(202o) An Extended Vrft Method for Controller Design of Nonlinear Hammerstein and Wiener Systems

Most dynamical systems can be better represented by nonlinear models, which are able to describe the global behavior of the system over wide ranges of operating conditions, rather than by linear ones that are only able to approximate the system around a given operating point. One of the most frequently studied classes of nonlinear models is the so-called block-oriented nonlinear model, which involves a cascade combination of a linear dynamic block and a nonlinear static (memoryless) one. Such model is related very closely to linear one and can be easily adapted to linear control techniques. Two typical block-oriented model structures are the Hammerstein and Wiener models. In the Hammerstein structure, the linear dynamic element is preceded by the nonlinear static element. The order of connection is reversed in the Wiener structure. These model structures have been successfully used to describe nonlinear systems in a number of practical applications in the areas of chemical processes, biological processes, signal processing, communications, and control.

In the last decades, a considerable amount of research has been carried out on identification and control of Hammerstein/Wiener Systems. In particular, various model-based controller design methods can be found in the literature. There are two steps in the model-based controller design: an empirical (low-order for linear dynamics) model of the process is identified first, which is subsequently used together with certain tuning algorithms to design a controller. Although these methods can give good controller design when the underlying process dynamics are reasonably described by the identified models, the effectiveness of these methods would degrade for complex (higher-order) process dynamics owing to the inevitable modeling error. In addition, because model identification and controller design are treated as two separated pieces of works, the identified model may not contains adequate control-relevant information for controller design.

The virtual reference feedback tuning (VRFT) method allows controller design directly from available process input-output data without resorting to the identification of a process model. Most existing results on the VRFT design are however restricted to the linear systems. This study presents a novel method for controller design of nonlinear Hammerstein and Wiener systems based on the VRFT design framework. In the proposed method, identification of a complete model of the nonlinear system is not required, and only the static nonlinearity has to be identified. Furthermore, the identification of nonlinearity and the controller design are performed simultaneously. This is in sharp contrast to the model-based design methods that require identifying an approximate process model beforehand. Simulation examples are provided to show the effectiveness of the proposed method.