共查询到20条相似文献，搜索用时 93 毫秒
1.
《Journal of The Franklin Institute》2019,356(5):2901-2918
In this paper, we present a new method in the reduction of large-scale linear differential-algebraic equation (DAE) systems. The approach is to first change the DAE system into a parametric ordinary differential equation (ODE) system via the ε-embedding technique. Next, based on parametric moment matching, we give the parameterized model order reduction (MOR) method to reduce this parametric system, and a new Arnoldi parameterized method is proposed to construct the column-orthonormal matrix. From the reduced-order parametric system, we get the reduced-order DAE system, which can preserve the structure of the original DAE system. Besides, the parametric moment matching for the reduced-order parametric systems is analyzed. Finally, the effectiveness of our method is successfully illustrated via two numerical examples. 相似文献
2.
A two-step iterative method (1,2) for a reduction in the order of linear continuous-time systems, given in the state equation or the transfer function, is extended to reduce discrete-time systems. The method requires the optimization of the residues and eigenvalues (or poles) belonging to an objective function. The objective function to be minimized is chosen as the finite sum of the squares of the error between the step responses of the reduced model and the original system. This scheme is continued cyclically until the objective function is satisfactorily minimized. By investigating the initial selection of the eigenvalues in the reduced-order model, it is found that the dominant eigenvalues of the original system give a good approximation. Further, the resulting model is always stable, assuming the original system is stable. As shown in a numerical example, the proposed method is superior to the other methods of model reduction in both steady-state and transient responses, and in the value of the sum of the squares of the error. 相似文献
3.
A simple iterative technique, which is free of certain shortcomings of the previous methods, is proposed for the approximation of large linear systems by a lower- order model. Here, the measure of the goodness of the approximate model is taken to be the value of the integral-square error between the step responses of the exact and the simplified systems. The proposed technique consists of a two-step iterative scheme. In the first step, the optimum residues are obtained by the minimization of the objective function, while the poles (or eigenvalues) are kept constant. In the second step, the poles are optimized while the residues remain fixed. This procedure is continued cyclically until the objective function is satisfactorily minimized. The necessary and sufficient conditions for existence of an optimum are satisfied in each step. The residues, poles and objective functions converge monotonically. The resulting reduced-order model obtained by this method is stable if the original system is stable. The method can also be applied to systems with repeated poles and to multivariable systems. The results are superior to those obtained previously in the steady-state, the point-by-point transient response, and the value of the integral-square error. Illustrative examples are presented. 相似文献
4.
Design procedures are proposed for model conversion and digital redesign of a singular system, which is controllable at finite and impulsive modes. In order to attain a standard regular problem, we use some techniques to decompose the singular system into a reduced-order regular subsystem and a nondynamic subsystem. As a result, some well-known design methodologies for a regular system can be applied to the reduced-order regular subsystem. Finally, we transform the results obtained back to those of the original coordinate system. 相似文献
5.
Mian Mohammad Arsalan Asif Mian Ilyas Ahmad Peter Benner Lihong Feng Tatjana Stykel 《Journal of The Franklin Institute》2021,358(3):2015-2038
We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions appearing in the input-output representation of the non-linear system. An existing technique achieves this for the first two multivariate transfer functions, in what is called the symmetric form of the multivariate transfer functions. We extend this framework to an equivalent and simplified form, the regular form, which allows us to show moment matching for the first three multivariate transfer functions. Numerical results for three benchmark examples of quadratic-bilinear systems show that the proposed framework exhibits better performance with reduced computational cost in comparison to existing techniques. 相似文献
6.
Meng Zhang Ming-Gang Gan Jie Chen Zhong-Ping Jiang 《Journal of The Franklin Institute》2019,356(12):6087-6105
This paper focuses on the optimal control of a DC torque motor servo system which represents a class of continuous-time linear uncertain systems with unknown jumping internal dynamics. A data-driven adaptive optimal control strategy based on the integration of adaptive dynamic programming (ADP) and switching control is presented to minimize a predefined cost function. This takes the first step to develop switching ADP methods and extend the application of ADP to time-varying systems. Moreover, an analytical method to give the initial stabilizing controller for policy iteration ADP is proposed. It is shown that under the proposed adaptive optimal control law, the closed-loop switched system is asymptotically stable at the origin. The effectiveness of the strategy is validated via simulations on the DC motor system model. 相似文献
7.
Motivated by the requirement for safe and pinpoint soft landing in future asteroids missions, a soft landing control method based on finite-time control (FTC) technique is developed in this paper. Firstly, in order to utilize the design philosophy of cascaded system, the landing error dynamics of asteroid probe are divided into two subsystems, including a position error subsystem (PES) and a line-of-sight angle error subsystem (LOSAES). Secondly, homogeneous system theory is employed to design the control law for LOSAES such that the states of LOSAES will be stabilized to the origin in finite time. For the reduced PES subsystem, a FTC law is designed such that the rest of states will converge to zero in finite time. Strict analysis shows that the whole system satisfies the finite time stability. Simulation results demonstrate that the proposed method provides faster convergence rates and better disturbance rejection properties compared with the traditional asymptotically stable control (ASC) method. 相似文献
8.
细胞信号转导网络的结构复杂,规模庞大,建立的数学模型维数高,变量多,具有高度非线性。在复杂系统分析设计中,模型简化始终是主要的研究问题之一。提出一种基于混合推理方法的模型简化策略,利用代谢控制分析、敏感性分析、主元分析和通量分析相结合,降低系统模型维数,减少生化反应个数,简化系统结构。以NF-κB信号转导网络作为研究对象,原模型由24个常微分方程和64个参数组成,简化模型则包括17个常微分方程,1个代数方程和52个参数。仿真结果表明,简化模型能够准确地预测系统的动态特性,为模型分析和参数辨识提供方便,验证了模型简化策略的有效性。 相似文献
9.
We present a model reduction method for bilinear systems based on the Laguerre series expansion of the kernels resulting from the Volterra representation theory. By employing a two-sided projection, the reduced order system preserves a desired number of Laguerre coefficients, thereby approximating the original system faithfully. Furthermore, the relationship between the proposed Laguerre-based methods and the moment matching methods is studied, which reveals that these two approaches are equivalent under some specific conditions. 相似文献
10.
This paper reports a new method for designing distributed reduced-order functional observers of a class of interconnected systems with time delays. The systems under consideration belong to a class of large-scale systems where each system is formed by a number of interconnected subsystems. Moreover, the interconnections and the states of the local subsystems are subject to heterogeneous time delays. The novel contribution of this paper lies in the development of new coordinate state transformations, which are used to transform the interconnected subsystems into decoupled subsystems. Most significantly, each decoupled subsystem does not contain any time delay in the state vector. Moreover, each decoupled subsystem is expressed in an observable canonical form, with time delays only appearing in the inputs and outputs of the system. Due to this novel structure, a reduced-order functional observer for each decoupled subsystem can be easily designed to estimate the unmeasurable local state vector. The designed observers for the local subsystems do not need to exchange the state estimates amongst themselves, and therefore, each observer for each local subsystem can be designed independently. Because of the state transformations, the designed observers have a more general structure than any of the existing distributed functional observers available in the literature. Numerical examples are given to illustrate the effectiveness and advantages of our results. 相似文献
11.
This paper investigates the problem of fault detection (FD) for discrete-time switched systems. Under a dwell time constraint, a switching rule that depends on the measured output is constructed for the system. Time-varying residual generators are designed such that the switched system is asymptotically stable and also with the detection performance under this switching rule. The advantages of the proposed technique are threefold: 1) It has the advantages of both slow switching and fast switching. 2) It can extend the classic design of time-invariant residual generator. 3) It can guarantee the switched system still has the desired fault detection performance even if all subsystems are without it. This feature reduces the performance requirements for each subsystem. A numerical example illustrates the effectiveness of the proposed method. 相似文献
12.
In this paper, the reduction method uses the concepts of stability-equation and important poles to find the denominator of the reduced model. Then the numerator of the reduced model is found by complex curve fitting. This method tends to simultaneously guarantee a stable reduced model from a stable system and obtain a satisfactory result, since it considers the distribution of important poles. Examples are presented to illustrate this advantage. 相似文献
13.
《Journal of The Franklin Institute》2022,359(12):6438-6466
In this article, the two-dimensional model is decomposed into two one-dimensional models using the minimal rank-decomposition condition, and the model reduction is conducted on these two one-dimensional models using time-limited Gramians. The proposed framework works for both one-dimensional and two-dimensional systems. The suggested approach addresses the primary flaw in Gawronski & Juang’s problem of reduced-order model instability. Researchers revealed some stability preservation solutions to address this key flaw, which ensure the stability of one-dimensional reduced-order systems; nevertheless, these strategies result in large approximation errors. However, to the best of the authors’ knowledge, there is no literature available for the stability preserving time-limited-intervals Gramians based model reduction framework for the two-dimensional discrete-time systems. In comparison to other stability-preserving strategies, the proposed framework provides an a priori error-bound formulation that is easily computable. The simulation results show that the proposed framework performs well compared to other existing stability-preserving methods, demonstrating its usefulness. 相似文献
14.
《Journal of The Franklin Institute》2023,360(13):9637-9662
This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators. 相似文献
15.
A new combined time and frequency domain method for the model reduction of discrete systems in z-transfer function is presented. First, the z-transfer functions are transformed into the w-domain by the bilinear transformation, z = (1+w)/(1?w). Then, four model reduction methods—Routh approximation, Hurwitz polynomial approxima- tion, stability equation, and retaining dominant poles—are used respectively to reduce the order of the denominator polynomials in the w-domain. Least squares estimate is then used to find the optimal coefficients in the numerator polynomials of the reduced models so that the unit step response errors are reduced to a minimum. The advantages of the proposed method are that both frequency domain and time domain characteristics of the original systems can be preserved in the reduced models, and the reduced models are always stable provided the original models are stable. 相似文献
16.
A method for model order reduction is proposed using response-matching technique. The step and impulse inputs have been considered. All types of pole configurations in the original high-order and reduced low-order system are included in this paper like real, complex and repeated. The proposed method is comparable in quality with similar existing methods and is capable of generating a reduced-order model with a desired pole pattern. 相似文献
17.
A vehicle system driven by two independent DC motors is presented here, one of which is used for the right wheel and the other is used for the left wheel. An adaptive compensator using Takagi-Sugeno fuzzy systems is proposed to control the vehicle system. The compensator includes an adaptive model identifier and adaptive controller. An online method is used to adjust the parameters of the identifier model to match the behavior model of the vehicle system. Then, the parameters of the identifier model are employed in a standard parallel-distributed compensator to provide asymptotically stable equilibrium for the closed-loop vehicle drive system, in which the velocity and direction angle of the vehicle are controlled. Results demonstrate that the proposed controller structure is robust to load changes and follows different trajectories very well. 相似文献
18.
This paper deals with asymptotic rejection of a multi-sinusoidal signal for linear single-input single-output stable systems with unknown structure. An adaptive orthogonal signals generator is used to both reconstruct the disturbance and cancel its effect on the system output. An interesting feature is that the disturbance is removed by the generated internal signals with no additional dynamics in the cancellation algorithm. A fractional-order controller is designed which guarantees the closed-loop stability of the system if the location of the plant frequency response at the estimated frequencies lies in a half-plane passing through the origin of the complex plane, i.e. no information about the order of the system to be controlled, the relative degree, the nature of its poles and zeros, is required. The case of multi-sinusoidal disturbance is also analyzed. Simulations and comparisons with existing approaches are presented that highlight the performances of the proposed method. 相似文献
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20.
A new event-triggered model predictive control (MPC) method is proposed for PWA systems with model-plant mismatch, such that, for a given asymptotically constant reference signal, exponential stability and unbiased tracking can be achieved. Firstly, for the PWA system, an observer is designed to estimate state and the model-plant mismatch. To guarantee the exponential stability, an event is introduced, and an event-triggered model predictive controller is designed as well. By introducing state error and estimate error, an augmented model is constructed. Then, using the model-dependent average dwell time (MDADT) method and Lyapunov stability theory, exponentially stable condition of the closed-loop system is derived, which is formulated by linear matrix inequalities (LMIs), and zero offset is also guaranteed under some mild assumptions. Moreover, the MDADT of each sub-system is given simultaneously. Finally, simulations have been taken to verify the effectiveness of the proposed method. 相似文献