Infoscience

Thesis

Data-driven controller tuning using the correlation approach

The essential ingredients of control design procedures include the acquisition of process knowledge and its efficient integration into the controller. In many practical control applications, a reliable mathematical description of the plant is difficult or impossible to obtain, and the controller has to be designed on the basis of measurements. This thesis proposes a new datadriven 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 closedloop 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. Both theoretical and implementation aspects of CbT are treated. For the decorrelation procedure, a correlation equation is solved using the stochastic approximation method. The iterative procedure converges to the solution of the correlation equation even in the case when an approximate gradient of the closed-loop output error with respect to controller The asymptotic distribution of the resulting controller parameter estimates is analyzed. When perfect decorrelation is not possible, the correlation reduction method can be used. That is, instead of solving the correlation equation, the norm of a cross-correlation function is minimized. A frequency domain analysis of the criterion shows that the algorithm minimizes the two-norm of the difference between the achieved and designed closed-loop systems.With the correlation reduction method, an unbiased estimate of the gradient of the closed-loop output error is necessary to guarantee convergence of the algorithm to a local minimum of the criterion. Furthermore, this criterion can be generalized to allow handling the mixed sensitivity specifications. 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 elements are tuned to mutually decouple the closed-loop outputs. The tuning of all decouplers and controllers can be made by performing only one experiment per iteration regardless of the number of inputs and outputs since all reference signals can be excited simultaneously. However, due to the fact that decoupling is imposed as a design criterion, simultaneous excitation of all references brings a negative impact on the variance of the estimated controller parameters. In fact, one must choose between low experimental cost (simultaneous excitation) and better accuracy of the estimated parameters (sequential excitation). The CbT algorithm has been tested on numerous simulation examples and implemented experimentally on a magnetic suspension system and the active suspension system benchmark problem proposed for a special issue of European Journal of Control on the design and optimization of restricted-complexity controllers.

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