signal

• Harmonic: it is considered as the appropriate valuer for fundamental frequency research. It provides magnitude and phase response

**Figure 54: Sine control block parameters **

When the simulation starts, it requires the initial condition in order to join into the loop. They usually are the homogeneous conditions in which, using the formulation of a dynamic second order system, are displacement and speed equal to zeros.

However, the block scheme implemented in Simulink is the “Discrete State Space”, shown in Figure 55. It come from the “Continuous State Space” system. In fact, how is described in “

pag. 92 Chapter 2: The State space systems”, this kind of mathematical formulation represent the best way in which to perform the control of a dynamic or electro-dynamic system.

Particularly, the discrete formulation comes from the continuous quantizing the matrix
operator with the "𝑡_{𝑠}" sampling time consistent of the data acquisition system of the vibration
facility.

Nevertheless, from the algorithm point of view, it is able to solve the differential equation using the same procedure of the finite difference.

**Figure 55: Simulink block for Discrete State Space **

On the other hand, the code is not able to undergoes to modification in terms of solver. In fact, it is written usign a “discrete logic”, so is not possible to replace the “Conotinuous state space block” using the Runge-Kutta method.

For sake of clarity, if Runge- Kutta is the exact approximation of a differential equation in time domain, the discrete state space solver is the approximation of this. In these term, the extracted curves using the discrete method will match in some points with them extrated using the continuous method.

When the simulation advance up to the maximum value of the frequency (typically 100 Hz for sine sweep) the Simulink model send out two matrix: “spectra.mat” and “spectra_notch.mat”

in which are recollect the requested output and classified by columns in term of time, frequency related notcher values and control profiles.

The output that is possible to extract to the sine control system are:

• 4 pilot curves: they describe the variation in time domain of the considered pilot. How we said before, talking in terms of signals, is necessary to guarantee 4 signals to the control system. They could be overlapped or not

• Up to 40 notched curves in frequency and time domain

• The control signal profile compared to the abort and alarm limits

• Two “on/off diagram” in which are shown if one, or more Dofs are notched and which of them

• The drive amplitude of the input

• The cola: it shows the sinusoidal input imposed to the coil

• The enhancement of the frequency during the simulation

Particularly, the control curve (i.e. the acceleration of the pilots handles by one of the controls and strategy criteria) is compared to the upper and lower abort and alarm limit.

pag. 93 Usually, during a vibration test if the control curve exceeds one of the two abort limit (±6 dB) it is interrupted. However, into the LMS vibration control environment we are to see the control curve during all the simulation span, in frequency or time domain, even if it exceeds the upper or the lower value.

Probably, in fact, the aim of do not interrupt the running simulation is to permit to the engineer to observe where and when the control “burst” or “disappears”. This, in order to apply the required modification to the control environment in terms of compression factor, notch profile, control strategy or damping model if the FEM model is unprovided.

In this way, the sine control lives in a wide set of simulation distinguished by the possible variation of each control parameter and under a precise strategy to distinguish the type of control.

Obviously, the final result of the VST activity is to suggest the more appropriate value at each control parameter, before the real vibration test into the facility centre, in order to observe some specified behaviours during the base excitation and guarantee that them do not provoke any rupture. For these reason does not exist a unique and unequivocal result, but it depends on what the test facility engineers want to observe. In these terms, the VST shall emanate a variety of output, based on what they want.

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