摘要:

Recently, optimally sensitive controls have been synthesized for systems that contain uncertain constant parameters in the plant dynamics. In this paper the concept of optimally sensitive control is extended to a class of problems containing unknown time-varying parameters. The optimal sensitivity equations are derived and closed-loop controls are synthesized based on these equations. It is shown that for the class of problems considered the optimally sensitive control structure is equivalent to that control obtained from the second variational method of deterministic control theory. Several numerical examples are presented to illustrate the effectiveness of this technique for the closed-loop control of stochastic systems. The examples also point out that the optimally sensitive systems are relatively insensitive to error in the a priori statistics of the stochastic inputs.

ISSN:0020-7179    

DOI:10.1080/00207177208932126

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

A compensation design technique is presented for discrete data automatic control systems which enables simultaneous satisfaction of specifications on the transient response and the steady-state error of the system. A unique design is possible with this technique, which avoids the usual trial-and-error process. The design is obtained through the solution of a set of equations giving the location of the real pole and zero of a cascade or feedback compensator which causes a pair of complex-conjugate roots of the characteristic equation to exist at a designated location in the z-plane, simultaneously with satisfaction of a specified open-loop gain, which may be different from original system gain. Thus, in effect, the method allows the designer to simultaneously specify the gain margin or relative stability of the system, as well as its steady-state accuracy, which may be modified from its original value. The technique is illustrated by means of a practical example.

ISSN:0020-7179    

DOI:10.1080/00207177208932127

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

A brief survey is given for the method of impulse analysis of scalar systems to show the distinct advantages of time-domain infinite matrices (t.d.i.m.) methods. To tackle the problem of describing and manipulating multivariable systems by these techniques. an extension of the algebra of lower semi-infinite matrices to the multivariable case is developed. Of special importance in this respect are now recursion formulae for inverting stationary and non-stationary impulse response matrices of any dimensions. It is shown that for stationary matrices of dimensionsn×n× ∞. the adjoint matrix has to be evaluated at the first sampling instant only. In terms of this evaluation the inverse matrix is generated at any sampling instant by carrying out simple algebraic operations (i.e. addition and multiplication). For non-stationary matrices similar conditions arc derived. The formulae of this paper are useful for the solution of a variety of problems in functional analysis.

ISSN:0020-7179    

DOI:10.1080/00207177208932128

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

A new method of synthesis for linear time-varying systems is put forward. This method presents certain advantages over the classical methods known to date.

ISSN:0020-7179    

DOI:10.1080/00207177208932129

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

For solving non-linear control problems several methods exist, the conjugate-gradient method being one of the most successful. Gradient and conjugate-gradient methods have also been extended to treat control problems with undetermined final time. Two basic approaches have been suggested; one in which the final time in each iteration is determined by a search and the other in which the final time for the next iteration is computed. In both approaches the number of steps in the numerical integration procedure is variable. In this paper an alternative approach is suggested. By augmenting the control vector with one additional component the problem with undetermined final time is transformed to a problem with fixed final time. A fixed number of steps can then be used. The same approach can be applied to the determination of unknown constant system parameters or unknown initial conditions of the state vector and for the computation of the on-off control.

ISSN:0020-7179    

DOI:10.1080/00207177208932130

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

In this paper the concept of phase plane analysis, which is well developed for second-order systems, is extended to a class of third-order non-linear systems. The method of analysis presented is applicable to the unity feedback closed-loop systems, having a third-order linear memory system and a single-valued zero-memory system in cascade combination in the forward path. The technique involves plotting a (x2, x3) master plane having all possible trajectories for x1 = 0. The variation and the initial condition of variable x1are incorporated by adding an origin shift scale on to the master plane. Using this master plane, the required (x1, x2) and (x1, x3) trajectories can be obtained for any set of initial conditions, following a simple procedure illustrated by typical examples. This technique is also applicable for the analysis of such systems for step inputs.

ISSN:0020-7179    

DOI:10.1080/00207177208932131

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

The problem of evaluation of the coefficients of the transfer function of a system, usually referred to as the parameter estimation problem, assumes the main importance in any general adaptive control system. If the input to the system is a polynomial int, then the steady-state response of a linear system is also a polynomial int. It is shown that the nth-order linear system is completely identified by a polynomial input of degree2n. The algebraic formulation given for evaluation of the system parameters needs the measurement of the derivatives of the input and output under the steady state. The scheme suggested here uses any arbitrary stable differential equation set-up on the analogue computer. The derivatives of the input and output are then computed by using a matrix transformation and are used in the given formulation to evaluate the system parameters. The use of the scheme is illustrated for tracking of time-varying parameters of a linear system.

ISSN:0020-7179    

DOI:10.1080/00207177208932132

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

In this note, some tests are developed to identify the limit cycles of a. second-order autonomous system invariant under an infinitesimal transformation. These test also establish whether the limit cycle is stable, unstable or semi-stable.

ISSN:0020-7179    

DOI:10.1080/00207177208932133

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

This paper discusses a method of obtaining feedback control for dynamic processes described by non-linear differential equations. Because an optimal feedback control law cannot generally be derived for non-linear processes, the technique described herein is sub-optimal, but the degree of sub-optimality is a design parameter of the technique.

ISSN:0020-7179    

DOI:10.1080/00207177208932134

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

Optimal linear control laws require the measurement of each and every state variable. However, in practice it is difficult to measure every state variable, and thus the optimal control is not widely accepted. This paper is concerned with overcoming this difficulty by considering the design of optimal linear regulator systems with some inaccessible state variables. Two methods leading to dynamic feedback control laws in terms of measurable output alone are developed. One of these methods is extended to time-varying problems.

ISSN:0020-7179    

DOI:10.1080/00207177208932135

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor