摘要:

This paper discusses the design of a single linear functional observer (SLFO) for a linear time-invariant system. The SLFO is used to estimate a scalar-valued linear function of the system state, and is generally of lower order than the Luenberger observer. Two cases are considered: (i) feedback gain included as a design parameter and designed at the same time as the SLFO (the SLFO with unfixed feedback gain), and (ii) feedback gain is previously specified, before the design of the SLFO (the SLFO with fixed feedback gain). A standard form, a canonical form and the minimal order are obtained and they are used to obtain the optimal SLFO for the single-input linear-quadratic (LQ) problem. The SLFO with unfixed feedback gain is more difficult to calculate but has the following advantages over the SLFO with fixed feedback gain: the order is generally lower, the cost for the LQ problem is smaller and the responses are improved.

ISSN:0020-7179    

DOI:10.1080/00207178608933620

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Linear time-invariant systems of the formE dx/dt = Ax + Buare considered, whereEis a square matrix, which may be singular, andBis a rectangular matrix having full column rank. It is assumed that for any ‘admissible’ initial statex(0−), any control vectoru(t) yields one and only one state vectorx(t). The problem is this: find a control vectoru(t) that will drive the system from an ‘admissible’ initial statex(0−) to a fixed final statexf, in a fixed timetfwhile minimizing some cost functional $. Only elementary matrix and variational techniques are used. Necessary conditions are derived for the existence of minima ofJ; the problem of findingsufficientconditions of the existence of minima ofJis not considered. It is shown that in many cases the necessary conditions for the existence of minima ofJyield a two-point boundary-value problem consisting of a system of ordinary differential equations containing only elements of,x(t) and the boundary conditions prescribed at 0− andtf. If some vectorx*is a solution of the two-point boundary-value problem, a control vectoru*such thatE dx*/dt=Ax*+Bu*,x*(0−) =x(0−) andx*(tf) =xfcan be obtained fromx*, andx*andu*will minimize the cost functionalJifJhas a minimum.

ISSN:0020-7179    

DOI:10.1080/00207178608933621

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In time-invariant linear quadratic optimal control problems there is a hidden ‘ideal model’ automatically encoded into each performance indexJ. These hidden ideal models, which are themselves linear and lower order than the original plant, are not visible under cursory examination ofJand have apparently been overlooked by many professors, textbook writers and industrial users of linear quadratic control theory. In this paper, a special cost-decomposition procedure is described that will uncover these concealed ideal models and clearly show their relevance to the original optimization problem. Three examples are worked out.

ISSN:0020-7179    

DOI:10.1080/00207178608933622

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The definition of the state-transition matrix for Roesser's model of 2-D systems with variable coefficients is introduced and the general response formula is derived. Necessary and sufficient conditions for local controllability are formulated. The minimum energy control problem for Roesser's model of 2-D systems with variable coefficients is formulated and solved.

ISSN:0020-7179    

DOI:10.1080/00207178608933623

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This paper considers the use of a discrete-time deadbeat control action on systems affected by noise. Variations on the standard controller form are discussed and comparisons are made with controllers in which noise rejection is a higher priority objective. Both load and random disturbances are considered in the system description, although the aim of the deadbeat design remains as a tailoring of reference input variations. Finally, the use of such a deadbeat action within a self-tuning control framework is shown to satisfy, under certain conditions, the self-tuning property, generally though only when an extended form of least-squares estimation is incorporated.

ISSN:0020-7179    

DOI:10.1080/00207178608933624

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In quantitative feedback theory (QFT) the plant uncertainty is defined by a setP= {P} ofpossible plants. The problem is to guarantee that the system response is in a specified acceptable setA, for allPinP. QFT has been developed for large classes of plants imbedded in continuous feedback structures. This paper extends QFT to sampled-data structures. A central problem is to find the minimum sampling frequency (ωs)minneeded. The greater the plant uncertainty and the narrower the performance tolerances, the larger must ( ωs)minbe. The detailed design procedure parallels very closely that for continuous systems, by using the complex variable w, which maps the unit circle in thez-domain to the imaginary axis in thew-domain.

ISSN:0020-7179    

DOI:10.1080/00207178608933625

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The non-minimum-phase (NMP( property is easily determined from the requirement that the plant input is bounded. In the single-input-single-output (SISO) system, a right-half-plane (RHP) plant zero ats = bconstrains the system transfer function to have a zero atb. Also, the available feedback benefits are significantly restricted. Then×nmultiple-input-multiple-output (MIMO) system is NMP if the plant determinant δhas any RHP zeros, say at plant transfer matrix andT = [tijis the closed-loop system transfer matrix. It has been thought that all n2tij(and the n2plant disturbance response function rfj),mustsuffer from the NMP liability in their feedback properties. It is shown that only one row of need so suffer, with a any fixed integer in [1, n].The remainingn(n— 1) elements can be completely free of the NMP liability. A mathematically rigorous synthesis technique previously developed for MP systems is shown to be well suited for precise numerical design for such NMP MIMO plants with significant uncertainties. In this technique, the MIMO design problem is converted into a number of equivalent SISO problems. An example involving disturbance attenuation in a highly uncertain 2×2 NMP plant is included.

ISSN:0020-7179    

DOI:10.1080/00207178608933626

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The aim of this paper is to introduce a new list of integers which is invariant under the action of biproper compensation and which plays a key role in the solution of the row-by-row decoupling problem. Several equivalent characterizations are provided within both the geometric and the transfer matrix approaches.

ISSN:0020-7179    

DOI:10.1080/00207178608933627

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The Taylor operational matrix of integration and the Taylor product operational matrix are introduced. These two operational matrices are applied to approximation of solutions of Fredholm and Volterra integral equations. The proposed method reduces solution of integral equations to the successive solution of a set of linear algebraic equations in matrix form. Owing to the simplicity of the operational matrix of integration, and the product operational matrix of the Taylor series, the algorithms derived possess considerable computational advantages over the orthogonal-polynomial approximation, provided that both input and output are analytic functions oft.

ISSN:0020-7179    

DOI:10.1080/00207178608933628

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The stability of a digital control system and its performance in terms of the continuous plant output are studied. A two-step controller design is proposed. In the first step, the assumption of no modelling error is made and a controller that combines properties of the algorithm that minimizes the sum of squared errors and a deadbeat-type algorithm is designed so that no intersample rippling appears. In the second step, a filter is designed so that appropriate conditions which guarantee robust stability and performance in the presence of model-plant mismatch are satisfied. The effect of the sampling time on the achievable performance and the robustness properties of the system is examined and the results are incorporated in a complete procedure for sampling-time selection and robust controller design. Finally, the procedure and some theoretical implications are illustrated with examples.

ISSN:0020-7179    

DOI:10.1080/00207178608933629

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor