Unity-feedback System Research Articles

On the suppression of limit-cycle oscillations

A procedure is presented for the suppression of limit-cycle oscillations in unity-feedback control systems which have an on-off type nonlinearity in cascade with a linear transfer function. The procedure is based on the introduction of a minor loop into the system. This produces a high-frequency periodic signal at the input of the nonlinearity, and thereby limit-cycle oscillations are suppressed.

Some useful expressions for optimum linear filtering in white noise

Optimum linear separation of random message from additive white noise of given spectral height realized as unity feedback system

Graphical method for finding the closed-loop frequency response of nonlinear-feedback control systems

The paper presents a graphical method for determining the closed-loop frequency response of nonlinear-feedback control systems. The necessary gain and phase conditions round the loop for possible harmonic oscillations are examined, and a universal chart is developed. The nonlinear element is represented by its describing function. The use of the universal chart for determining the frequency response of unity-feedback systems having one single-valued nonlinearity is illustrated by suitable examples.

Synthesis of control systems based on approximation to a third-order system

IN RECENT YEARS the high-speed performance and accuracy demanded of military applications and industrial processes have placed increasing emphasis on the dynamic characteristics of control systems. However, system design is most effective when both steady-state and transient performance specifications can be realized. Ordinarily the designer works from the open-loop to the closed-loop specifications, i.e., trial-and-error modifications are made to the fixed portion of the system until a compensation network is found that eventually leads to an acceptable closed-loop performance. In contrast, another approach, synthesis, proceeds from the closed-loop specifications to an appropriate open-loop system, which upon closure of the feedback path, satisfies the specifications. The methods of Guillemin1 and Aaron2 accomplish this transition, but not without difficulties and complications which arise from the fact that a closed-loop transfer function must be selected that simultaneously: 1. exhibits a pole-zero excess equal to or greater than the excess of the fixed portion of the system, and 2. satisfies a set of closed-loop specifications. Recently, Aseltine3 introduced an inverse-root locus method that graphically determines the open-loop pole locations from a given closed-loop pole-zero configuration. However, none of these methods provides a simple procedure indicating how a closed-loop transfer function can be formulated directly from a detailed set of transient and steady-state specifications. This paper presents a quick and accurate method of synthesizing a linear, continuous, unity-feedback system from a set of specifications that eliminates the foregoing disadvantages. Attention is confined to a type I system that is compensated by an R-C realizable transfer function. To be R-C realizable, the poles of this function must be simple on the negative real axis, the origin and infinity excluded, i.e., its pole-zero excess must be equal to or greater than zero.

Determination of the maximum modulus, or of the specified gain, of a servomechanism by complex-variable differentiation

A problem of frequent occurrence in servomechanism analysis and design is that of determining the maximum modulus Mm, and the angular frequency at which it occurs, of the over-all frequency-transfer function M(jω) = C(jω)/R(jω). Those textbooks1¯ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> which present a comprehensive, integrated account of basic servomechanism theory advance, in considerable detail, two procedures for determining the maximum modulus Mm of M(jω) for a unity feedback system, namely, by plot of the transfer function G(jω) on a chart of circles of constant values of modulus |M(jω)|, or on a Nichol's chart of circles of constant values of modulus |M(jω)|. Further, if the feedback transfer function H(s) although nonunity is yet a pure numeric H(s) = Kn, then, according to well-known theory $\eqalignno{{C(j \, \omega) \over R (j \, \omega)} = M (j \omega) \cr = {1 \over K_{h}} \, {G(j \omega) K_h \over 1 +G(j \omega) K_{h}} \cr = {1 \over K_{j}} \times M_{1}(j \omega) \hbox{(1)}}$ and Mm can yet be determined by obtaining M1m through plot of G1(jω) = G(jω)Kh as just mentioned and thence calculating Mm from Mm = M1m/Kh.