摘要:

In this article, the use of variable structure feedback control strategies is proposed for the asymptotic stabilization of nonlinear dynamic systems describing chemical processes. The proposed discontinuous controller is dynamic in nature and it effectively eliminates the traditional bang-bang nature of the control input signals and the associated chattering responses. The controller is based on recent results of the differential algebraic approach to system dynamics; in particular Fliess's generalized observability canonical form is used in the derivation of the dynamical discontinuous controller. Some illustrative examples, including simulations, are provided.

ISSN:0020-7179    

DOI:10.1080/00207179208934300

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The minimum phase property of single-input single-output linear compartmental systems (i.e. networks of linear reservoirs) is considered in this paper. The analysis shows that minimum phase cannot be lost through cascade and feedback connections and that acyclic networks of reservoirs are minimum phase provided all the reservoirs have roughly the same time constant and all the paths from input to output go through almost the same number of reservoirs. The conjunctive use of these results often allows one to ascertain the minimum phase of a complex compartmental system. Some extensions to larger classes of dynamical systems are discussed at the end of the paper.

ISSN:0020-7179    

DOI:10.1080/00207179208934301

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

In this paper we consider the problem of robust stabilization for systems with parameter uncertainty. We first formulate a design methodology and then demonstrate how it leads to analytical and graphical solutions. We show that in the case of SISO plant families with linear uncertainty and, two-parameter compensators, one can obtain a representation of all robustly stabilizing controllers of a fixed order. By introducing a ‘rectangular overbound’ of value sets in the complex plane we also show how one can obtain representations ofm-parameter robustly stabilizing compensators of a fixed order.

ISSN:0020-7179    

DOI:10.1080/00207179208934302

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The problem of determining linear time-invariant models of flexible structures is considered. The approach is first to identify the modal parameters by using free response measurement records that could be contaminated with noise. The stiffness and damping matrices are then extracted from the identified modal parameters. The identification technique, which is developed in the time-domain is based on least square linear regression theory and is organized as a systematic and easy to implement scheme. The estimates are produced without the need of solving an eigenvalue problem or singular value decomposition of a data matrix. The effect of measurement noise on estimation accuracy is discussed. A numerical example is presented to illustrate the results.

ISSN:0020-7179    

DOI:10.1080/00207179208934303

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A QFT type methodology is developed for an SISO system for maximizing the size of a persistent bounded disturbance in the presence of hard time domain constraints on system states, control input, output and the bandwidth. It is assumed that the system dynamics can be represented by a combination of structured uncertainty in the low frequencies and unstructured uncertainty in the high frequencies. The design procedure is based on mapping the time domain constraints into an equivalent set of frequency domain constraints which are then used to determine an allowed design region in the amplitude-phase plane, for the nominal loop transfer function. Once such a region is found, classical loop shaping determines a suitable loop transfer function. The pole-zero structure of the compensator is a natural consequence of loop shaping and is not preconceived. A procedure is also presented for determining the maximum size of the nominal persistent bounded disturbance that can be tolerated by the resulting closed loop system.

ISSN:0020-7179    

DOI:10.1080/00207179208934304

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The convergence of the solution of the differential and difference periodic Riccati equation with non-negative initial condition is studied. In particular, with reference to the Riccati equation for optimal filtering, we consider detectable but not necessarily stabilizable systems and no restrictive assumption is imposed on the modulus of the unreachable characteristic multipliers. Then, a new condition for the convergence to the periodic strong solution is provided. As a corollary, it follows that, for any positive definite initial condition, the solution of the periodic Riccati equation converges to the periodic strong solution. The new condition encompasses as particular cases the convergence results already available in the literature.

ISSN:0020-7179    

DOI:10.1080/00207179208934305

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

We consider the design ofH∞optimal discrete-time (digital) controllers in continuous-time systems. An apparent difficulty, especially in utilizing moderntransform-domainanalysis in this context, stems from the absence of an appropriate (transfer function) model for the hybrid-time (discrete and continuous) closed-loop system. This difficulty is overcome through the introduction of an equivalent difference-equation model for the continuous-time system, with distributed inputs and outputs; equivalence being in the sense that the continuous-and discrete-time inputs and outputs are essentially identical. Using the interplay between the discrete and the continuous time models, solutions of the well-known purely continuous-time and purely discrete-time standard problems extend to solutions of the problem at hand. They comprise Riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed-loop induced input-output norm, and parameterization of compensators. We consider a general setting that includes as particular instances both the case where the sensor's analog-to-digital (A/D) convertor and the control-hold (D/A) component are predetermined and cases where the design of either or both of these elements is part of the overall problem.

ISSN:0020-7179    

DOI:10.1080/00207179208934306

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The command generator tracker (CGT) approach to model reference adaptive control of linear time invariant multi-input multi-output plants which are not almost strictly positive real (ASPR) is considered. Three new algorithms are proposed which are characterized by the insertion of supplementary dynamics in (i) feedback with the plant; (ii) in parallel with the plant; and (iii) in cascade with the plant, respectively. The three different implementations are shown to be special cases of a metasystem representation for the adaptive system. The new algorithms extend earlier results by introducing adaptive gains for the supplementary dynamics in addition to adaptive gains for the controller. A stability proof is presented which shows that the error between the plant and model outputs is bounded in the presence of bounded input and output disturbances. If the model input is constant fort≥t1, and no disturbances exist, then conditions are obtained for the choice of the design parameters in the parallel supplementary dynamics case which guarantee that the output error is asymptotically vanishing.

ISSN:0020-7179    

DOI:10.1080/00207179208934307

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The optimal projection approach to solving theH2reduced order model problem produces two coupled, highly nonlinear matrix equations with rank conditions as constraints. Owing to the resemblance of these equations to standard matrix Lyapunov equations, they are called modified Lyapunov equations. The algorithms proposed herein utilize probability-one homotopy theory as the main tool. It is shown that there is a family of systems (the homotopy) that makes a continuous transformation from some initial system to the final system. With a carefully chosen initial problem, a theorem guarantees that all the systems along the homotopy path will be asymptotically stable, controllable and observable. One method, which solves the equations in their original form, requires a decomposition of the projection matrix using the Drazin inverse of a matrix. It is shown that the appropriate inverse is a differentiable function. An effective algorithm for computing the derivative of the projection matrix that involves solving a set of Sylvester equations is given. Another class of methods considers the equations in a modified form, using a decomposition of the pseudogramians based on a contragredient transformation. Some freedom is left in making an exact match between the number of equations and the number of unknowns, thus effectively generating a family of methods.

ISSN:0020-7179    

DOI:10.1080/00207179208934308

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

An augmented UD identification (AUDI) algorithm for system identification is developed by rearranging the data vectors and augmenting the covariance matrix of Bierman's UD factorization algorithm. The structure of the augmented information (covariance) matrix is particularly easy to interpret and it is shown that the AUDI algorithm is a direct extension of the familiar recursive least squares (RLS) algorithm. The proposed algorithm permits simultaneous identification of the model parameters plus loss functions for all orders from 1 to n at each time step with approximately the same calculation effort as «th order RLS. This provides a basis for simultaneous model order and parameter identification so that problems due to over- and under-estimation of model can be avoided. Based on its least-squares properties, numerical robustness, theoretical basis and the fact that it simultaneously estimates multiple models, the proposed AUDI algorithm is recommended for use in place of RLS and Bierman's UD factorization algorithms.

ISSN:0020-7179    

DOI:10.1080/00207179208934309

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor