Sensitivity of linear control systems to large parameter variations.
Large parameter variations effect on linear feedback control systems performance, optimal or suboptimal
Aggarwal, J. K.↗
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Collisional effect on the quasilinear process associated with the ion-wave instability
Quasi-linear feedback effect of enhanced ion-wave fluctuations on average electron distribution in current-carrying plasma
Nishikawa, K.↗
A lower bound on the performance of optimal regulators
Linear feedback control system with quadratic penalty function, deriving lower bound on optimal performance for suboptimality evaluation
Canales, R.↗
Introduction to linear system analysis and design by use of state vector approach
Analysis and synthesis of linear feedback control systems using state vector control
Vector, R. C.↗
4-D guidance system design with application to STOL air traffic control.
A new guidance technique, referred to as 4-D guidance, is being developed to improve the operation of future STOL aircraft transportation systems. 4-D guidance refers to a technique of synthesizing a complex three-dimensional flight path from simple pilot inputs and flying the aircraft along the path according to an ATC specified time schedule. The two major elements of a 4-D guidance system are the trajectory synthesizer and the control law for flying the aircraft along the synthesized trajectory using the aircraft's autopilot and autothrottle. Inputs to the trajectory synthesizer are the three-dimensional coordinates of waypoints, the turning radius, the speed range, the acceleration limits and the arrival time at time control waypoints. First the three-dimensional trajectory is computed using circular arcs and straight lines. Then the airspeed profile, compensated for wind, is calculated to achieve the desired arrival times. The pilot is informed if the arrival times cannot be achieved. The synthesized trajectory is stored as a time sequence of reference states and controls which the aircraft is forced to track using a linear feedback law.
Erzberger, H.↗
Application of modern control theory to the design of optimum aircraft controllers
The synthesis procedure presented is based on the solution of the output regulator problem of linear optimal control theory for time-invariant systems. By this technique, solution of the matrix Riccati equation leads to a constant linear feedback control law for an output regulator which will maintain a plant in a particular equilibrium condition in the presence of impulse disturbances. Two simple algorithms are presented that can be used in an automatic synthesis procedure for the design of maneuverable output regulators requiring only selected state variables for feedback. The first algorithm is for the construction of optimal feedforward control laws that can be superimposed upon a Kalman output regulator and that will drive the output of a plant to a desired constant value on command. The second algorithm is for the construction of optimal Luenberger observers that can be used to obtain feedback control laws for the output regulator requiring measurement of only part of the state vector. This algorithm constructs observers which have minimum response time under the constraint that the magnitude of the gains in the observer filter be less than some arbitrary limit.
Power, L. J.↗
Guidance strategies and analysis for low thrust navigation
A low-thrust guidance algorithm suitable for operational use was formulated. A constrained linear feedback control law was obtained using a minimum terminal miss criterion and restricting control corrections to constant changes for specified time periods. Both fixed- and variable-time-of-arrival guidance were considered. The performance of the guidance law was evaluated by applying it to the approach phase of the 1980 rendezvous mission with the comet Encke.
Jacobson, R. A.↗
The 4-D guidance of STOL aircraft in the terminal area
Advanced STOL aircraft for the improvement of the nation's air transportation system by the elimination of delays and congestions associated with today's air travel are discussed. A new guidance technique, referred to as 4-D guidance, is being developed for STOL aircraft. The 4-D guidance technique synthesizes complex three-dimensional flight paths from a minimum set of input and files the aircraft along the paths according to a prespecified time schedule. The two major elements of a 4-D guidance system are the trajectory synthesizer and the control law. Inputs to the trajectory synthesizer are the three-dimensional coordinates of way points, the turning radii, the speed ranges, the acceleration limits, and the arrival times at time control way points. First, the three-dimensional trajectory is computed by using circular arcs and straight lines. Then the airspeed profile, compensated for wind, is calculated to achieve the desired arrival times. The synthesized trajectory is stored as a time sequence of reference states which the aircraft is forced to track by using a linear feedback law.
Pecsvaradi, T.↗
Four-D guidance of STOL aircraft in the terminal area
The primary objective of advanced STOL aircraft is the improvement of the nation's air transportation system by the elimination of delays and congestions associated with today's air travel. A new guidance technique, referred to as 4-D guidance, is being developed to achieve this objective. The 4-D guidance technique synthesizes complex three-dimensional flight paths from a minimum set of input data and flies the aircraft along the paths according to a prespecified time schedule. The two major elements of a 4-D guidance system are the trajectory synthesizer and the control law. Inputs to the trajectory synthesizer are the three-dimensional coordinates of way points, the turning radii, the speed ranges, the acceleration limits, and the arrival times at time control way points. First, the three-dimensional trajectory is computed by using circular arcs and straight lines. Then the airspeed profile, compensated for wind, is calculated to achieve the desired arrival times. The synthesized trajectory is stored as a time sequence of reference states which the aircraft is forced to track by using a linear feedback law.
Pecsvaradi, T.↗
On the design of optimal input signals in system identification
The problem of designing optimal inputs in the identification of linear systems with unknown random parameters is considered using a Bayesian approach. The information matrix, which is positive definite for the class of systems analyzed, gives a measure of performance for the system inputs. The computation of the optimal closed-loop input mappings is shown to be a nontrivial exercise in adaptive control. Deterministic optimal inputs are shown to be easily computable. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given.
Lopez-Toledo, A. A.↗
A guidance and navigation system for continuous low thrust vehicles
A midcourse guidance and navigation system for continuous low thrust vehicles is described. A set of orbit elements, known as the equinoctial elements, are selected as the state variables. The uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time nominal trajectory is defined and the equation of motion and the measurement equation are linearized about this nominal trajectory. An exponential cost criterion is constructed and a linear feedback guidance law is derived to control the thrusting direction of the engine. Using this guidance law, the vehicle will fly in a trajectory neighboring the nominal trajectory. The extended Kalman filter is used for state estimation. Finally a short mission using this system is simulated. The results indicate that this system is very efficient for short missions.
Tse, C. J. C.↗
A constrained discrete optimal guidance strategy for low-thrust space flight
A low-thrust guidance algorithm suitable for operational use is formulated. Using linear stochastic control theory, a linear feedback control law is obtained for a minimum terminal miss performance criterion. The control variables are restricted to constant values over specified time intervals and are explicitly limited. Both fixed and variable time-of-arrival guidance are considered. Guidance equations are presented in deterministic (operational) and in statistical form; and computational procedures necessary for implementation are outlined. The performance of the guidance algorithm is evaluated by applying it to the approach phase of the 1980 rendezvous mission with the comet Encke.
Jacobson, R. A.↗
Families of shift-register sequences with impulsive correlation properties
A study of the linear feedback shift registers corresponding to a subset of nonprimitive irreducible polynomials over GF(2) has uncovered a class of sequences with interesting structures and cyclic correlation properties. These families of sequences are made up of interleaved identical sequences which are from primitive irreducible polynomials. Furthermore, they have correlation functions which are two or three valued, being constant at zero or a small value throughout most of their length with the exception of a small number of impulses. Each interval between such impulses on the correlograms uniquely corresponds to (and thus uniquely identifies) the member sequence or sequences producing it. It is shown that these families of sequences have direct application as error-correcting codes.
Lee, J.-J.↗
Application of modern control theory to the design of optimum aircraft controllers
A procedure is described for synthesis of optimal aircraft control systems by application of the concepts of optimal control theory to time-invariant linear systems with quadratic performance criteria. Essential in this synthesis procedure is the solution of the Riccati matrix equation which results in a constant linear feedback control law for an output regulator which maintains a plant in an equilibrium in the presence of impulse disturbances. An algorithm is derived for designing maneuverable output regulators with selected state variables for feedback.
Power, L. J.↗
A new approach to the design of time-varying control systems with application to the Space Shuttle Boost
A general approach to the analysis and design of closed-loop control for slowly time-varying linear systems is presented. The approach uses the method of generalized multiple scales in which slow and fast dynamics are systematically separated by employing different 'clocks' which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, are chosen in such a manner that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock function is shown to satisfy an algebraic characteristic equation and can be determined in terms of the coefficients. The approach can be viewed as an extension of time-invariant linear feedback control theory.
Ramanth, R. V.↗
A synthesis theory for self-oscillating adaptive systems /SOAS/
A quantitative synthesis theory is presented for the Self-Oscillating Adaptive System (SOAS), whose nonlinear element has a static, odd character with hard saturation. The synthesis theory is based upon the quasilinear properties of the SOAS to forced inputs, which permits the extension of quantitative linear feedback theory to the SOAS. A reasonable definition of optimum design is shown to be the minimization of the limit cycle frequency. The great advantages of the SOAS is its zero sensitivity to pure gain changes. However, quasilinearity and control of the limit cycle amplitude at the system output, impose additional constraints which partially or completely cancel this advantage, depending on the numerical values of the design parameters. By means of narrow-band filtering, an additional factor is introduced which permits trade-off between filter complexity and limit cycle frequency minimization.
Horowitz, I.↗
A guidance and navigation system for continuous low-thrust vehicles
A midcourse guidance and navigation system for continuous low thrust vehicles was developed. The equinoctial elements are the state variables. Uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time trajectory is defined; equations of motion and measurements are linearized about this trajectory. An exponential cost criterion is constructed and a linear feedback quidance law is derived. An extended Kalman filter is used for state estimation. A short mission using this system is simulated. It is indicated that this system is efficient for short missions, but longer missions require accurate trajectory and ground based measurements.
Jack-Chingtse, C.↗
On the design of optimal input signals in system identification
The problem of designing optimal inputs in the identification of multi-input multi-output linear systems with unknown time-varying parameters is considered using a Bayesian approach. A sensitivity index gives a measure of performance for the closed-loop system inputs. The computation of the optimal closed-loop mappings is shown to be a nontrivial exercise in stochastic control with no analytic solution, but optimal open-loop and affine laws yield much more tractable problems. For time-invariant systems, the sensitivity index considered is shown to be equivalent to the trace of the (strictly positive definite) information matrix associated with the system. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given.
Lopez-Toledo, A. A.↗