Discussion on transient response analysis based on DSP

Taking the high bypass ratio turbofan engines as the research object for the dual-rotor system under the load of blade loss, a simplified four disk dual rotor system is established. The motion differential equation of the dual rotor system is established by the finite element method, and the transient response of the dual rotor system under the blade loss load is simulated and calculated with the Newmark-β integral method, considering the effects of rotor speed, eccentricity, supporting stiffness and damping. The results show that the transient response of the system has obvious impact characteristics under the excitation of the blade loss load, and the stiffness and damping of the bearing at the rear of the fan have a significant influence on the transient response.

The overall objective of this dissertation is to effectively and efficiently obtain some important characteristic functions of acoustic transducers, such as electrical impedance function, transmitting voltage response (TVR) and beam pattern (BP). Oftentimes, one makes measurements on these functions through traditional ways, e.g., stepped harmonic analysis method and Fourier-based analysis method. To improve the accuracy and efficiency of computing these characteristics, new approaches by pole-residue operations are developed and verified in this dissertation. In this new approach, the poles and residues associated with the input and output signals are extracted with the multi-signal Prony-SS method, which is an extension and improvement of the classical Prony’s method. The system functions can be computed by the operations of those poles and residues from input and output signals. Compared with traditional methods, the new one not only turns out effective and computationally efficient but also overcomes the leakage and the frequency resolution problems, by getting a continuous function in the frequency domain without periodic assumption. In addition, many significant characteristics, such as modal frequencies and modal damping, can be precisely calculated from the system poles other than reading them from the plotting of system functions in traditional ways. When a periodic loading excites the linear system, the calculation of transient response is discussed in manuscript 1. Compared with time-domain methods, frequency-domain methods are more computationally efficient when computing the responses of linear dynamic systems. However, frequency-domain methods can only compute the steady-state response instead of the total response. To the author’s best knowledge, the transient response of a dynamic system to arbitrary periodic loading can not be solved analytically. In the first manuscript, a closed-form solution for the transient responses of linear multi-degree-of-freedom (MDOF) systems to arbitrary periodic excitations is derived. By taking advantage of the fast Fourier transform (FFT) algorithm, a very efficient numerical method is developed to compute the transient and total responses of MDOF systems, suitable for both damped and undamped systems. In the newly developed method, the computational time required for obtaining the transient response is much less than that for the steady state response. Three numerical examples are provided in this manuscript to verify the correctness, and demonstrate the effectiveness as well, of the newly developed method. Discussed in the second manuscript is the impedance function, which is very essential for a transducer. The impedance function contains many important characteristics, such as the resonant frequencies, anti-resonant frequencies, and

The traditional frequency domain transfer path analysis has become a popular method to detect and diagnose vehicle NVH problems. Unfortunately, due to its reliance on frequency transfer functions, the approach is strictly effective only for linear time-invariant system and steady-state response. This limitation prevents the method from being applied to transient and/or nonlinear behavior such as clunk, shudder, and tip-in and tip-out. In this paper, a novel time domain transfer path analysis is proposed to deal with a class of non-linear transient response problems. It combines the versatility of the transfer path analysis for tracking transmission of vibratory energy between substructures and generality of the time domain analysis for treating transient response that is also nonlinear in nature. The formulation that is derived by combining the spectral-based substructure method and a discrete, piecewise convolution theory is applied to a lumped parameter system, and the results are compared with output from a direct numerical integration of the nonlinear equations of motion. Comparison results show significant promise and appear to be usable for solving real-life vehicle problems that are highly transient with moderate level of nonlinearity present.

We consider the problem of shaping the transient step response of nonlinear systems to satisfy a class of integral constraints. Such constraints are inherent in hybrid energy systems consisting of energy sources and storage elements. While typical transient specifications aim to minimize overshoot, this problem is unique in that it requires the presence of an appreciable overshoot to satisfy the foregoing constraints. The problem was previously studied in the context of linear systems and this article extends that work to nonlinear systems. A combined integral and feedforward control, that requires minimal knowledge of the plant model, is shown to make the system amenable to meeting such constraints. Broadly, the compensation is effective for nonlinear plants with stable open‐loop step response and a positive DC gain. However, stability of the resulting closed‐loop system mandates bounds on the integral gain. In this regard, we state and prove generalized stability theorems for first and higher‐order nonlinear plants.

As a new type of seismic structure system, the self-centering structure has been widely concerned by researchers because of its ability to recover functions quickly after being subjected to an earthquake. At present, the research on self-centering structure mainly focuses on deterministic experimental research, while the research on the random analysis of the structure is still immature. In this paper, the transient response of a self-centering nonlinear system under stochastic excitation is studied. The restoring force of the self-centering nonlinear system adopted the Graesser model of the simplified flag-shaped model. It is described by a discontinuous function. The exponential polynomial closed (EPC) method is further developed for such a case. Response PDF approximation at different time instants is verified by the simulated ones. Good agreement proves the efficiency of the EPC method in the case of a discontinuous random process. Besides, the influences of excitation intensity and hysteretic energy dissipation coefficient on the transient response are discussed.

The introduction of the root-locus method in the z-plane simplifies the investigation of sampled-data control systems, by demonstrating the correlation between transient response and the location of the roots. It is shown that by establishing the correlation between frequency locus and the root locus, the correlation between frequency and transient response of sampled-data systems can be demonstrated.

Synthesis of optimal controller for synchronous power system

ABSTRACTIn this study, we propose a novel adaptive control architecture that provides dramatically better transient response performance compared to conventional adaptive control methods. This is accomplished by the synergistic employment of a traditional adaptive neural network (ANN) controller and a long short‐term memory (LSTM) network. LSTM structures can take advantage of the dependencies in an input sequence, which can help predict uncertainty. We introduce a training approach through which the LSTM network learns to compensate for the deficiencies of the ANN controller. This improves the transient response of the system and allows the controller to quickly react to unexpected events. Through careful simulation studies, we demonstrate that this architecture improves the estimation accuracy on a diverse set of uncertainties. We also provide an analysis of the contributions of the ANN controller and the LSTM network, identifying their roles in compensating low‐ and high‐frequency error dynamics. This analysis provides insight into why and how the LSTM augmentation improves the system's transient response. The stability of the overall system is analyzed via a rigorous Lyapunov analysis.

Design sensitivity analysis for transient response of non-viscously damped systems based on direct differentiate method

A modal projection-based reduction method for transient dynamic responses of viscoelastic systems with multiple damping models

During fast gas-turbine engine acceleration and deceleration, the transient vibration effects in bladed disk vibration become significant and the transient response needs to be calculated. In this paper, an effective method is developed for efficient calculations of the transient vibration response for mistuned bladed disks under varying rotation speeds. The method uses the large-scale finite element modeling of the bladed disks allowing the accurate description of the dynamic properties of the mistuned bladed disks. The effects of the varying rotation speed on the natural frequencies and mode shapes of a mistuned bladed disk and its effects on the amplitude and the spectral composition of the loading are considered. The dependency of the modal characteristics on the rotation speed is based on the evaluation of these characteristics at reference points followed by the interpolation to obtain values at any rotation speed from the operating range. A new method has been developed for the interpolation of mode shapes while preserving the orthogonality and mass normalization of the mode shapes. The method of mode shape interpolation is elaborated for tuned and mistuned bladed disks. The accuracy and efficiency of the method are demonstrated on test examples and on analysis of transient forced response of realistic bladed disks.

As a critical element within liquid rocket engine turbopumps, the end face seal plays a vital role. The stability and dynamic behavior of the rotor system are profoundly impacted by the hydrodynamic pressure effects emerging from the fluid film within the seal clearance. This study aims to investigate the liquid film's dynamic properties and their impact on the rotor system's transient behavior during both rapid acceleration and steady-state phases. Initially, a calculation model for the fluid film's equivalent stiffness and damping coefficients is developed using the small perturbation technique based on the Reynolds equation. This model explicitly accounts for axial and angular disturbances of the sealing ring, analyzing how these coefficients shift with varying parameters like film thickness and rotation speed. Findings indicate that higher rotational speeds intensify the dynamic pressure effect, leading to an overall elevation in stiffness coefficients across all directions. Subsequently, a finite element model representing a specific liquid rocket engine turbopump is constructed. By integrating time-variant seal dynamic parameters into the rotor's equations of motion, a coupled seal-rotor dynamic model is established. Numerical simulations were performed to evaluate the system's transient response during a rapid startup sequence (accelerating to 40,000 r / min within 2 seconds). The simulation outcomes highlight how seal parameters affect rotor stability and vibration magnitude, underscoring the necessity of accurately incorporating end face seal dynamics in rotor analysis. Consequently, this work offers valuable theoretical insights for the design and dynamic analysis of liquid rocket engine turbopumps.

The transient response sensitivity analysis of the transmission line is a new hotspot problem in transmission line problems. In this paper, a sensitivity analysis method based on fast Fourier transform is proposed in the transient response sensitivity analysis of the transmission line network. The method firstly establishes the circuit equation of the whole transmission line network characteristic, and transforms the partial differential equation in the time domain into the ordinary differential equation in the frequency domain by Fourier transform. Then we find the derivative of a certain distribution parameter of the transmission line by the ordinary differential equation. The network transient response sensitivity problem is transformed into solving the transient response of the transmission line network and the partial derivative of the network parameter matrix to the circuit parameters, which greatly simplifies the analysis of the transient response sensitivity of the transmission line network, and the sensitivity analysis of the transient response of any node of the transmission line network to any network parameters is realized. The method does not need to decouple the coupled transmission line, and can accurately and quickly calculate the transient response sensitivity of any type of transmission line network. The result of the example shows that the method is correct and effective. This method provides a new reference method for the sensitivity analysis of transmission line network transient response.

Introduction. In an electrical power system, the output of the synchronous generators varies due to disturbances or sudden load changes. These variations in output severely affect power system stability and power quality. The synchronous generator is equipped with an automatic voltage regulator to maintain its terminal voltage at rated voltage. Several control techniques utilized to improve the response of the automatic voltage regulator system, however, proportional integral derivative (PID) controller is the most frequently used controller but its parameters require optimization. Novelty. In this paper, the chaotic sequence based on the logistic map is hybridized with particle swarm optimization to find the optimal parameters of the PID for the automatic voltage regulator system. The logistic map chaotic sequence-based initialization and global best selection enable the algorithm to escape from local minima stagnation and improve its convergence rate resulting in best optimal parameters. Purpose. The main objective of the proposed approach is to improve the transient response of the automatic voltage regulator system by minimizing the maximum overshoot, settling time, rise time, and peak time values of the terminal voltage, and eliminating the steady-state error. Methods. In the process of parameter tuning, the Chaotic particle swarm optimization technique was run several times through the proposed hybrid objective function, which accommodates the advantages of the two most commonly used objective functions with a minimum number of iterations, and an optimal PID gain value was found. The proposed algorithm is compared with current metaheuristic algorithms including conventional particle swarm optimization, improved kidney algorithm, and others. Results. For performance evaluation, the characteristics of the integral of time multiplied squared error and Zwe-Lee Gaing objective functions are combined. Furthermore, the time-domain analysis, frequency-domain analysis, and robustness analysis are carried out to show the better performance of the proposed algorithm. The result shows that automatic voltage regulator tuned with the chaotic particle swarm optimization based PID yield improvement in overshoot, settling time, and function value of 14.41 %, 37.91 %, 1.73 % over recently proposed IKA, and 43.55 %, 44.5 %, 16.67 % over conventional particle swarm optimization algorithms. The improvement in transient response further improves the automatic voltage regulator system stability for electrical power systems.

Shaping the transient response of incommensurate fractional order systems is a challenge. In this paper, incommensurate fractional order controllers are employed to control a two-order incommensurate fractional order system. An appropriate RST control structure is employed to construct a closed loop system with a commensurate fractional order transfer function. Then, the characteristic ratios of this transfer function are chosen to reach a low overshoot step response. The transient response speed is adjusted by selecting the appropriate generalized time constant. A numerical example is given to show the efficiency of the proposed method for shaping the transient response of an incommensurate fractional order system.