Extremum Seeking With Enhanced Convergence Speed for Optimization of Time-Varying Steady-State Behavior of Industrial Motion Stages

Recently, an extremum-seeking control (ESC) approach has been developed for optimization of generically time-varying steady-state responses of nonlinear systems. A generic filter structure was introduced, the so-called dynamic cost function, which has been instrumental in facilitating the use of ESC in the more generic, time-varying context. However, the dynamic cost function must operate sufficiently slow compared to the time-varying nature of the system responses, thereby compromising the convergence speed of the ESC scheme. In this work, a modified ESC approach is proposed that incorporates explicit knowledge about the user-defined dynamic cost function, able to enhance the convergence speed of the ESC scheme. Moreover, we provide a stability analysis for this extended approach. The main contribution of this work is the experimental demonstration of both ESC approaches for the performance optimal tuning of a variable-gain control (VGC) strategy employed on a high-accuracy industrial motion stage setup, exhibiting generically time-varying steady-state responses. VGC is able to enhance the system performance by balancing the typical linear control tradeoff between low-frequency disturbance suppression properties and sensitivity to high-frequency disturbances in a more desirable manner. We experimentally show that, for the unknown disturbance situation at hand, the variable-gain controller can be automatically tuned using both ESC approaches to achieve the optimal system performance. In addition, enhanced convergence speed with the modified ESC approach is evidenced experimentally.acceptedVersio

Direct Learning for Parameter-Varying Feedforward Control: A Neural-Network Approach

The performance of a feedforward controller is primarily determined by the extent to which it can capture the relevant dynamics of a system. The aim of this paper is to develop an input-output linear parameter-varying (LPV) feedforward parameterization and a corresponding data-driven estimation method in which the dependency of the coefficients on the scheduling signal are learned by a neural network. The use of a neural network enables the parameterization to compensate a wide class of constant relative degree LPV systems. Efficient optimization of the neural-network-based controller is achieved through a Levenberg-Marquardt approach with analytic gradients and a pseudolinear approach generalizing Sanathanan-Koerner to the LPV case. The performance of the developed feedforward learning method is validated in a simulation study of an LPV system showing excellent performance.Comment: Final author version, accepted for publication at 62nd IEEE Conference on Decision and Control, Singapore, 202