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Concept# Time constant

Summary

In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system.
In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input. In the frequency domain (for example, looking at the Fourier transform of the step response, or using an input that is a simple sinusoidal function of time) the time constant also determines the bandwidth of a first-order time-invariant system, that is, the frequency at which the output signal power drops to half the value it has at low frequencies.
The time constant is also used to characterize the frequency response of various signal processing systems – magnetic tapes, radio transmitters and receivers, record cutt

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Performance of any model-based control scheme depends on the quality of model. When these schemes deliver poor loop performance due to model-plant mismatch (MPM), a detection of the same needs to be in place. A recently introduced plant model ratio (PMR) not only detects MPM but also facilitates a unique identification of the source of mismatch, namely, gain, dynamics (time constant) and delay mismatches. The prime objective of this work is to improve the PMR approach in a few key aspects, namely, estimation and experimental effort, and assessment procedure by taking a fresh perspective of PMR and conducting a detailed theoretical study of its signatures. A rigorous assessment procedure based on the theoretical properties of PMR is devised. Three threshold-based hypotheses tests are proposed for significance testing of PMR. A key contribution of this work is the design of set-point with minimal excitation for diagnosis of MPM, based on the features of PMR. The revised methodology is demonstrated and compared with the existing method through simulation examples. The study also demonstrates the potential of the proposed method in serving as a prelude to full/partial model re-identification.

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2021