Sonlu boyutlu filtreler ile gürbüz smith öngörücüsü tasarımı

The time delay is a widely recognized inherent phenomenon present in practical control systems, and it has been a subject of extensive research over the past century. Unless managed appropriately, even a minor delay can deteriorate performance and potentially lead to instability. Therefore, incorporating a model for time delay and designing the controller to mitigate its effects are crucial steps to attain the desired robustness and performance criteria in control theory. Additionally, owing to its infinite-dimensional structure, the majority of predictor-based controllers comprise finite impulse response filters, necessitating approximation with finite-dimensional transfer functions for seamless integration into physical systems. Controller designs based on the Smith predictor can effectively cancel out the impact of dead-time delay. This study introduces an extension of the Smith predictor to formulate stabilizing controllers for LTI SISO systems with multiple unstable modes and time delay. The main contribution of this approach lies in the streamlining of previous predictor-based control designs intended for unstable plants. The main contribution of this methodology lies in the simplification of previous predictor-based control designs tailored for unstable plants. The predictor filters are crafted by solving a Nevanlinna-Pick interpolation problem to attain optimal robust stability. The process also upholds the fundamental essence of the Smith predictor scheme, allowing the design of a controller based on the non-delayed nominal plant. Despite the susceptibility of Smith predictor-based designs to uncertain delays, the robustness of the proposed configuration surpasses that of the H-infinity optimal controller design, as demonstrated in the relevant section. The proposed design is also extensible to a category of distributed parameter SISO systems and MIMO plants. For distributed parameter SISO systems, it is assumed that the plant's transfer function can be expressed through coprime factorization. The fundamental idea underlying this approach is treating the infinite-dimensional inner factor of the plant as a "time delay", and, in turn, determining the predictor structure accordingly. The modeling and controller design steps expounded here are exemplified using a flexible beam model. Regarding MIMO systems, provided specific conditions are met, the tangential Nevanlinna-Pick interpolation technique can be employed to derive the controller and filters according to the proposed configuration. While numerous studies have addressed model order reduction in the context of H-infinity-norm error, achieving optimal H-infinity approximation remains a challenging and unresolved problem. This study introduces an alternative model reduction method that seeks to minimize the H-infinity norm of the difference between the reduced model and the original FIR structure. The proposed method essentially reduces the order of a given function by one with the minimum H-infinity-norm error, employing a high-order Padé approximation of the time-delay term. As the method reduces the order by one, an iterative algorithm is devised to recursively decrease the order of a given plant from n to a desired order of m, repeating the procedure (n-m) times following the outlined steps. The main contribution of the proposed technique is that it provides a new perspective against H-infinity-norm approximation by using Chebyshev equioscillation theorem on rational functions. Various examples are provided to elucidate the methodology of the suggested controller design and the robust stability condition in the context of approximating the infinite-dimensional predictor structure. Furthermore, the proposed model order reduction method is compared with the most recent state-of-the-art techniques within the literature. Finally, potential avenues for further research are deliberated, encompassing both the controller structure and H-infinity approximation.