Model order reduction of commensurate linear discrete-time fractional-order systems

Rydel, Marek; Stanisławski, Rafał; Latawiec, Krzysztof J.; Galek, Marcin

doi:10.1016/j.ifacol.2018.05.090

Cited by 14 publications

(5 citation statements)

References 16 publications

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“…As in the former controller and observer tuning, it has been assured that when the controller dynamics are dominant over the observer, it is possible to reduce model order. The methods to achieve model reduction are given in [54]. Among them, singular perturbation approximation (SPA) has been selected as the most appropriate, as it preserves steady-state gain, and there is no need to apply special system transformations to achieve it.…”

Section: Current Control Model Reductionmentioning

confidence: 99%

“…Putting a simplified converter model (37) into (52) and neglecting mismatch d v (k), the worst case possible ∆v o (k + 1), i.e., ∆V o,P , can be gained in (54). By selecting the appropriate border value of i L,r , that is, I L,r , and border value of i o , that is, I o , the equation can give the worst case achievable incremental voltage change ∆V o,P .…”

Section: Design Of a Disturbance Observer For Voltage Controlmentioning

confidence: 99%

“…By using (53) and (54) in (55), two cases of requirements of K p are gained in (56). Equations for both are similar, only the minimal (min) and maximal (max) worst-case values are different, as they were selected to give the most restrictive worst case.…”

Section: Design Of a Disturbance Observer For Voltage Controlmentioning

confidence: 99%

See 2 more Smart Citations

Control of a Multiphase Buck Converter, Based on Sliding Mode and Disturbance Estimation, Capable of Linear Large Signal Operation

2019

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Power-hardware-in-the-loop systems enable testing of power converters for electric vehicles (EV) without the use of real physical components. Battery emulation is one example of such a system, demanding the use of bidirectional power flow, a wide output voltage range and high current swings. A multiphase synchronous DC-DC converter is appropriate to handle all of these requirements. The control of the multiphase converter needs to make sure that the current is shared equally between phases. It is preferred that the closed-loop dynamic model is linear in a wide range of output currents and voltages, where parameter variations, control signal limits, dead time effects, and so on, are compensated for. In the case presented in this paper, a cascade control structure was used with inner sliding mode control for phase currents. For the outer voltage loop, a proportional controller with output current feedforward compensation was used. Disturbance observers were used in current loops and in the voltage loop to compensate mismatches between the model and the real circuit. The tuning rules are proposed for all loops and observers, to simplify the design and assure operation without saturation of control signals, that is, duty cycle and inductor current reference. By using the proposed control algorithms and tuning rules, a linear reduced order system model was devised, which is valid for the entire operational range of the converter. The operation was verified on a prototype 4-phase synchronous DC-DC converter.

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Section: Current Control Model Reductionmentioning

confidence: 99%

Section: Design Of a Disturbance Observer For Voltage Controlmentioning

confidence: 99%

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Control of a Multiphase Buck Converter, Based on Sliding Mode and Disturbance Estimation, Capable of Linear Large Signal Operation

2019

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“…Other avenues for warranting numerical stability need different approximation methods. One approach focused on using Laguerre functions to create an approximation of impulse response [7,8], which was used among the others in [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Practical Applications of Diffusive Realization of Fractional Integrator with SoftFrac

2021

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Fractional calculus has found multiple applications around the world. It is especially prevalent in the domains of control and electronics. One of the key elements of fractional applications is the fractional integral (or integrator) which is a backbone of famous PIλD controller. It gives advantages of traditional PID with a limited phase lag. The are, however, issues with implementation, which will allow good low-frequency behavior. In this paper, we consider a diffusive realization of a fractional integrator with the use of quadratures. We implemented this method in numerical package SoftFrac, and we illustrate how different quadratures work for this purpose. We show superiority of bounded domain integration with logarithmic transformation and explain issues with behavior for extremely low frequencies.

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“…The classical Balanced Truncation (BT) method introduced for classical integer-order systems has been extended to discrete-time fractional-order systems [15]. The reduction paradigms used by the BT method enforce an accurate approximation for the whole range of frequencies.…”

Section: Introductionmentioning

confidence: 99%

Balanced Truncation Model Order Reduction in Limited Frequency and Time Intervals for Discrete-Time Commensurate Fractional-Order Systems

2019

Self Cite

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In this paper we investigate an implementation of new model order reduction techniques to linear time-invariant discrete-time commensurate fractional-order state space systems to obtain lower dimensional fractional-order models. Since the models of physical systems correctly approximate the physical phenomena of the modeled systems for restricted time and frequency ranges only, a special attention is given to time- and frequency-limited balanced truncation and frequency-weighted methods. Mathematical formulas for calculation of the time- and frequency-limited, as well as frequency-weighted controllability and observability Gramians, are extended to fractional-order systems. An instructive simulation experiment corroborates the potential of the introduced methodology.

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Model order reduction of commensurate linear discrete-time fractional-order systems

Cited by 14 publications

References 16 publications

Control of a Multiphase Buck Converter, Based on Sliding Mode and Disturbance Estimation, Capable of Linear Large Signal Operation

Control of a Multiphase Buck Converter, Based on Sliding Mode and Disturbance Estimation, Capable of Linear Large Signal Operation

Practical Applications of Diffusive Realization of Fractional Integrator with SoftFrac

Balanced Truncation Model Order Reduction in Limited Frequency and Time Intervals for Discrete-Time Commensurate Fractional-Order Systems

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