Řízení systémů se zpožděním - Algebraický přístup

The presented dissertation thesis is focused on control of single-input single-output time delay systems by algebraic means in the ring of special meromorphic functions, on its use in the autotuning and on the tuning of obtained anisochronic controllers. Time delay systems description as well as controller design is based on the utilization of the extended and revised ring of stable proper quasipolynomial meromorphic functions. The solution of a Diophantine equation (Bezout identity) together with Youla-Kucera parameterization in the ring constitutes the set of all stabilizing controllers. The approach enables to satisfy inner feedback system stability, asymptotic reference tracking and input disturbance attenuation. A benefit of the methodology is that one can acquire a finite spectrum of some feedback transfer functions using a non-trivial control system. Contrariwise, a sufficiently accurate model of the controlled process is needed. Proven stability conditions for some quasipolynomials (since it is crucial for the correct controller design) and a generalized Nyquist criterion for time delay systems and a special control system structure are derived as well. The thesis then comprises design of selected controller tuning approaches for the obtained anisochronic controllers. Namely, a continuous feedback system spectrum shifting, a quasioptimal dominant pole placement and a pole placement when a desired transfer function overshoot is prescribed. Some original ideas are involved in the methods. Analytically derived formulas for the identification of unknown model parameters from feedback-relay experiment with saturation relay in order to find a sufficiently accurate process model are presented as well. For real-world applications with digital computers, control algorithms ought to be discretized and simplified; hence, some approaches are briefly described and implemented. A numerous examples together with MATLAB/Simulink results clarify theoretic statements throughout the thesis. Selected complex examples involve. Last but not least, results of identification and control of a laboratory heating plant with significant delays, with a basic robust stability and robust performance analysis, are presented in the thesis, which clearly affirms the practical applicability of the approach.