Issue 3 • Date August 1960
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[Front cover and table of contents]
Page(s): 0 
Preface to issue
Page(s): 157 
[Back cover]
Page(s): 0 
Optimum compensation of a position servo with a magnetic clutchactuator
Page(s): 220  228In the past decade improvements have been made in the design of dry powder magnetic clutches which now make them competitive with hydraulic devices for missile servo actuator applications. Some of the inherent advantages of magnetic clutch actuators are: (a) increased control system reliability, (b) simplified equipment requirements, (c) properties remain constant with usage, (d) environmental requirements are quite compatible with an orbiting vehicle. The dynamic servo response of the magnetic clutch servo actuator is required in order to incorporate these advantages in missile and space control system design. This paper presents a synthesis procedure for the optimum design of a position servo based upon the closedloop transient response to a step input. The transient response of the position servo is described by four independent parameters. These parameters are the rise time, damping ratio, undamped natural frequency, and the steadystate gain. The synthesis procedure is based upon a theoretical model of a dry powder magnetic clutch, which is an airgap, ironcare transformer with a oneturn secondary. The air gap is filled with dry ferrite particles. To provide simple analytic functions, a definition for rise time is developed which corresponds to the first crossing of unity gain to a high order of accuracy. The theoretical model of the magnetic clutch has two, firstorder time lags. These two time lags are derived from the properties of the theoretical clutch model. They arise from the inductive properties of the clutch excitation coil and the clutch rotor induced eddy current, which is the current in the equivalent transformer singleturn secondary. The compensation for the excitation coil time lag consists of excitation current feedback, which decreases the effective transfer function time constant. The induced rotor eddy current time lag is optimally compensated by the proper selection of feedback gains as outlined in the synthesis procedure. The position servo drives an undamped inertial load. This is characteristic of a control system for an outer space vehicle or a guided missile which utilizes swivel rocket nozzles for control. It is also a firstorder approximation to an airframe control servo utilizing neutral aerodynamic surfaces with low da mping. The position servo characteristics are provided by a position feedback branch, and the basic servo stability is provided by a tachometer feedback. The theoretical model results in a thirdorder system which cannot be unstable. Practical magnetic clutches differ from the theoretical model primarily because they have ferromagnetic hysteresis. At high frequencies, hysteresis appears as a constant time delay which makes servo instability possible. An additional constraint to the synthesis procedure is given which guarantees a stable, closedloop position servo with the desired performance characteristics. The entire analysis in this paper is based upon the application of RootLocus analytical methods to extract the theoretical roots of the thirdorder system describing the magnetic clutch actuator position servo. View full abstract»

Decoupling techniques in multiloop control systems
Page(s): 209  219The stability and accuracy of a control system consisting of two interwoven loops are affected by interaction among all transfer functions and all inputs. This is undesirable, since the design of each transfer function must be compromised to account for the interaction effects. In some cases, the two loops can be decoupled by the addition of an appropriate feedback path. This paper describes the application of this technique to a radar angle tracking loop. The technique described has the following advantages: 1. The required matching takes place within the loop so that the effect of any mismatch is attenuated by the open loop gain. 2. For the example used, the output angular rate accuracy becomes independent of aircraft motion. 3. Subject to the rather minor restriction implied by item 1, the two loops become independent as far as stability is concerned. Decoupling, which is described in this paper by illustrating its application to a particular system, is applicable to any complex control system. However, to the author's knowledge, no formal procedure for general application is available. View full abstract»

Flywheel control of space vehicles
Page(s): 247  259An analytic study of flywheel autopilots for attitude control of space vehicles is described, and the results of a threeaxis analog computer program are presented. The objectives of this study were to determine the requirements, capabilities and limitations of flywheel autopilots as functions of desired accuracy and speed of response, disturbing moments, differential gravity restoring torques, component uncertainties, and vehicle initial attitude and attitude rate errors. The stability and accuracy degradations that resulted from not compensating for gyroscopic crosscoupling torques are summarized. Design tools are presented for synthesizing a threeaxis autopilot in accordance with specified design criteria of size, power, accuracy, response rate and error disturbances. View full abstract»

On the optimum synthesis of sampled data multipole filters with random and nonrandom inputs
Page(s): 193  208This paper considers the synthesis of optimum sampled data multipole filters with n inputs and m outputs. The signal portion of each input is assumed to consist of a stationary random component and a polynomial with unknown coefficients but known maximum order. Each signal is corrupted by stationary random noise. The filter under investigation is linear, timeinvariant, and has finite memory. Each input to the filter consists of a sequence of impulses with a constant period T. Each impulse is assumed to have an area equal to the value of the signal plus noise at the sampling instant. The synthesis procedure to be developed is to specify the weighting functions of the filter such that the system error, which is defined as the difference between the actual and ideal outputs, has zero ensemble mean and the system ensemble mean square error is minimum. The weighting functions thus obtained will have, in general, abrupt jumps at the sampling instants but they are continuous within the sampling intervals. The synthesis procedure is extended to the case shown in Appendix A where each of the nonrandom signals can be expressed as an arbitrary linear combination of a set of known time functions. Further generalization is possible to the synthesis of timevarying filter with sampled nonstationary random inputs as given in Appendix B. View full abstract»

A study of asynchronously excited oscillations in nonlinear control systems
Page(s): 179  192This study was initiated as an effort to explain certain oscillatory phenomena observed in an aircraft and weapon control system operated in a particular mode. The oscillations in question were of the undamped limitcycle type and their presence could very clearly be correlated with the degree of noise corruption of the signals. It is demonstrated in this paper that certain types of nonlinear systems although being inherently stable may be driven into oscillatory modes not only by random signals but also by any high frequency periodic or nonperiodic signal possessing a certain energy content. It is of interest to note that the tendency for hunting and also the hunt frequency usually are completely independent of the frequency of the excitation signal, i.e., the phenomenon is of asynchronous nature. A general theory, the validity of which has been tested by both analog and digital means, is presented and utilized to demonstrate how this phenomenon may be predicted from information on circuit data. View full abstract»

Design of optimum beam flexural damping in a missile by application of rootlocus techniques
Page(s): 237  246The control of a missile in freefall in the presence of external disturbances requires that the control system be stable when various body bending modes are excited. It is an inevitable consequence of the internal and external missile environment that all body bending modes are excited. The general method of stabilizing a missile is to choose a minimum of inertial sensors such as rate and attitude gyros, and through the use of passive electrical networks in the information paths, generate stabilizing poles and zeros in the control system openloop transfer functions. Generally, the electrical shaping networks are approximations to "maximally" flat functions with the cutoff frequency below the first bending mode resonant frequency, and in extreme cases, a notch filter is needed to eliminate body bending information. Tae basic purpose of the electrical shaping networks is to attenuate the high signal frequencies circulating in the control loop without the loss of important low frequency data. In some applications the use of passive shaping networks becomes very difficult because of the large attenuation required near the first body bending resonant frequency and the required amplitude flatness at lower frequencies. If passive shaping cannot be used, then active networks must be substituted. This is an undesirable complexity. This paper presents an optimum design procedure to utilize the characteristic properties of completed airframe and missile structures to acquire a maximum increase in modal damping without auxiliary equipment and further autopilot complexity by the proper choice of the subassembly attaching fixtures. Completed airframes and missiles are composed of a very lightweight integral structure in which a large number of equipment subassemblies are attached. The subassemblies or equipment modules are generally massive and of small volume so that they act as a rigid mass attached to the lightweight integral structure via an equivalent lateral spring constant and viscous damper. For example, the guidance package and the rocket engine of a ballistic missile are usually attached fore and aft of the missile integral tank structure. Each of these elements can be quite rigid and will act as a separate mass from the integral tank structure. The proper choice of the equivalent lateral spring constant and viscous damper of the attaching fixtures that hold the subassemblies to the basic lightweight missile or airframe integral structure will result in an optimum increase in modal damping for a particular beamflexural mode of the completed structure. To determine the values of the proper equivalent spring constant and viscous coefficient, the dynamic principles underlying the Frahm damper are used by extending the analysis of the Frahm damper concept to include a general linear flexural beam which satisfies a linear partial differential equation which can be solved by the product of the solutions of two ordinary, linear differential equations. The extension of these principles is accomplished by deriving the solution of the attached subassembly to the integral structure through normal servomechanism analysis. This analysis uses the analytical relationships of the Evans or RootLocus method. View full abstract»

Synthesis of a self adaptive autopilot for a large elastic booster
Page(s): 229  236The design of a conventional autopilot requires a detailed knowledge of the structural dynamics of the missile that is not easily obtainable. The selfadaptive autopilot considered in this paper would not depend on this detailed knowledge. This system would, ideally, adjust itself to maintain optimum performance in an environment of changing inertial, aerodynamic, and structural parameters. The mechanization of a suitable self adaptive system is complicated by the difficulty of getting a continuous measure of system performance. The method used, in this study, to obtain the basic modes is based on decomposition of the transient response. View full abstract»

On the existence and uniqueness of the optimal multivariable system synthesis
Page(s): 166  170First Page of the ArticleView full abstract» 
On optimal and suboptimal policies in the choice of control forces for finalvalue systems
Page(s): 171  178A simple control system whose state variable x
n is described by the difference equation (1) is considered. xn+l = α xn +rn +vn , n = 1, 2 ...N , o<α<1 (1) where Vn is the control force of the system and rn is the Bernoulli random noise with the probability parameter p. If 4 (x ~) is the performance index of the finalvalue system, then the problem is to find a sequence of control forces vn , n = 1, 2 . . .N, which minimizes the expecte d l value of 4 (xN). An optimal sequence of vn is determined by solving a recurrence relation on n of the criterion function hn (x;p) defined a s follows: hn (x;p) = Min Min . . . Min E [4 (XJ] v1v2 . .. vn = the minimum of the expected value of 4 (xn ) obtainable in the nstage control process by employing an optimal policy, starting from the initial state variable x when the probability parameter of the random disturbance is p. The recurrence relation is obtained by the usual application of the principle of optimality of dynamic programming technique. It is proved that hn (x;p) = hn (x; 1p) holds and this fact is used in reducing by half the amount of computation when it is necessary to solve the recurrence relation numerically. If the values of control variable vn (x;p) are restricted to 1 and 1 as in contactor servo systems, the boundaries between 1 and 1 control forces become too complicated to be determined analytically except for few special cases. By solving vn (x;p) computationally for the 4 (XN) = XN case, It is seen that vn (x;p) agrees with v1 (x;p) fairly well for all n > 1, v1 (x;p) is the optimal control force when there remains only one chance of exerting control forces. Hence, the suboptimal policyof a l w w  plying control forces as if onLx one more erxor correction is possible may be expected to.be cl=se toLh2 ot!mal pohcy in minimizing E(x$). The control fzrce vi .(x;.p) is IiKear ii~ x Gdp &d F is a much more simple function to mechanize. : his suboptimal policy is tried by the Monte Carlo method and found to be only slightly inferior ; memtimal policy. The behavior of X, is invest igated by assuming the control forces are given by the suboptimal policy. This approximate analysis should be good in view of the agreements between the optimal and suboptimal policies. It is important to realize that if the adoption of a suboptimal policy results in a simplified mechanization of the optimal control forces, with only a slight reduction in the system performance, then the suboptimal policy might be optimal in a certain enlarged performance index. What seems to be the most desirable approach to engineering problems is a unified o r wellintegrated one where the analytical and computational algorithms are used to supplement each other. In this paper, an attempt is made to illustrate the point, presenting at the same time a new approach to analysis and synthesis of a certain class of control systems. View full abstract» 
The incremental phase plane for nonlinear sampled data systems
Page(s): 159  165An analysis technique for nonlinear sampled data systems is developed, using the incremental phase plane. This method is analogous to the phase plane method for continuous systems. A sampled data system with saturation is analyzed to demonstrate the use of the incremental phase plane in system analysis. Path tangent curves are introduced which allow the graphical solution of systems with more general types of nonlinearities. A difference equation analog of Van der Pol's equation is solved using the path tangent curves. View full abstract»
Aims & Scope
The theory, design and application of Control Systems. It shall encompass components, and the integration of these components, as are necessary for the construction of such systems. The latest title for this publication is IEEE Transactions on Automatic Control.
This Transactions ceased publication in 1958. The current retitled publication is IEEE Transactions on Automatic Control.