Browsing by Subject "Coprime factorization"

Now showing 1 - 2 of 2

Open Access
On feedback stabilization of neutral time delay systems with infinitely many unstable poles
(Elsevier B.V., 2018) Gumussoy, S.; Özbay, Hitay
It is shown that strictly proper neutral time delay systems having at least one asymptotic pole chain converging to a vertical line Re(s) = σ > 0 cannot be stabilized by a proper controller. A special coprime factorization can be obtained for such systems with infinitely many unstable poles, provided they are bi-proper (i.e. proper, but not strictly proper). From this factorization, stabilizing feedback controllers are obtained. Necessarily, all stabilizing controllers for this type of plants are also bi-proper.
Open Access
Robust Smith predictor design with finite dimensional filters
(2024-01) Yeğin, Mustafa Oğuz
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 infinitedimensional 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 Linear Time Invariant (LTI) Single-Input SingleOutput (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∞ optimal controller design, as demonstrated in the relevant section. The proposed design is also extensible to a category of distributed parameter SISO systems and Multi-Input Multi-Output (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∞-norm error, achieving optimal H∞ approximation remains a challenging and unresolved problem. This study introduces an alternative model reduction method that seeks to minimize the H∞ norm of the difference between the reduced model and the original Finite Impulse Response (FIR) structure. The proposed method essentially reduces the order of a given function by one with the minimum H∞-norm error, employ ing a high-order Pade 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∞-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∞ approximation.