Analytical Design of Fixed-structure Fractional-order Controllers in Frequency Domain

Sayyaf, Negin | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 50659 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Tavazoei, Mohammad Saleh
  7. Abstract:
  8. Due to the simplicity and generality, design of feedback control systems in the frequency domain is among the most prominent topics in the control systems engineering. The problem of compensation means properly adjusting the loop frequency response at critical frequencies. Considering the point that the traditional methods usually use trial and error procedures for compensation, analytical design of fixed-structure controllers for exactly adjusting such values has great importance. Benefitting from the capability of fractional-order dynamics, the compensation problem is studied from three aspects in this thesis. At first according to the importance of adjusting the system frequency response at two critical frequencies, a new fractional-order phase-lead/lag compensator is presented to provide the mentioned objective. Since the values of gain margin, phase margin and crossover frequencies verify the system stability, performance and robustness, the problem of adjusting gain and phase margins at crossover frequencies is investigated. As the multiplicity of crossover frequencies may result a control system that does not meet the intended objectives, sufficient conditions for uniqueness of the crossover frequencies are derived. In addition, the model-based control methods depend on accurate model of a plant, while finding models for industrial plants is not simple. Accordingly, an analytical model-free procedure with exact formulas is proposed to desirably adjust the values of gain and phase margins at arbitrary crossover frequencies and the steady-state specifications, while the existence of a compensator with no zero and pole in the right half-plane and the uniqueness of the crossover frequencies are simultaneously satisfied. Since the suggested procedure directly uses the frequency data of the plant in a finite range, the compensator can be tuned independent of the plant order and complexity. By presenting hardware-in-the-loop experimental results, the proposed tuning procedure is validated. On the other hand, the existence of uncertainties in the model of real-world systems is inevitable. Many of complex systems have a zero or pole, whose uncertainty has great impact on the system performance. In the second part of the thesis, a family of fractional-order compensators is proposed to satisfy robust compensation at an arbitrary frequency, e.g. invariant phase/gain margin, in control of the plants having an uncertain fractional pole or zero. Also, the infinite ranges for the uncertain parameter of the plant, in which robust compensation specifications are satisfied, are exactly specified and control system stability is analyzed. Numerical simulation and experimental results are also presented to verify the effectiveness of the achievements. From the third point of view, many real-world processes can be well described using a parameterized linear time invariant model, where more than one parameter of the plant model can vary under the influence of external conditions. In this case, the above-mentioned methods can not satisfy the robustness, in spite of uncertainty on the process model parameters. Considering this point, a novel robustness criterion is presented to preserve the compensation objective, despite of variations in the general parameter of the plant model. The family of transport processes with long memory is a kind of these processes, which are characterized by the parameterized time-fractional diffusion equations. Hence, the aforementioned problem is studied for microscopic and macroscopic diffusion processes. Investigating the problem solvability and closed loop system stability conditions, an analytical procedure is suggested to tune stabilizing fractional-order PI/PD compensators for simultaneously adjusting the values of mentioned specifications and satisfying the robustness feature for diffusion processes. Moreover, simulation results of robust temperature control in the tumor hyperthermia and machining are presented to confirm the usefulness of the achievements
  9. Keywords:
  10. Phase Margin ; Gain Margin ; Frequency Domain Analysis ; Fractional-Order Compensation ; Analytical Design Method ; Crossover Frequency ; System Robustness

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