Search

THE synthesis of a feedback control system by means of phase-angle loci originates from Evan's root-locus method1 which enables one to find all possible roots of the characteristic equation of a feedback control system. Once the roots are chosen, the transient response then may be worked out. Thus, it allows the synthesis of feedback control system in time domain. However, the plotting of the root locus requires some sort of guesswork. This is not surprising because the analytical difficulty in extracting the roots of the characteristic equation is imposed on the graphical work, yet help in the effort to solve the problem can be given.

Although the optimal control theory has been much developed in recent years, the theory requires assumption that all the components of state vector are detected, but detection of all components of state vector is not always possible. The usual application of optimal control theory of incomplete feedback control system leads us to the inconvenience such that the optimal control law varies depending upon the initial point. this paper proposes a design method of incomplete feedback control system, where only the detected components are used to feedback. In order to get rid of dependence of optimal control law on the initial point, the method to optimize incomplete feedback control system in the sense of mini-max is contrived. The design method is explained in detail.

This paper gives an exact solution in the form of a perfect Fourier series for the harmonic response to a sinusoidal input of a feedback control system including an element with a dead zone. The process of analysis used is quite the same as that introduced by the author for calculating forced vibrations in an unsymmetrical piecewise-linear system and utilized for the solution of a feedback control system including an element with saturation characteristics.

The frequency response of a feedback control system containing a nonlinear element of piecewise-linear type subjected to sinusoial input is exactly obtained by a new method utilizing appropriate Fourier series expansion. This method is in principle the same as that introduced by the author to solve the steady vibrations in an unsymmetrical piecewise-linear system subjected to a harmonic exciting force. It has the following main features : 1) Linealizing the nonlinear differential equation governing the dynamic behavior of the system by expanding the nonlinear part of the output of the piecewise-linear element into a Fourier series with the same period as of the given sinusoidal input. 2) Obtaining the formal solution of thus linealized equation by regarding the above-mentioned nonlinear part as if it were an exciting force from without. This solution contains unknown coefficients of the Fourier expansion above assumed. 3) Determining these unknown coefficients from the conditions that the above obtained solution satisfies the given piecewise-linear characteristics of the system. Certain process of convergency improvement by means of series transformation may prove highly effective in this step. As an example of the piecewise-linear element, we treat an element with a dead zone, and give the procedure of analysis for a feedback control system with such an element. Some numerical results and diagrams for the frequency response of the system are added. Also a few examples of wave forms for certain amplitudes and frequencies of the sinusoidal input are shown. These procedures of analysis and their results may contribute to the removal of uncertainties involved in the describing function analysis usually applied to obtain the frequency response of the nonlinear control system.

An analytical method is developed For selecting the optimum gain in a linear feedback control system with first derivative action. Based on the stability considerations the method simultaneously derives the coefficient of the derivative action corresponding to the critical gain. Examples are presented at the end of the paper which are verified by the known graphical technique.

This paper deals with optimization of the response of a self organizing feedback control system in presence of inherent coupling signals. The system contains lenses and phototubes as a sensing element and it always orients its front surface in the direction of the tracked object with the help of light signals received. Adaptive Step Size Random Search (ASSRS) has been used and parameter optimization in presence of different coupling signals was achieved. The results obtained are verified by an inverse sensitivity method. Finally the merits of random search technique are compared with those of the inverse sensitivity method.

A new graphical method for feedback control system compensation design yields the parameters of simple compensators which will place a closed-loop pole at a designated location in the 5-plane with arbitrary open-loop gain. The gain limits for compensators with single or multiple identical sections are easily determined by this method, which is simple, easy to apply, fast, and accurate. Examples are given to illustrate its utility.

In most control applications in the chemical process industries it is not realistic to attempt to define a unique mathematical statement of the control objective, for many criteria will satisfy the physical requirement of the rapid elimination of errors in the product stream as the result of an upset. The strong dependence of the structure of an optimal control system on the choice of objective then makes optimal control theory irrelevant in such situations, since the control engineer has no assurance that a complicated controller is a necessity of the process, rather than a consequence of an unfortunate choice of objective. In this paper an inverse problem is considered, in which an easily implementable feedback control system is first chosen and then is shown to be optimal for a physically meaningful objective in a large class of systems.

A NEW describing-function technique is used in this paper to show the effects of several gain-controlling nonlinearities on the limit-cycle stability of an aircraft roll-stabilization system. The new method leads to a stability diagram which is divided not into the usual two regions of ?stable? and ?unstable? operation but rather into numerous regions each of which is associated with a particular type of limit-cycle oscillation or singular point. Such a diagram gives considerable insight into the mechanism of oscillations often observed in physical equipment. Very satisfactory agreement with analog computer studies is demonstrated for the new technique.

In this paper the periodic response to a sinusoidal input of a single-loop automatic control system including a piecewise-linear element is exactly analysed by a new method, which gives the solution in the form of a perfect Fourier series. The piecewise-linear element treated is such that its characteristics are composed of two segments of straight lines for an unsymmetrical case and of three segments of them for a symmetrical case, and the switching over conditions between these segments may have hysteresis and jump. To offer the mathematical foundation, both the problem of existence for the solution of the infinite set of simultaneous linear equations utilized in the way of the solving procedure and that of convergency of the approximate solution by truncation method are discussed briefly.

EARLIER literature has suggested the design of the so-called optimum relay control system, where the term ?optimum? is based on the system having the fastest possible response in terms of reducing the error to minimum following a step or ramp input.1?4 It has been pointed out that these systems are optimum only in this special sense, and that their response to other types of input may be undesirable.5

A synthesis procedure is developed for a dominant third-order system (as opposed to the usual dominant second-order system) where the size of the complex closed-loop pole region is not specifically restricted but is contained within a circular boundary. The plant considered is of third order, with a real pole at the origin and a pair of complex poles with negative real parts. The added real pole affords an additional degree of freedom with which to meet the system-time domain specifications. The compensation prescribed is a biquadratic network with complex zeros, and compensation poles are constrained to exhibit only second-order effects. The procedure is based on the association of the desired closed-loop pole parameter values with open-loop parameter values in the ( \Omega^{2},\Sigma ) plane, which is in actuality the natural-frequency-squared damping-constant plane. A constant gain factor is assumed, but this constraint may be removed if a tandem gain control system is employed. This assures that the gain variations are much slower than the system response. Relations between the desired nominal closed-loop poles and the plant region and compensation locations are derived for a prescribed circular closed-loop pole region. The nominal plant pole location is a design specification, while the allowable plant region depends on the closed-loop pole location and region, i.e., a change in size of one region is reflected as a proportional change in size of the plant closed-loop pole region. The remote compensation pole location is primarily determined by minimizing transient distortion while ensuring a specified degree of stability.

The problem of parameter optimization for the purpose of synthesis and design of feedback control systems is considered. A flexible performance index, which permits direct consideration of performance specifications such as rise time, settling time, peak overshoot, and bandwidth, in addition to the usual analytic forms, is developed and adapted to a modified version of Rosenbrock's pattern -search algorithm. Modifications of Rosenbrock's method include: 1) scaling of parameters to ensure coordinate orthogonalization; and 2) employing variable step sizes at the beginning of each new stage, the steps being a function of previous failures and successes. The efficiency of each stage is thus improved and the sensitivity to initial estimates of step size is reduced.

An analytical study of feedback stabilization of a continuum is done in the context of plasma confinement in a TOKAMAK device. Linear and nonlinear "bang-bang" feedback from discrete stations is investigated to find acceptable sensor and enforcer element geometries, compare their effectiveness, and predict the important parameters in their realization. The primary method used is an extension of the energy method.

THERE is a class of control systems whose objective is to control precisely and maintain a relationship between several dimensions. A simple example of this type of system is the contour-cutting lathe-tool control where the cutting edge of the tool is made to trace out a path in two dimensions, one in the direction of the bed movement and the other in the direction of the tool feed. One approach to the synthesis of a system to control the movement of the tool is to cause the bed to progress either at constant speed or at a programmed speed consistent with the particular cutting operation being performed. In any case, the movement in one dimension of the tool movement is open-cycle and the burden of following the prescribed path is placed entirely on the system which controls the depth movement of the tool. The latter control is usually closed-cycle and the system must have dynamic response to maintain the tool position to within given specifications as the bed is moved in its programmed path.

In this paper the stability problem for n general class of non-linear feedback control systems governed by parabolic partial differential equations is considered. Sufficient conditions for asymptotic stability are derived by the method of comparison functions. Two classes of feedback control systems are considered. The basic tool in the analysis is the Westphal-Priodi theorem and an extension originally suggested by Szarski. The main results are applied to an illustrative example.