Transient Response of Linear Systems Under Integral Constraints

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Bilal Salih ◽  
Tuhin Das
Keyword(s):  
Transfer Function ◽  
Power Systems ◽  
Transfer Functions ◽  
Adaptive Estimation ◽  
Sufficient Conditions ◽  
Parametric Uncertainty ◽  
Step Response ◽  
Integral Constraints ◽  
Second Order Systems ◽  
Necessary And Sufficient

Abstract The requirement of satisfying an integral constraint imposed on a linear system's transient step-response is considered in this paper. The problem is first analyzed to determine the specific structure of a system's transfer function that helps satisfy such constraints. Analytical results are derived for a class of second-order systems with an additional zero. The results are extended to higher order transfer functions. Subsequently, a standard compensation consisting of a combination of feedforward and feedback actions is proposed to transform a given transfer function to the desired structure. Necessary and sufficient conditions to guarantee stability of the resulting closed-loop system are derived. Next, the problem of satisfying integral constraints in the presence of parametric uncertainty is addressed by augmenting adaptive estimation strategies to the feedforward and feedback compensation structure. Simulation results are provided for validation. The theory presented here is an abstraction from power management algorithms for hybrid power systems, such as a fuel cell hybridized with an ultracapacitor. Further work is ongoing to extend the theory to nonlinear systems.

Placing Minimum Phase Zeros to Shape Transient Response: Generalization From Control of Hybrid Power Systems

2017 ◽  
Author(s):  
Bilal S. Salih ◽  
Tuhin K. Das
Keyword(s):  
Power Systems ◽  
Transient Response ◽  
Transfer Functions ◽  
Higher Order ◽  
Second Order ◽  
Step Response ◽  
Minimum Phase ◽  
Hybrid Power Systems ◽  
Hybrid Power ◽  
Second Order Systems

Conservation of energy can be applied in designing control of hybrid power systems to manage power demand and supply. In practice, it can be used for designing decentralized controllers. In this paper, this idea is analyzed in a generalized theoretical framework. The problem is transformed to that of using minimum phase zeros to generate a specific type of transient response admitted by dynamical systems. Here, the transient step response is shaped using an underlying conservation principle. In this paper, emphasis is placed on second order systems. However, the analysis can be extended to higher order transfer functions. Analytical results relating zero location to the matched/ mismatched areas of the transient response are established for a class of second order systems. A combination of feedback and feedforward actions are shown to achieve the desired zero placement/addition and the desired transient response. The proposed analysis promises extension to nonlinear systems. Optimization studies also seem appropriate, especially for higher order transfer functions.

Noncollocated passivity-based PD control of a single-link flexible manipulator

Robotica ◽  
2003 ◽  
Vol 21 (2) ◽  
pp. 117-135 ◽  
Author(s):  
Liang-Yih Liu ◽  
King Yuan
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Sufficient Conditions ◽  
Angular Acceleration ◽  
Flexible Manipulator ◽  
Infinite Dimensional ◽  
Single Link ◽  
Acceleration Feedback ◽  
Necessary And Sufficient ◽  
Irrational Transfer Function

The passivity property of a noncollocated single-link flexible manipulator with a parameterized output is studied. The system can be characterized by either the irrational transfer function of an infinite-dimensional model or its truncated rational transfer functions. Necessary and sufficient conditions for these transfer functions to be passive are found. It is also shown that a non-passive, marginal minimum-phase, truncated transfer function can be rendered passive by using either the root strain feedback or the joint angular acceleration feedback. For the noncollocated truncated passive transfer function, a PD controller suffices to stabilize the overall system. Numerical results are given to show the efficacy of the proposed approaches.

Transfer functions and conditions for stationarity of bilinear models with gaussian residuals

1985 ◽  
Vol 400 (1819) ◽  
pp. 315-330 ◽  
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Function System ◽  
Bilinear Models ◽  
Special Cases ◽  
Necessary And Sufficient

The aim of this paper is to construct the transfer function system of bilinear models with gaussian residuals and to give necessary conditions and sufficient conditions for stationarity. In some special cases, the necessary and sufficient conditions are given.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

Lyapunov Stability, Semistability, and Asymptotic Stability of Matrix Second-Order Systems

1995 ◽  
Vol 117 (B) ◽  
pp. 145-153 ◽  
Author(s):  
D. S. Bernstein ◽  
S. P. Bhat
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Viscous Damping ◽  
Stability And Instability ◽  
The Stability ◽  
Second Order Systems ◽  
Necessary And Sufficient

Necessary and sufficient conditions for Lyapunov stability, semistability and asymptotic stability of matrix second-order systems are given in terms of the coefficient matrices. Necessary and sufficient conditions for Lyapunov stability and instability in the absence of viscous damping are also given. These are used to derive several known stability and instability criteria as well as a few new ones. In addition, examples are given to illustrate the stability conditions.

scholarly journals Transfer Function with Nonlinear Characteristics Definition Based on Multidimensional Laplace Transform and its Application to Forced Response Power Systems

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4061
Author(s):  
Villalón ◽  
Medina-Rios
Keyword(s):  
Transfer Function ◽  
Power Systems ◽  
Power System ◽  
Laplace Transform ◽  
Frequency Response ◽  
Transfer Functions ◽  
Volterra Series ◽  
Forced Response ◽  
Nonlinear Characteristics ◽  
Test Power

In this research, the concept of nonlinear transfer function with nonlinear characteristics is introduced through the multidimensional Laplace transform and modal series (MS) method. The method of modal series is applied to the power systems dynamics analysis in order to consider nonlinear oscillations and modal interactions, which contribute to the response of the system's dynamic following disturbances. The method of MS allows the inclusion of input excitation functions obtained as Laplace domain kernels superposed to obtain a transfer function. Applying the Volterra series expansion through kernels decomposition, a transfer function with nonlinear characteristics is obtained which incorporates some of the main modal characteristics of the nonlinear system. Following the same schematic procedure, it is possible to determine second and higher order transfer functions. Once the transfer functions both linear and with nonlinear characteristics are determined, a time domain and frequency response analyses can be performed. The methodology is exemplified by denoting the numerical and analytical properties with the application to a synchronous machine-infinite busbar test power system and to a three synchronous machines–nine buses test power system. Bode and Nyquist analysis are utilized to demonstrate the transfer functions accuracy and frequency response.

Simultaneous Compensation of the Gain, Phase, and Phase-Slope

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Vahid Badri ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Phase Margin ◽  
Phase Plot ◽  
Phase Slope ◽  
Loop Transfer Function ◽  
Sample Application ◽  
Arbitrary Frequency ◽  
Necessary And Sufficient

This paper deals with the problem of simultaneous compensation of the gain, phase, and phase-slope at an arbitrary frequency by using a fractional-order lead/lag compensator. The necessary and sufficient conditions for feasibility of the problem are derived. Also, the number of existing solutions (i.e., the number of distinct fractional-order lead/lag compensators satisfying the considered compensation requirements) is analytically found. Moreover, as a sample application, it is shown that the obtained results for the considered compensation problem are helpful in tuning fractional-order lead/lag compensators for simultaneously achieving desired phase margin, desired gain cross frequency, and flatness of the Bode phase plot of the loop transfer function at this frequency.

scholarly journals Estimation of Transfer Function Coefficients for Second-Order Systems via Metaheuristic Algorithms

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4529
Author(s):  
Omar Rodríguez-Abreo ◽  
Juvenal Rodríguez-Reséndiz ◽  
Francisco Antonio Castillo Velásquez ◽  
Alondra Anahi Ortiz Verdin ◽  
Juan Manuel Garcia-Guendulain ◽  
...  
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Standard Form ◽  
Estimation Method ◽  
Second Order ◽  
Parametric Estimation ◽  
Metaheuristic Algorithms ◽  
Step Response ◽  
Gray Wolf ◽  
Final Value

The present research develops the parametric estimation of a second-order transfer function in its standard form, employing metaheuristic algorithms. For the estimation, the step response with a known amplitude is used. The main contribution of this research is a general method for obtaining a second-order transfer function for any order stable systems via metaheuristic algorithms. Additionally, the Final Value Theorem is used as a restriction to improve the velocity search. The tests show three advantages in using the method proposed in this work concerning similar research and the exact estimation method. The first advantage is that using the Final Value Theorem accelerates the convergence of the metaheuristic algorithms, reducing the error by up to 10 times in the first iterations. The second advantage is that, unlike the analytical method, it is unnecessary to estimate the type of damping that the system has. Finally, the proposed method is adapted to systems of different orders, managing to calculate second-order transfer functions equivalent to higher and lower orders. Response signals to the step of systems of an electrical, mechanical and electromechanical nature were used. In addition, tests were carried out with simulated signals and real signals to observe the behavior of the proposed method. In all cases, transfer functions were obtained to estimate the behavior of the system in a precise way before changes in the input. In all tests, it was shown that the use of the Final Value Theorem presents advantages compared to the use of algorithms without restrictions. Finally, it was revealed that the Gray Wolf Algorithm has a better performance for parametric estimation compared to the Jaya algorithm with an error up to 50% lower.

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