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Optimal control problems for Markov chains solved by iterative method, using nonlinear finite difference equations to approximate degenerate elliptic functions
Application and extension of modern automatic control theory to nuclear rocket dynamics and control
Linear optimal feedback control theory for nuclear rocket dynamics and control problems
Automatic control theory applied to nuclear rocket dynamics and control using stochastic algorithms
The idea of control theory and its application to project management is not new, however literature on the topic and real-world applications is not as readily available and comprehensive in how all the principals of Guidance, Navigation and Control (GN&C) apply. This paper will address how the fundamental principals of modern GN&C Theory have been applied to NASA's Constellation Space Suit project and the results in the ability to manage the project within cost, schedule and budget. A s with physical systems, projects can be modeled and managed with the same guiding principles of GN&C as if it were a complex vehicle, system or software with time-varying processes, at times non-linear responses, multiple data inputs of varying accuracy and a range of operating points. With such systems the classic approach could be applied to small and well-defined projects; however with larger, multi-year projects involving multiple organizational structures, external influences and a multitude of diverse resources, then modern control theory is required to model and control the project. The fundamental principals of G N&C stated that a system is comprised of these basic core concepts: State, Behavior, Control system, Navigation system, Guidance and Planning Logic, Feedback systems. The state of a system is a definition of the aspects of the dynamics of the system that can change, such as position, velocity, acceleration, coordinate-based attitude, temperature, etc. The behavior of the system is more of what changes are possible rather than what can change, which is captured in the state of the system. The behavior of a system is captured in the system modeling and if properly done, will aid in accurate system performance prediction in the future. The Control system understands the state and behavior of the system and feedback systems to adjust the control inputs into the system. The Navigation system takes the multiple data inputs and based upon a priori knowledge of the input, will develop a statistical-based weighting of the input to determine where the system currently is located. Guidance and Planning logic of the system with the understanding of where it is (provided by the navigation system) will in turn determine where it needs to be and how to get there. Lastly, the system Feedback system is the right arm of the control system to allow it to affect change in the overall system and therefore it is critical to not only correctly identify the system feedback inputs but also the system response to the feedback inputs. And with any systems project it is critical that the objective of the system be clearly defined for not only planning but to be used to measure performance and to aid in the guidance of the system or project.
The results of optimal control theory are used to synthesize a feedback filter. The feedback filter is used to force the output of the filtered frequency response to match that of a desired optimal frequency response over a finite frequency range. This matching is accomplished by employing a nonlinear programing algorithm to search for the coefficients of the feedback filter that minimize the error between the optimal frequency response and the filtered frequency response. The method is applied to the synthesis of an active flutter-suppression control law for an aeroelastic wind-tunnel model. It is shown that the resulting control law suppresses flutter over a wide range of subsonic Mach numbers. This is a promising method for synthesizing practical control laws using the results of optimal control theory.
Optimization problems in control theory in terms of criterion function, controller, and information available to controller
Linear multivariable control system design using modern control theory, and application to coupled core reactor control
Optimal final value control theory, applying variational calculus and functional analysis to control function selection for dynamic systems
A digital computer-based state variable controller was designed and applied to the 70-m antenna axis servos. The general equations and structure of the algorithm and provisions for alternate position error feedback modes to accommodate intertarget slew, encoder referenced tracking, and precision tracking modes are descibed. Development of the discrete time domain control model and computation of estimator and control gain parameters based on closed loop pole placement criteria are discussed. The new algorithm was successfully implemented and tested in the 70-m antenna at Deep Space Network station 63 in Spain.
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.
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.
Controllability of nonlinear dynamic feedback systems based on Liapunov-like stability approach and optimal control theory
Control theory application in news magazine publishing
In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.
The method of harmonic linearization (harmonic balance), first proposed by N. M. Krylov and N. N. Bogolyubov for the approximate investigation of nonlinear vibrations, has been developed and received wide practical application to problems in the theory of automatic control. Recently, some doubt has been expressed on the legitimacy of application of the method to these problems, and assertions were made on the absence in them of a small parameter of any kind. Nevertheless, the method gives practical, acceptable results and is a simple and powerful means in engineering computations. Hence, the importance of questions arises as to its justification. The underlying principle of the method is the replacement of the given nonlinear equation by a linear equation. In establishing the method, a small parameter is considered whose presence makes it possible to speak, with some degree of approximation, of the solution of this new equation to the solution of the given nonlinear equation. In an article by the author, certain considerations were given on the presence of the small parameter, but this question has not as yet received a final answer. In the present report, a somewhat different approach to the problem is applied that permits: (a) establishing, in the clearest manner, the form of the presence of the small parameter in nonlinear problems of control theory, solvable by the method of harmonic linearization; (b) connecting it with previous intuitive physical concepts (with the "filter property") and extending the class of problems possessing this property; and (c) discussing various generalizations of the method.
Control systems have had a profound impact on society as theories, techniques, and algorithms have migrated from the laboratory to thousands of products. As the control community continues to improve its solutions, ideas are being generated for a new era of applicationws that are fundamentally different from their predecessors.
Using automatic control theory with simple pilot model for synthesizing helicopter landing approach flight director control laws