System identification for robust and inferential control : with applications to ILC and precision motion systems

Abstract

Feedback control is able to improve the performance of systems in the presence of uncertain dynamical behavior and disturbances. Although a properly designed controller can cope with large uncertainty, certain knowledge regarding the system behavior is crucial for control design. Hence, high performance control design requires a mathematical model of the true system. System identification is a reliable, fast, and inexpensive methodology to construct accurate models from experimentally obtained data. The resulting model, however, is never an exact representation of the physical system. Robust control design can be employed to deal with the model imperfections by guaranteeing a certain performance for an uncertain model set. In the last decades, important achievements have been obtained in the fields of system identification and robust control. These results in these fields have mainly been established independently of each other. As a result, the interrelation between system identification and robust control is untransparent. To connect system identification and robust control in a coherent methodology, the pursued approach involves 1. improved system identification methodologies for nominal models; 2. quantification of model uncertainty by confronting the identified model with new measurement data to test its predictive power, as a result a model set is obtained that encompasses the true system behavior; 3. the design of a robust controller that performs well with the entire model set, hence also when implemented on the true system. New theoretical developments and algorithms are presented that transparently connect Steps 1, 2, and 3. Firstly, a new connection between control-relevant system identification and coprime factorization-based system identification is presented. The system identification procedure directly delivers a model that is internally structured as a novel coprime factorization. In addition, the resulting control-relevant model aims to accurately represent the phenomena of the true system that are to be compensated. The resulting coprime factorization exploits the unexplored freedom in constructing a coordinate frame for model uncertainty. As a result, a novel coprime factorization-based model uncertainty structure is obtained that transparently connects Steps 1, 2, and 3, above. In many high quality control applications, including precision motion systems, the performance variables generally cannot be measured in real-time during normal operation. In this case, model-based control design is essential, since a model can be used in conjunction with the measured variables to infer the performance variables. Although the performance of the resulting controlled system hinges on the model quality, standard robust control design approaches, system identification techniques, and uncertainty models cannot deal with this inferential control situation. Thereto, new controller interconnection structures, new control criteria, new system identification techniques, and new model uncertainty structures are presented that can deal with the inferential control situation. In addition, these new developments enable a transparant connection between Steps 1, 2, and 3, above. Besides the model uncertainty interconnection structure, the actual quantification of model uncertainty is essential for a reliable and nonconservative robust control design. In model validation, the nominal model is confronted with independent measurement data to test its predictive power, thereby enabling a quantification of model quality. By exploiting the freedom in experiment design, a suitable characterization of disturbances is obtained and averaging properties of these disturbances are enforced. As a result, a well-posed validation-based uncertainty modeling procedure is obtained that results in correct asymptotic results and an uncertainty model that is directly useful for robust control design. The new developments and algorithms further intertwine system identification and robust control. As a consequence, a non-conservative high performance robust control design can be obtained. The developed methodology is experimentally verified on several systems, including an industrial wafer stage, a flexible beam setup, and a continuously variable transmission system. Experimental results confirm an improved robust control performance and the ability of the developed algorithms to reliably deal with multivariable systems and unmeasured performance variables. Finally, iterative learning control for sampled-data systems is investigated. Iterative learning control enables the performance improvement for batch repetitive processes by iteratively updating the command signal from one experiment to the next. Although many physical systems evolve in the continuous time domain, common iterative learning control algorithms are implemented in a digital computer environment. Thereto, iterative learning control algorithms for sampled-data systems are presented that explicitly address the intersample behavior. In addition, any iterative learning algorithm requires a certain approximate system knowledge. To obtain such models, parametric system identification algorithms for sampled-data iterative learning control are developed. Furthermore, low-order iterative learning control synthesis algorithms are presented.