Multiple-Input Multiple-Output (MIMO) Sine-on-Random Vibration Control
Introduction
Sine-on-Random (SoR) vibration testing is a widely used method for simulating complex dynamic environments that contain both broadband random excitations and deterministic sinusoidal tones. These combined vibration conditions occur frequently in real-life applications such as rocket launches, aircraft operations, and automotive environments, where random background vibrations coexist with strong tonal components generated by rotating machinery, engines, or other periodic sources.
Traditionally, SoR testing was implemented on single-axis vibration systems, using a single-input single-output (SISO) control scheme. However, as test requirements evolved toward more realistic multi-axis environments, engineers began to pursue multiple-input multiple-output (MIMO) SoR control to accurately replicate the combined vibration energy acting on a structure from multiple directions simultaneously.
Traditional Approach: Single-Axis Sequential Testing
In the traditional vibration testing setup, SoR control was performed one axis at a time. Each axis (X, Y, or Z) was tested independently using a single shaker and a single control loop. During each run:
The controller generated a random excitation with superimposed sinusoidal tones (Sine-on-Random).
The response was measured at one or more control points, and the system adjusted the drive signal to match the specified target PSD and sine tone amplitudes.
After completing one axis, the test article was rotated or repositioned, and the process repeated for the next axis.
This sequential single-axis method offered good control accuracy and system stability, but it had significant limitations:
It could not capture cross-axis coupling effects that occur naturally in multi-directional excitation.
The total test duration increased since each axis had to be tested separately.
The dynamic behavior of the test article under combined directional loading could not be accurately represented.
Thus, while single-axis SoR testing was effective for basic qualification, it did not truly replicate the complex, coupled vibration environments seen in real-world systems.
Early Multi-Axis Approach: 3-Axis MIMO using TWR Control
To address the limitations of single-axis testing, the next advancement was MIMO Sine-on-Random control using Time Waveform Replication (TWR) techniques. In this approach, vibration data (waveforms) are generated from the broadband random profiles, sine tones as well as the run schedule. These time-domain waveforms along the three axes are then controlled using the MIMO Time Waveform Replication control engine.
In MIMO TWR control:
The target time histories for each axis (X, Y, Z) were provided as input.
The control system attempted to reproduce these waveforms simultaneously by iteratively adjusting the drive signals of multiple shakers.
The control algorithm used frequency-domain matrix inversion and adaptive filtering to account for cross-coupling between the input and response channels.
This method enabled multi-axis excitation, but it was not true MIMO Sine-on-Random control in the strict sense. It had several drawbacks:
No true separation of sine and random components: The control algorithm replicated recorded waveforms rather than generating independent, controllable random and sine elements.
Limited flexibility: The sine tones and random background were inherently linked in the waveform, restricting the user’s ability to modify test conditions, tone amplitudes, or PSD levels.
Although the 3-axis TWR approach was a significant step forward, it did not provide the level of control fidelity or flexibility required for rigorous qualification testing according to modern standards.
Breakthrough: Crystal Instruments’ True MIMO Sine-on-Random Control
Crystal Instruments (CI) introduced a true MIMO Sine-on-Random (SoR) control system, marking a major technological breakthrough in multi-axis vibration testing. Unlike previous approaches that relied on waveform replication or sequential axis testing, CI’s implementation enables simultaneous control of multiple shakers with independent and coordinated sine and random components across all axes.
Multiple shakers (inputs) and multiple control points (outputs) are managed through a full MIMO control matrix. The system continuously measures and updates the transfer function matrix H(f)to account for cross-coupling between all channels. The controller simultaneously regulates both the random PSD and the deterministic sine amplitudes and phases at all control locations.
Users can define any number of discrete sine tones (each with target amplitude and phase) superimposed on a specified broadband random PSD. The controller separates and processes the random and sine components in the frequency domain, maintaining precise control of each without interference.
The control algorithm continuously adapts to variations in the system’s dynamic response, ensuring accurate control even under nonlinear or time-varying conditions. This results in excellent stability, coherence, and repeatability across all controlled axes.
True simultaneous MIMO SoR testing becomes possible, capturing realistic multi-directional vibration environments that were previously unachievable.
Up to 16 sine tones can be configured on top of the broadband random profiles.
For a 3-axis shaker system, the X, Y, and Z directional sine tone amplitudes can be independently set for each tone.
Sine tones can be activated through the Run Schedule, or turned on and off manually at any time during the test, providing exceptional flexibility and control during operation.
Conclusion
Traditional SoR control methods, whether single-axis sequential testing or multi-axis TWR waveform replication, have significant limitations in representing true multi-directional vibration environments. The development of Crystal Instruments’ real MIMO Sine-on-Random control overcomes these barriers by integrating advanced adaptive MIMO algorithms with independent control of sine and random components. This breakthrough enables engineers to perform genuine multiple-input multiple-output sine-on-random testing, bringing vibration simulation technology closer than ever to real-world dynamic conditions.