Novel Characteristics Evaluation of Critically DampedSecond-order-like Dynamic Systems

{{Abstract:This paper is presents a novel evaluation procedure for the settling time, delay time and rise time as important time-based characteristics of critically damped second-order-like dynamic systems with 0/2 and 1/2 orders. The time-based characteristics are defined by simple analytical model giving the characteristic as proportional to the reciprocal of the system natural frequency for 0/2 systems. Polynomial models is fitted for each characteristic against the time constant of the simple zero of the 1/2 dynamic system. The evaluation procedure finds optimal values for the 1/2 dynamic system natural frequency. The feasibility of the proposed approach is examined using two case studies where the time-based characteristics are compared (exact and present) with statistical measures. }}

{{IV.CONCLUSIONS -This research paper investigated a novel evaluation procedure for the characteristics of critically damped second-order-like dynamic systems. -The characteristics covered: settling time, delay time and rise time. -The work is unique for critically damped second-order-like dynamic systems of 0/2 and 1/2 types. -The objective was to define the specific characteristic in the form of Kij/ωn. – The gain Kij had a unique value for each of the characteristic elements for type 0/2 critically damped second-order- system independent of the natural frequency of the dynamic system. -The dynamics of the 1/2 critically damped second-order system were function of the time constant of its simple zero and its natural frequency. Because of which the research work found an optimal value for the system natural frequency leading to a minimum settling time. -For the 1/2 critically damped second-order system the gain Kij was function of the time constant of the system simple zero. Curve fitting techniques were applied to fit a reasonable polynomial for the characteristic gain. -Two case studies were presented for each type of the investigated second-order dynamic systems. The time-based characteristics were compared between the exact characteristic values and the evaluated ones using the derived polynomial models. The maximum difference was 0.023 % for the first case study and 2.37 % for the second case study.IV.CONCLUSIONS -This research paper investigated a novel evaluation procedure for the characteristics of critically damped second-order-like dynamic systems. -The characteristics covered: settling time, delay time and rise time. -The work is unique for critically damped second-order-like dynamic systems of 0/2 and 1/2 types. -The objective was to define the specific characteristic in the form of Kij/ωn. – The gain Kij had a unique value for each of the characteristic elements for type 0/2 critically damped second-order- system independent of the natural frequency of the dynamic system. -The dynamics of the 1/2 critically damped second-order system were function of the time constant of its simple zero and its natural frequency. Because of which the research work found an optimal value for the system natural frequency leading to a minimum settling time. -For the 1/2 critically damped second-order system the gain Kij was function of the time constant of the system simple zero. Curve fitting techniques were applied to fit a reasonable polynomial for the characteristic gain. -Two case studies were presented for each type of the investigated second-order dynamic systems. The time-based characteristics were compared between the exact characteristic values and the evaluated ones using the derived polynomial models. The maximum difference was 0.023 % for the first case study and 2.37 % for the second case study.}}

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