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1.
In this paper, a new algebraic approach to the on-line signal derivatives estimation is proposed. The proposed approach is based on the conversion of the truncated Taylor series expansion to the set of linearly independent equations regarding the signal derivatives. The nonhomogeneous parts of the obtained set of equations are convolution integrals, which can be transformed to the stable linear state-space filter realization. The proposed algebraic estimator provides stable convergence without the need for periodic re-initialization, as in the case of the conventional algebraic estimators. In contrast to the Taylor series-based tracking differentiators, the proposed estimator also provides an estimation of the arbitrary number of the higher-order signal derivatives. In addition, the tuning of the estimator parameters does not depends on the filter dimension. The efficiency of the proposed estimator is illustrated by the simulation examples and experimental results related to the monitoring of the surgical drilling process.  相似文献   

2.
In this paper, the mean-square and mean-module filtering problems for polynomial system states over polynomial observations are studied proceeding from the general expression for the stochastic Ito differentials of the estimate and the error variance. The paper deals with the general case of nonlinear polynomial states and observations. As a result, the Ito differentials for the estimates and error variances corresponding to the stated filtering problems are first derived. The procedure for obtaining an approximate closed-form finite-dimensional system of the sliding mode filtering equations for any polynomial state over observations with any polynomial drift is then established. In the examples, the obtained sliding mode filters are applied to solve the third-order sensor filtering problems for a quadratic state, assuming a conditionally Gaussian initial condition for the extended second-order state vector. The simulation results show that the designed sliding mode filters yield reliable and rapidly converging estimates.  相似文献   

3.
The so-called “percolation operations” which involve simultaneous heat and mass transport are defined in terms of a system of mixed partial differential equations which are nonlinear and include variable coefficients. Second-order interpolation followed by integration over an increment of the time or space variable is proposed as a method for arriving at finite difference equation equivalents of the original partial differential equations. A model change is also used to give physical significance to finite difference equivalents associated with derivatives in the space dimension. It is shown that second-order interpolation has the advantage over linear interpolation that it introduces a factor β which in a stability analysis based on cencentrations offers a range of choices that will insure stable calculation on a digital machine.  相似文献   

4.
The paper considers a process controlled by a system of delayed differential equations. Under certain assumptions, a control function is determined such that the zero solution of the system is asymptotically stable and, for an arbitrary solution, the integral quality criterion with infinite upper limit exists and attains its minimum value in a given sense. To solve this problem, Malkin’s approach to ordinary differential systems is extended to delayed functional differential equations, and Lyapunov’s second method is applied. The results are illustrated by examples, and applied to some classes of delayed linear differential equations.  相似文献   

5.
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6.
By applying hybrid functions of general block-pulse functions and Legendre polynomials, linear Volterra integrodifferential systems are converted into a system of algebraic equations. The approximate solutions of linear Volterra integrodifferential systems are derived. Using the results we obtain the optimal control and state as well as the optimal value of the objective functional. The numerical examples illustrate that the algorithms are valid.  相似文献   

7.
In this paper a new approach to algebraic parameter identification of the linear SISO systems is proposed. The standard approach to the algebraic parameter identification is based on the algebraic derivatives in Laplace domain as the main tool for algebraic manipulations like elimination of the initial conditions and generation of linearly independent equations. This approach leads to the unstable time-varying state-space realization of the filters for the on-line parameter estimation. In this paper, the finite difference and shift operators in combination with the frequency-shifting property of Laplace transform is applied instead of algebraic derivatives. Resulting state-space realization of the estimator filters is asymptotically stable and doesn’t require switch-of mechanism to prevent overflow of the estimator variables. The proposed method is especially suitable for applications in closed-loop on-line identification where the stable behavior of the estimators is a necessary requirement. The efficiency of the proposed algorithm is illustrated on three simulation examples.  相似文献   

8.
A class of unstable relay-controlled plants possessing one pole at the origin and two non-zero distinct real poles is studied. Cases corresponding to one or both non-zero poles in the right half-plane are considered. In each case a controller which simultaneously reduces the error and its first and second derivatives to zero in minimum time is designed. Also the class of admissible inputs is found which, after a minimum transient time, can be followed without any error. Through some linear transformations, it is shown that the equations of the switch curve and the switch surface can be made independent of the plant's constant gain and dependent only on the ratio of the non-zero pole values. It is established that in both regulating and tracking modes the error and its first and second derivatives can be reduced to zero with at most two switching reversals of the control provided that the initial values of error and/or its derivatives fall in a “controllable region”.  相似文献   

9.
We study in this paper solutions to several kinds of linear bimatrix equations arising from pole assignment and stability analysis of complex-valued linear systems, which have several potential applications in control theory, particularly, can be used to model second-order linear systems in a very dense manner. These linear bimatrix equations include generalized Sylvester bimatrix equations, Sylvester bimatrix equations, Stein bimatrix equations, and Lyapunov bimatrix equations. Complete and explicit solutions are provided in terms of the bimatrices that are coefficients of the equations/systems. The obtained solutions are then used to solve the full state feedback pole assignment problem for complex-valued linear system. For a special case of complex-valued linear systems, the so-called antilinear system, the solutions are also used to solve the so-called anti-preserving (the closed-loop system is still an antilinear system) and normalization (the closed-loop system is a normal linear system) problems. Second-order linear systems, particularly, the spacecraft rendezvous control system, are used to demonstrate the obtained theoretical results.  相似文献   

10.
A useful identity expressing the derivative of an unknown variable xk of X with respect to an entry in the coefficient matrix of a linear system AX = B is presented. If the derivatives of xk with respect to each entry of A or their combinations are required, then the identity avoids the repeated solution of the linear equations, and may result in a symbolic solution provided A-1 is known. A method to measure the sensitivity in an n-port linear system is proposed, and its relationships to Kron's method of tearing and Branin's formulae are also discussed.  相似文献   

11.
We pursue the numerical implementation of a boundary controllability problem for the 1D wave equation based on a recent variational approach to deal with such situations that consists in analyzing an error functional defined for feasible functions complying with appropriate initial, boundary, and final constraints. The nature of such scheme, as a minimization process for a certain error functional, leads to a natural numerical implementation by using typical descent algorithms. Our aim here is to explore the basic ingredients to set up such practical numerical approximations which allow us to address linear and semilinear equations with the same numerical scheme.  相似文献   

12.
This paper devotes to stabilize nonlinear systems based on Takagi-Sugeno (T-S) fuzzy models, where only sampled state is available. Note that the membership functions (MFs) between T-S fuzzy models and fuzzy controllers are asynchronous under a sampling mechanism, a fuzzy state feedback controller with asynchronous MFs is introduced. A new parameterized fuzzy Lyapunov-Krasovskii functional (PFLKF) approach is presented to ensure that the closed-loop system is exponentially stable and there exists a large well-defined domain of attraction. In general, it is difficult to compute in advance the upper bounds of the time derivatives of MFs, where these time derivatives appear in the time derivative of the PFLKF or the errors of the asynchronous MFs. To this end, a novel quadratic inequality is established to characterize the time derivatives of MFs. Then an MF-dependent exponential stability criterion is given in terms of linear matrix inequalities, and a co-design method for the controller gains and the domain of attraction is presented. Finally, three illustrative examples show the effectiveness and advantages of the proposed approach.  相似文献   

13.
Subject to the assumptions of zero starting pressure, covolume equal to charge volume, burning rate proportional to pressure, constant burning surface, and no heat loss through gas or projectile friction, the equations of interior ballistics are presented in simple form.It is hoped that these simple equations will be of some aid in making ready approximate evaluations of the effect of variation of any parameter.The general equations are listed in section I. In section II the expressions for the maximum pressure and muzzle velocity are discussed more fully, and the derivatives with respect to various parameters are given.  相似文献   

14.
Using block-pulse functions (BPFs)/shifted Legendre polynomials (SLPs) a unified approach for computing optimal control law of linear time-varying time-delay systems with reverse time terms and quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamical systems are converted into linear algebraic equations by using operational matrices of orthogonal functions (BPFs and SLPs). The problem of finding optimal control law is thus reduced to the problem of solving algebraic equations. One example is included to demonstrate the applicability of the proposed approach.  相似文献   

15.
本文基于珠江三角洲地区3000多位农民工的实证调查数据,考察了农民工劳动权益的性别差异及其原因.结果表明,农民工,不管是男性还是女性,在企业打工期间并没有获得理应获得的劳动权益,而且他们在工资、工资拖欠、技能培训、辞工自由、日常福利、人身权利等劳动权益的获得方面存在较为明显的性别差异.进一步分解导致农民工在上述劳动权益方面存在的性别差异的原因,本文发现,性别歧视可能是导致当前我国农民工劳动权益的性别差异的一个最为重要的原因,此外,人力资本因素和组织制度因素也为这种性别差异提供了较强的解释力.  相似文献   

16.
A Chebyshev collocation method, an expansion method, has been proposed in order to solve the systems of higher-order linear integro-differential equations. This method transforms the IDE system and the given conditions into the matrix equations via Chebyshev collocation points. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Chebyshev coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the systems of differential and integral equations.  相似文献   

17.
A new method is presented for determining the stability and vibration modes of a class of parametric oscillations where the damping terms in the Mathieu-Hill type of differential equations are complex as well as periodic. The imaginary terms are converted to phase lagged terms in a set of simultaneous first-order differential equations used to express these equations with first-order derivatives treated as additional variables, thereby doubling the number of equations but allowing matrix methods to be conveniently used in a bifurcation procedure to obtain solutions and stability boundaries. The method has advantages over methods using series expansions in determining stability boundaries and vibration modes where convergence and summability become important considerations in the case of differential-difference equations with periodic damping terms. A particular example of a fluttering helicopter blade in slow forward flight is studied and stability boundaries shown to be displaced by up to 10% from those when the nature and extent of the rows of wakes below the rotor are neglected. The range of the parameters governing the stability are given for a specific numerical example. Application to an actual blade motion study shows reconciliation with previous experimental results and theory when the new method is applied. The importance of the effect of lagged arguments in simultaneous differential-difference equations is discussed with reference to two other examples in structural vibrations.  相似文献   

18.
A numerical method is proposed for solving multi-dimensional hyperbolic–parabolic differential equations with the nonlocal boundary condition in t and Dirichlet and Neumann conditions in space variables. The first and second order of accuracy difference schemes are presented. The stability estimates for the solution and its first and second orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic–parabolic differential equations with variable coefficients in x and two-dimensional hyperbolic–parabolic equation.  相似文献   

19.
Control problems in Hilbert spaces are treated in a measure-theoretical framework; instead of dealing with a set of admissible trajectory-control pairs, a set of measures defined by the boundary conditions and the differential equations of the problem are considered. The concept of weak controllability is introduced; a system has this property if every pair of initial and final points, (ta,xa) and (tb,xb) can be weakly joined; this is possible if a set of linear equalities involving measures has a solution. In turn, this is shown to be equivalent to the possibility of extending a linear functional in a positive manner. Necessary and sufficient conditions for controllability are derived, and applied to the study of a finite-dimensional system with the control appearing linearly.  相似文献   

20.
本文基于一阶剪切变性板理论,运用能量交分得到问题的控制方程以及自然边界条件,并运用二维问题的微分求积法对其进行了求解.可以看出对于线性弯曲问题,微分求积法的收敛性很好.  相似文献   

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