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Recent Trends in Adaptive Control Theory
Published in V. V. Chalam, Adaptive Control Systems, 2017
Elliott et al. [89] present a proof of global stability for direct and indirect adaptive control schemes which arbitrarily assign the closed-loop poles of a SISO system. The results are applicable to the control of either minimum or non-minimum-phase systems. Both hybrid continuous-time and discrete-time formulations are given. They verify the persistent excitation condition for potentially unbounded data resulting from closed-loop adaptive control using a sequential estimation procedure. Hence the convergence of a sequential least-squares identification algorithm is proved. The results are applicable to standard sequential least squares, and least squares with a covariance test. The main limitation of the results is that they are applicable only to the case of sinusoidal excitation. An important extension would be for other persistently exciting input signals. Some suggestions are given on the lines on which future work can be done. Goodwin and Teoh [90] establish a general convergence result for parameter estimates in the presence of possibly unbounded signals. Trulsson [91] has analyzed an instrumental variable scheme to establish parameter convergence with possibly unbounded noisy signals.
Crossovers
Published in Douglas Self, Audio Engineering Explained, 2012
The selection of the target function is somewhat more complicated than it may initially appear, because the phase shifts and group delays associated with the filters, and the physically induced delays due to the different drive units occupying different points in space, lead to non-minimum-phase responses. A minimum-phase response is one where the correction of the amplitude towards a flat response also leads to a corresponding flattening of the phase response, or vice versa. In the case of a non-minimum-phase response, the correction of either the amplitude or the phase response does not automatically correct the other. Non-minimum-phase responses give rise to situations where a flat amplitude response cannot be accompanied by an accurate transient (time) response. The amplitude and phase responses are defined by the time response, and vice versa, which is why the Fourier Transform and Inverse Fourier Transform can be used to derive the frequency response from the impulse response or the impulse response from the frequency response. The frequency response, in this case, is referring to the complete frequency response, i.e., the amplitude and the phase. Non-minimumphase effects are typically associated with the recombination of non-time-synchronous signals, such as a recombination of a reflexion with a direct signal, or the summation of signals where different group delays or digital latency have been incurred.
The room environment: problems and solutions
Published in John Borwick, Loudspeaker and Headphone Handbook, 2012
Note that the term ‘minimum-phase’ relates to how the amplitude and phase responses track each other and has no relevance to the absolute quantity of a phase change. Essentially, a minimum-phase response is one where every change in the amplitude response has a corresponding change in the phase response, and vice versa. When the restoration to flatness of either response does not restore the other, the response is said to be ‘non-minimum-phase’, and cannot be corrected by a causal inverse filter. The degree of non-minimum-phase deviation is known as ‘excess phase’ and tends to build up with the summation of many types of time-shifted signals, or the re-combination of filters.
Control of non-minimum phase systems with dead time: a fractional system viewpoint
Published in International Journal of Systems Science, 2020
Shaival Hemant Nagarsheth, Shambhu Nath Sharma
Moreover, filter fractionality, non-minimum phase, and exponentially decaying terms result in the fractional quasi-characteristic polynomial instead of the traditional characteristic polynomial. Thus, stability analysis is presented for fractional quasi-characteristic polynomials resulting from ‘the two illustrative examples considered in this paper’. The fractional filter-PID controllers of this paper for two second-order non-minimum phase systems with dead time are compared with the existing methods of Shamsuzzoha and Lee (2008), Luyben (2000), Luyben (2003) and Pai et al. (2010). Sensitivity analysis is also carried out to demonstrate the ability of resulting feedback systems to handle process parameter variations. Controller and sensitivity performance indices are employed to evaluate the closed-loop performance of the proposed controller in comparison to the existing methods. The proposed controllers improve the responses of non-minimum phase systems by reducing IAE, ISE, OS and ST. The stability under the influence of process parameter variations is also preserved.
Accurate Computation of Vocal Tract Filter Parameters Using a Hybrid Genetic Algorithm
Published in Applied Artificial Intelligence, 2019
Mathew Mithra Noel, Venkataraman Muthiah-Nakarajan, Ruban Nersisson
The approach presented in this paper can be used to design stable and minimum phase filters with an arbitrary frequency response from experimentally obtained samples of the amplitude response. The fundamental issue in the design of digital filters with complex frequency responses such as instability and finite precision effects are discussed.