K. Smolders, Tracking Control of Continuous-Time Nonlinear Systems: A Model-Based Iterative Learning Approach, 2007

Abstract

This thesis aims at designing accurate tracking controllers for nonlinear systems based on iterative learning control (ILC) techniques. ILC combines the advantages of both feedback control (robustness with respect to model uncertainty) and feedforward control (no lag) and is applicable to systems that perform a certain task repeatedly.

A new integrated nonlinear model-based ILC approach is developed and validated experimentally. It combines the identification of a new nonlinear continuous- time state space model structure based on experimental data with a new nonlinear model-based ILC law.

The model structure consists of a linear and a nonlinear part. An iterative two-step identification algorithm is developed to estimate the model’s parameters. It is shown that both the model structure and its accompanying identification algorithm fit within a grey-box system modeling and identification approach and are particularly suited for lumped mechanical systems.

The critical step at each learning iteration of the new nonlinear modelbased ILC design consists of calculating the inverse signal for the model that produces a certain output. A new algorithm based on Newton’s method is presented to calculate this so-called steady-state inverse signal in case of a periodic, bandlimited, output. It is shown that the calculation can be performed efficiently in the frequency domain and that a maximum frequency can be defined up to which learning is allowed.

The presented methods and model structure have been developed for the specific application of service load simulations, that is, to control hydraulic vibration simulators to perform durability tests on prototypes of cars/vehicles, subassemblies or parts. These vibration simulators have to excite the device under test such that selected and processed force and/or acceleration trajectories, derived from signals measured during short test drives, are replicated as accurately as possible. For this application it has been observed that ILC based on linear models fails if the test object is highly nonlinear.

The integrated nonlinear model-based ILC approach is validated experimentally on a hydraulic quarter car test rig and compared with a linear model-based ILC. The nonlinear model-based ILC outperforms the linear model-based ILC on three criteria: (1) the RMS value of the initial tracking error is three times smaller; (2) the ILC algorithm converges three times faster; and (3) the RMS value of the final tracking error is three times smaller.

Order Code

Code: 07D15