摘要:

This paper is concerned with the determination of suboptimal feedback laws for the linear systems with quadratic performance criteria. The time-varying gains are approximated by the piecewise constant gains which are naturally determined by using Walsh functions. An increase of the number of intervals of Walsh functions enables us to approximate the true optimal control more closely ; and a decrease of the number of intervals makes the implementation easier. Therefore the proposed method is simple in theory and flexible in practice. The beginning part of the paper, being tutorial in nature, is on Walsh functions, the middle part developes an operational method for solving state equations and the final part is concentrated on the Walsh functions approach to the solution of piecewise constant gains of optimal control.

ISSN:0020-7179    

DOI:10.1080/00207177508922043

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

Absolute stability of non-linear systems is examined using the conventional techniques, and a representation of Popov line in the logarithmic gain and phase versus frequency plane. A grapho-analytical procedure is advanced for the Popov line transference to the Bode plane. The technique may be used either as an analytical tool for investigating absolute stability of systems with specified non-linearity sector, or as a synthesis technique for compensator design. The application of the proposed method for substantiating compensator design results is illustrated by two examples.

ISSN:0020-7179    

DOI:10.1080/00207177508922044

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The problem of designing a state feedback controller which drives the eigenvalues of a linear multivariable system to prespecified positions is studied. The approach followed is that of transforming the system under control to a phase-variable canonical form prior to the application of the control design procedure. This transformation is possible only when the system is state-controllable which implies that it is also mode-controllable. The single-input design problem is first considered and solved by an elegant utilization of the concept of state similarity transformation. By this transformation one essentially converts the original problem of designing the state feedback modal controller matrix gainFto that of determining the associated similarity transformationT. The multi-input controller design problem is then treated by an extension of the above results which yield the most general state feedback modal controller possible. The state feedback modal controller derived is utilized, and the most general solution to the output (incomplete state) feedback modal-controller design problem is found. A set of examples is provided to illustrate most aspects of the theory.

ISSN:0020-7179    

DOI:10.1080/00207177508922045

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

A direct method for optimization of a class of linear distributed parameter systems with stochastic distributed disturbances is presented. The method is based on expanding control systems, Green's function and covariance matrices in terms of a finite number of elements taken from complete sets of orthonormal basis in both time and space. Practical considerations are considered in the application of the method. A minimum-variance filter is designed using noisy discrete observations from a finite number of measuring points. Then the synthesis of a pointwise controller is carried out to minimize a quadratic performance index. The optimal coefficients of control are determined via simple algebraic relations in terms of the state conditional mean. A discussion of the properties and computational aspects of the method is given.

ISSN:0020-7179    

DOI:10.1080/00207177508922046

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The problem of pole assignment in linear multivariable systems by means of unity rank output feedback is studied in this paper. It is shown that when the number of specified poles is equal to the number of inputs or outputs of the system, exact pole assignment can be achieved and the feedback matrix is calculated from a set of simple linear equations. When the number of specified poles exceeds this value, the pole assignment problem becomes non-linear. Three different formulations of the problem are considered and three numerical techniques are described for the calculation of the feedback matrix. Numerical examples are given for illustration.

ISSN:0020-7179    

DOI:10.1080/00207177508922047

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The paper describes a simple frequency-domain method for the design of physically realizable dynamic output feedback compensators to achieve pole assignment in single-input, single-output and multivariate systems. The system is augmented by the dynamic compensator and the compensator parameters are then calculated so as to position the closed-loop poles at specified locations in the complex plane. It is shown that depending on the order of the compensator used, some or all poles of the closed-loop system can be positioned arbitrarily. In addition, the minimal order of the compensator required to position all the poles is given. A number of numerical examples are solved to illustrate the method,

ISSN:0020-7179    

DOI:10.1080/00207177508922048

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The behaviour of a non-linear continuous stirred tank reactor (CSTR) with time-delay in the feedback control is determined by expanding the delay factors by means of a series approximation. The resulting system approximates the original system quite well, and is considerably easier to analyse. The region of stability obtained by this method is substantially larger than that obtained by the application of Liapunov's method.

ISSN:0020-7179    

DOI:10.1080/00207177508922049

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

We discuss the analogy between the classical factor analysis model and the ‘ state-space ’ representation of a discrete parameter multivariate linear stochastic system. Using the ‘ regression approach ’ to factor analysis the well-known Kalman—Buey linear filter is derived.

ISSN:0020-7179    

DOI:10.1080/00207177508922050

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

Feedback systems containing linear, minimum-phase plants with large parameter uncertainty may be designed to achieve specified performance tolerances over the entire range of parameter uncertainty. The principal ‘cost of feedback’ is in the feedback loop bandwidth, which is generally much larger than that of the system as a whole. This makes the system very sensitive to sensor noise and high-frequency parasitics. It is shown how a non-linear ‘first-order reset element’ (FORE) may be used to drastically decrease the feedback loop transmission bandwidth. One is logically led to FORE by simple, linear feedback frequency response concepts. The paper assumes that the primary design problem is to satisfy quantitative response tolerances to command inputs. However, disturbances at the plant are not neglected, but the specification on such disturbances is in the damping of the step response. An important feature of the non-linear design is that the system response to command inputs is almost exactly that of a linear system designed for the same specifications, permitting linear superposition for such inputs. The disturbance response is nonlinear.

ISSN:0020-7179    

DOI:10.1080/00207177508922051

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

The problem of optimally locating a given number of Bensors for observing a general linear distributed parameter system is considered. Measurements at the sensors are assumed to be available continuously in time, and the design criterion is minimization of a scalar measure of the covariance of the estimate error in the optimal linear filter. Necessary conditions for optimality are derived based on the formulation of a distributed parameter matrix minimum principle. A computational algorithm is developed for determining the optimum set of measurement locations. The algorithm is applied to the problem of optimally locating temperature sensors in a solid undergoing transient heat conduction.

ISSN:0020-7179    

DOI:10.1080/00207177508922052

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor