Data-driven model-free controller-tuning approaches try to lump the identification, controller design and controller reduction together and present a direct “data-to-control” algorithm. This is very attractive, particularly when a mathematical model of the plant is not available and/or the nonlinear behavior of the plant cannot be identified easily and considered for controller design.
Iterative Correlation-based Controller Tuning (ICbT)
This project proposes a new data-driven method labeled Correlation-based Tuning (CbT). The underlying idea is inspired by the well-known correlation approach in system identiﬁcation. The controller parameters are tuned iteratively either to decorrelate the closed-loop output error between designed and achieved closed-loop systems with the external reference signal (decorrelation procedure) or to reduce this correlation (correlation reduction). Ideally, the resulting closed-loop output error contains only the contribution of the noise and perfect model-following can be achieved. By the very nature of the control design criterion, the controller parameters are asymptotically insensitive to noise.
An extension of this method for the tuning of linear time-invariant multivariable controllers
is proposed for both procedures. CbT allows tuning some of the elements of the controller
transfer function matrix to satisfy the desired closed-loop performance, while the other ele-
ments are tuned to mutually decouple the closed-loop outputs.
The CbT algorithm has been tested on numerous simulation examples and implemented
experimentally on a magnetic suspension system and the active suspension system bench-
mark problem proposed for a special issue of European Journal of Control on the design and
optimization of restricted-complexity controllers.
Correlation-based Controller Tuning (CbT) with Guranteed Stability
In this project data-driven controller tuning is considered. In this approach, the controller is designed without the use of a model. Instead, a control objective is minimized directly using the data. An advantage of such direct methods is that the order of the controller can be fixed, in contrast to many model based methods where the order of the controller depends on the order of the model. Furthermore, the problem of undermodeling is omitted since no plant model is used.
Iterative approaches as Iterative Feedback Tuning (IFT) and Iterative Correlation Based Tuning (ICbT) as well as the non-iterative Virtual Reference Feedback Tuning (VRFT) have shown to be effective in practice. However, they all suffer from the same drawback; closed-loop stability can in general not be guaranteed and since no model is available the well-known robustness margins cannot be evaluated.
This project focusses on the stability question in a non-iterative approach. A stability condition that can be implemented in the controller design step is proposed. Furthermore the effect of measurement noise is studied and the correlation approach is used to reduce it.
Tracking Improvement of Systems Subject to Stochasic Disturbances
In this project data-driven approaches, which by-pass the system modelling step and so do not suffer from unmodelled dynamics, are being investigated to improve the tracking performance of systems subject to stochastic disturbances.
For the general tracking problem, a precompensator controller is used to filter the desired output signal before it is applied as an input to the system. The precompensator’s parameters are tuned directly using measured data. This data is affected by stochastic disturbances, such as measurement noise. The effect of these disturbances on the calculated parameters is being studied and the correlation approach is used to reduce it.
For the specific problem where the tracking task is repetitive, a situation frequently encountered in industrial applications, Iterative Learning Control (ILC) is proposed. ILC uses measurements from previous repetitions to adjust the system’s input for the current repetition in a manner so as to improve the tracking. As measurements are used, the calculated input is sensitive to the stochastic disturbances affecting them. The effect of these disturbances on the learning procedure is being examined and algorithms that are less sensitive to their presence are being developed.
Additionally, the proposed methods are being extended for use on Linear Parameter Varying (LPV) systems, in which the system’s dynamics change as a function of a scheduling parameter.