Observability in Systems with Extreme Multistability. Dataset & Interfaces

An observer's robustness is directly related to its ability to accurately estimate a system's state variables under a wide range of initial conditions and operational parameter variations. However, analyses of this nature are usually performed numerically through computational simulations. This work provides experimental data from implementing a linear electronic observer applied to a chaotic electronic oscillator with six state variables.

The dataset includes two main series:1.    One in which only the bias voltage of the oscillator is modified while the observer’s bias voltage remains constant.2.    Another in which both the bias voltage of the observer and the oscillator are modified simultaneously.

We provide detailed time series data for each experimental configuration of the electronic oscillator and the observer. The bias voltage was varied from ±8 V to ±15.1 V in increments of 0.1 V. At each voltage increment, 100,000 samples were recorded for the outputs of each system (the first six columns from the oscillator and the following six from the observer), repeating the experiment 20 times to ensure a diversity of initial conditions.

File Description time series data are organized into compressed files according to the experiment performed, following the naming convention:•    TS_ObsDin_exp_x.rar for the experiment where the observer’s and the system’s bias voltage are modified simultaneously.•    TS_ObsStat_exp_x.rar for the experiment where only the system’s bias voltage is modified while the observers remain constant.

The variable "x" in the file name represents the experiment run, ranging from x = 1 to x = 19. Thus, each experiment produces 20 datasets.Each compressed folder contains 72 .dat files, named according to the following structure:

"MuestraObsStat_Y_Z.dat"

Where:

•    Y corresponds to the experiment’s bias voltage, ranging from 8.000000 to 15.100000 in increments of 0.1 V.•    Z denotes the experiment repetition, ranging from Z = 0 to Z = 19.

This structured format allows easy identification and analysis of the data obtained under different experimental conditions.

Description of the LabVIEW Virtual Instrument (VI) for Dual Power Supply Control

This LabVIEW Virtual Instrument (VI) executes the control routine for signal acquisition from both the multistable system and the observer while simultaneously managing two independent power supplies. One power supply maintains a constant polarization voltage, while the other varies incrementally to analyze the system’s response under different operating conditions. This setup ensures automated voltage control and synchronized data acquisition, facilitating precise and repeatable experiments.

Operational Workflow of the VI:

Initialization and Configuration:

The VI begins by setting up the file path and naming convention for storing the acquired data.

It then establishes and configures the serial communication with both GwInstek GPD-2303S power supplies:

One power supply remains fixed at 15V to power the observer.

The second power supply undergoes controlled voltage variations to power the multistable system.

Main Control Loops:

The outer loop manages the number of complete experimental repetitions, ensuring that each test is performed multiple times for statistical consistency.

Inside this loop, an inner loop controls the voltage variation of the system power supply, adjusting it incrementally from 8V to 15V in 0.1V steps.

Communication Verification and Voltage Adjustment:

Before applying voltage changes, the VI performs a communication status check between the computer and both power supplies.

If a communication failure is detected, the system attempts to reconfigure the connection until successful.

Once verified, the VI configures the system power supply for the current iteration while ensuring that the observer power supply remains constant at 15V.

Data Acquisition Setup:

After setting the voltage, the VI defines the sampling parameters, including:

Sampling rate (100 kHz)

Number of samples per iteration

Selection of acquisition channels, recording the multistable system's six state variables and the observer's six estimated states.

Real-Time Visualization and Data Storage:

The acquired signals are displayed in real-time within the graphical interface, allowing continuous monitoring of system behavior.

The collected data is stored in a .dat file, ensuring secure and structured data logging for later analysis.

This version of the LabVIEW VI enables precise dual power supply control, maintaining the observer’s voltage constant while systematically varying the system voltage. This automation ensures high repeatability and reliability in evaluating the observer’s performance under different system conditions.

Description of the LabVIEW Virtual Instrument (VI)

This LabVIEW Virtual Instrument (VI) executes the control routine for signal acquisition from both the multistable system and the observer. The VI ensures automated voltage control and synchronized data acquisition, streamlining the experimental process and minimizing manual intervention.

Operational Workflow of the VI:

1.      Initialization and Configuration:

The VI begins by setting up the file path and naming convention for storing the acquired data.

It then establishes and configures the serial communication with the power supply unit responsible for voltage variations.

2.      Main Control Loops:

The outer loop controls the number of complete experimental repetitions, ensuring the process is conducted multiple times for statistical reliability.

Inside this loop, an inner loop manages the voltage variation steps, where the polarization voltage is incrementally modified as per the experiment’s predefined range.

3.      Communication Verification and Voltage Adjustment:

Before applying the voltage changes, the VI checks the communication status between the computer and the power supply.

If communication fails, the system attempts to reconfigure the connection until it is restored.

Once the connection is verified, the VI configures the voltage values for the current iteration, ensuring accurate and synchronized control.

4.      Data Acquisition Setup:

After voltage configuration, the VI proceeds to define the sampling parameters, including:

Sampling rate (100 kHz)

Number of samples per iteration

Selection of the acquisition channels corresponding to the state variables of the system and observer.

5.      Real-Time Visualization and Data Storage:

The acquired signals are displayed in real-time within the graphical interface, allowing for continuous monitoring of the system’s behavior.

Finally, the collected data is saved to a preconfigured .dat file, ensuring that all measurements are securely stored for later analysis.

This structured VI enables precise control over voltage variations, robust signal acquisition, and seamless data storage, ensuring a high degree of automation and repeatability in the experimental process.