Data-Driven Linear Parameter-Varying Control: A Frequency-Domain Approach


Operating condition-aware control algorithms are essential to keep up with the ever-increasing need to improve the performance, accuracy, and efficiency of next-generation mechatronic systems, ranging from vibration isolation equipment, pick-and-place machines, and lithography scanners to health-care applications. To meet with these challenging performance demands, next-generation machines in these sectors are envisioned to exhibit complex nonlinear behavior, such as position-dependent or operating condition-dependent dynamics. Developing mathematical models for control that accurately describe such complex dynamics is difficult based on first principles knowledge or even data and it is often subject to high model uncertainty. Designing controllers directly from measured system data can circumvent the involved modeling steps, shifting the focus directly on the control objective.

Figure 1: Illustration of an operating-condition dependent motion system.


Our work aims to improve the performance of future mechatronic systems by developing control strategies for such complex systems, while at the same time simplifying the involved modeling step using data. Presently, performance of the available methods that use measurement data to design directly operating-condition-unaware Linear Time-Invariant (LTI) framework controllers can be severely limited in the face of complex dynamics. We address the following challenges.

  1. Firstly, to be able to adapt to varying conditions of the system, an operating-condition-aware controller is required.
  2. Secondly, to avoid the modeling step, the controller should be selected such that stability and performance can be analyzed and guaranteed during control design based on measurement data without knowing the underlying data generating system.
Figure 2: Traditional system identification based control design approach versus a direct data-based control design approach.

A Data-Driven Control Framework

To overcome these challenges, a data-driven Linear Parameter-Varying (LPV) framework control design framework is developed that provides performance improvements for complex mechatronic systems by incorporating knowledge about the operating conditions. This results in the following main contributions towards achieving the posed challenges.

  1. Firstly, an LPV parameterization of the controller is introduced that ensures adaptability and awareness of the controller on the operating conditions of the system.
  2. Secondly, the modeling step is circumvented by substituting mathematical models with local Frequency Response Function (FRF) estimates that result from measured data, for which algorithms are developed to analyze and design LPV controllers even in case of multiple inputs and multiple outputs.
  3. Thirdly, it is shown that the proposed LPV controller parameterization together with a special realization algorithm provides global guarantees during operation (even under varying scheduling trajectories) in terms of universal shifted stability and performance.

These results allow for reliable data-driven design of operating condition-aware controllers that enable performance improvements and wide-range stability guarantees for complex mechatronic systems compared to LTI designs.


Performance of the developed methods is demonstrated on applications ranging from laboratory-scale setups to industrial applications. It is shown that designing controllers directly from available data, while incorporating knowledge about the position-dependent or operating condition-dependent behavior significantly improves the performance of next-generation complex mechatronic systems. Figure 3 demonstrates the effectiveness of the proposed solution on a state-of-the-art active vibration isolation test bench aimed to isolate vibrations whose harmonics vary over time.

Figure 3: Experimental results of the data-driven LPV controller without (blue) vibration isolation and with (orange) active vibration isolation.

For more details on this research see:

Bloemers, T.A.H., ‘Data-Driven Linear Parameter-Varying Control: A Frequency-Domain Approach’, PhD Thesis, Electrical Engineering, Eindhoven.