共查询到20条相似文献，搜索用时 547 毫秒
1.
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
2.
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
3.
A combined method making use of the advantages of the stability-equation method and the Padé approximation method for reducing high order transfer functions of single-input/single-output systems and multivariable systems is presented. The reduction procedure is simple and computer-oriented. All the reduced models are guaranteed to be stable if the original system is stable. The proposed method is applied to the investigation of (1) the effect of model reduction on the limit-cycle of non-linear systems and (2) the effect of model reduction on Horowitz compensators. Detailed calculations are given and comparisons with results in the current literature are made. 相似文献
4.
In this paper, moment matching model reduction problem for negative imaginary systems is considered. For a given negative imaginary system with poles at the origin, our goal is to find a reduced-order negative imaginary system such that a prescribed number of the moments and the poles at the origin are preserved. Firstly, the original negative imaginary system is split into an asymptotically stable subsystem, a lossless negative imaginary subsystem and an average subsystem. Then, moment matching model reduction is implemented on the asymptotically stable subsystem and the lossless negative imaginary subsystem. The resulting reduced-order system preserves the negative imaginary structure and the poles at the origin. Also, the proposed model reduction method is extended to the positive real systems. Numerical examples demonstrate the effectiveness of the proposed model reduction method. 相似文献
5.
Constantine P. Therapos 《Journal of The Franklin Institute》1984,318(4):243-251
A new method for the model reduction of linear discrete stable systems in Z-transfer functions is presented. First, a set of parameters is defined, whose values uniquely determine the given system. Then an always stable reduced approximant is obtained by neglecting the parameters which do not contribute significantly in the formation of the system's responses. The proposed method slightly modified also preserves, in the reduced model, the rank of the given system. Formulae are provided to select the reduced order. 相似文献
6.
Model order reduction based on general orthogonal polynomials in the time domain for coupled systems
In this paper, we present a new model order reduction (MOR) method based on general orthogonal polynomials for coupled systems in the time domain. By constructing proper projection matrices, the reduced system not only can preserve the structure of the original system but also can match the first several coefficients of the original output. We study the error bound and the stability of the reduced system as well. Finally, two numerical examples are shown to illustrate the effectiveness of the method. 相似文献
7.
The terminal iterative learning control is designed for nonlinear systems based on neural networks. A terminal output tracking error model is obtained by using a system input and output algebraic function as well as the differential mean value theorem. The radial basis function neural network is utilized to construct the input for the system. The weights are updated by optimizing an objective function and an auxiliary error is introduced to compensate the approximation error from the neural network. Both time-invariant input case and time-varying input case are discussed in the note. Strict convergence analysis of proposed algorithm is proved by the Lyapunov like method. Simulations based on train station control problem and batch reactor are provided to demonstrate the effectiveness of the proposed algorithms. 相似文献
8.
An algorithm, amenable for programming on a digital computer, has been presented for the modelling of linear discrete-time systems, as an alternative to the procedure of Shamash (1). The transformations inherent in the procedure are easily accomplished by the synthetic division technique. With the use of modified Cauer form of continued fraction (MCF), the new method matches a set of both the time-moments and Markov parameters of the system and of the model, as in the procedure of Parthasarathy and Singh (2), giving a better approximation to the system response at all times. A distinct feature of the proposed algorithm compared with the earlier methods of discrete system reduction (1),(2), is that a number of reduced-order models are generated simultaneously; this allows scope for better selection in choosing the right model for system analysis and design. 相似文献
9.
《Journal of The Franklin Institute》2023,360(7):4753-4783
For the multi-input single-output (MISO) system corrupted by colored noise, we transform the original system model into a new MISO output error model with white noise through data filtering technology. Based on the newly obtained model and the bias compensation principle, a novel data filtering-based bias compensation recursive least squares (BCRLS) identification algorithm is developed for identifying the parameters of the MISO system with colored noise disturbance. Unlike the exiting BCRLS method for the MISO system (see, in Section 3), without computing the complicated noise correlation functions, still the proposed method can achieve the unbiased parameters estimation of the MISO system in the case of colored process noises. The proposed algorithm simplifies the implementation of and further expands the application scope of the existing BCRLS method. Three numerical examples clearly illustrate the validity of and the good performances of the proposed method, including its superiority over the BCRLS method and so on. 相似文献
10.
11.
A new method for the calculation of time responses of lumped time invariant networks is presented. It is based on the numerical inversion of the Laplace transform and involves the computation of the frequency domain function at pre-assigned complex points and forming a weighted sum. The method exactly inverts a certain number of terms of the Taylor expansion of the time response and is thus equivalent to the methods used for the integration of differential equations. This equivalence is established on two examples. The order of integration can be changed between 1 and 46 without any difficulty. Additional properties resulting from the application of the numerical Laplace transform inversion are also discussed and some novel applications indicated. 相似文献
12.
A computer-aided method for simplification and identification of linear discrete systems via step-response matching is presented. Golub's algorithm for solving least-squares problem is used to find the optimum coefficients of the reduced model. The advantages of this method are (1) for model reduction, both the time response and frequency response within the bandwidth region of the reduced model are very close to those of the original system; and (2) for system identification, the identified model is very close to the original system. In the illustrative examples considered in this paper the results of the proposed method appear to be better than those of other methods in the current literature. 相似文献
13.
This paper is devoted to the investigation of the delay-dependent H∞ filtering problem for a class of discrete-time singular Markov jump systems with Wiener process and partly unknown transition probabilities. The class of stochastic singular model under consideration is more general and covers the stochastic singular Markov jump time-varying delay systems with completely known and completely unknown transition probabilities as two special cases. Firstly, based on a stochastic Lyapunov–Krasovskii candidate function and an auxiliary vector function, by employing some appropriate free-weighting matrices, the discretized Jensen inequality and combining them with the structural characteristics of the filtering error system, a set of delay-dependent sufficient conditions are established, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, causal and stochastically stable, but also satisfy a prescribed H∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the sufficient conditions for the solvability of the H∞ filtering problem are obtained in terms of a new type of Lyapunov–Krasovskii candidate function and a set of linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed method in the paper. 相似文献
14.
A method of model reduction for reducing a high-order transfer function to its low-order models is introduced based upon the stability-equation method. The transfer functions of reduced orders are obtained directly from the pole-zero patterns of the stability-equations of the original transfer function. Comparisons with methods in the current literature are made. Extension of the proposed method to discrete systems is given. 相似文献
15.
Minlin Wang Xuemei Ren Xueming Dong Qiang Chen 《Journal of The Franklin Institute》2019,356(13):6817-6841
In this paper, a novel composite controller is proposed to achieve the prescribed performance of completely tracking errors for a class of uncertain nonlinear systems. The proposed controller contains a feedforward controller and a feedback controller. The feedforward controller is constructed by incorporating the prescribed performance function (PPF) and a state predictor into the neural dynamic surface approach to guarantee the transient and steady-state responses of completely tracking errors within prescribed boundaries. Different from the traditional adaptive laws which are commonly updated by the system tracking error, the state predictor uses the prediction error to update the neural network (NN) weights such that a smooth and fast approximation for the unknown nonlinearity can be obtained without incurring high-frequency oscillations. Since the uncertainties existing in the system may influence the prescribed performance of tracking error and the estimation accuracy of NN, an optimal robust guaranteed cost control (ORGCC) is designed as the feedback controller to make the closed-loop system robustly stable and further guarantee that the system cost function is not more than a specified upper bound. The stabilities of the whole closed-loop control system is certified by the Lyapunov theory. Simulation and experimental results based on a servomechanism are conducted to demonstrate the effectiveness of the proposed method. 相似文献
16.
This paper presents a decomposition based least squares estimation algorithm for a feedback nonlinear system with an output error model for the open-loop part by using the auxiliary model identification idea and the hierarchical identification principle and by decomposing a system into two subsystems. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm has a smaller computational burden. The simulation results indicate that the proposed algorithm can estimate the parameters of feedback nonlinear systems effectively. 相似文献
17.
S.G. Tzafestas 《Journal of The Franklin Institute》1978,305(4):199-220
This paper considers the problem of identifying the parameters of dynamic systems from input-output records. Both lumped-parameter and distributed-parameter systems, deterministic and stochastic, are studied. The approach adopted is that of expanding the system variables in Walsh series. The key point is an operational matrix P which relates the coefficient matrix Г of the Walsh series of a given function with the coefficient matrix of its first derivative. Using this operational matrix P one overcomes the necessity to use differentiated data, a fact that usually is avoided either by integration of the data or by using discrete-time models. Actually, the original differential input-output model is converted to a linear algebraic (or regression) model convenient for a direct (or a least squares) solution. A feature of the method is that it permits the identification of unknown initial conditions simultaneously with the parameter identification. The results are first derived for single-input single-output systems and then are extended to multi-input multi-output systems. The case of non-constant parameters is treated by assuming polynomial forms. Some results are also included concerning the identification of state-space and integral equation models. The theory is supported by two examples, which give an idea of how effective the method is expected to be in the real practice. 相似文献
18.
In this paper, based on Stirling’?s polynomial interpolation formula, the Second-order Central Difference Predictive Filter (CDPF2) is proposed for nonlinear estimation. To facilitate the new method, the algorithm flow of CDPF2 is given first. Then, the theoretical deductions demonstrate that the estimated accuracy of the model error and system state for the CDPF2 is higher than that of the conventional PF. In addition, the stochastic boundedness and the error behavior of CDPF2 is analyzed for general nonlinear systems in a stochastic framework. The theoretical analysis presents that the estimation error will remain bounded and the covariance will remain stable if the system?s initial estimation error, disturbing noise terms and model error are small enough, which is the core part of the CDPF2 theory. All of the results have been demonstrated by numerical simulations for a nonlinear example system. 相似文献
19.
The input-output finite-time filtering problem is addressed for a class of switched linear parameter-varying systems in this paper. Firstly, by constructing a parameter-dependent Lyapunov function and resorting to the average dwell time approach, sufficient conditions ensuring finite-time boundedness and input-output finite-time stability are established for the augmented filtering error system. Then, a parameter-dependent asynchronous filter is designed such that the augmented filtering error system are both finite-time bounded and input-output finite-time stable. Finally, the active magnetic bearing model is introduced and verifies the main algorithms in this paper. 相似文献
20.
《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