Abstract
This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects for a range of frequencies. Suppressing the nonlinear effects of a reset element for the desired frequency range while maintaining it for the rest is beneficial, especially when it is used in the framework of a “Constant in gain, Lead in phase” (CgLp) filter. CgLp is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation—the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies. However, CgLp’s ideal behaviour is based on the describing function, which is a first-order approximation that neglects the effects of the higher-order harmonics in the output of the filter. Although CgLp is fundamentally a nonlinear filter, its nonlinearity is not required for all frequencies. Thus, it is shown in this paper that using the proposed reset element architecture, CgLp gets closer to its ideal behaviour for a range of frequencies, and its performance will be improved accordingly.
Highlights
PID is still the workhorse of the industry when it comes to the term “control.” in some fields, precision motion control, there is an increasingly high demand for more precise, faster and more robust controllers
3 Fractional-order single state reset element (FOSRE). This sections introduces a new structure for reset elements in the framework of CgLp and discusses the architecture, frequency response and its superiority over first-order reset element (FORE) and second-order reset element (SORE) in the framework of CgLp
The architecture of the FOSRE is similar to that of the SORE with the difference being that the second linear integrator is replaced with a fractional one, and only first integrator, which is a linear one is reset
Summary
PID is still the workhorse of the industry when it comes to the term “control.” in some fields, precision motion control, there is an increasingly high demand for more precise, faster and more robust controllers. It was shown that this phenomenon could be used to the benefit of improving steady-state precision of the overall controller at that certain frequency This architecture cannot be used to suppress higher-order harmonics in a broad range of frequencies. This element robustly stabilises the system by providing the phase lead required in the bandwidth region; unlike the derivative part of PID, it does not violate the loop-shaping requirements This ideal behaviour is based on the assumptions of the describing function (DF) method, which is a first-order approximation neglecting higherorder harmonics in the output of a nonlinear element. As an extension to SOSRE, this paper couples a fractional-order integrator with a reset one which creates the ability to selectively higher-order harmonics, in a range of frequencies where nonlinearity does not have a clear benefit. The paper concludes with some remarks and recommendations about ongoing works
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