On the control of a linear functional- differential equation with quadratic cost
Linear functional differential equations control with quadratic cost
Barnea, D. I.↗
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Toward Real Time Neural Net Flight Controllers
NASA Ames Research Center has an ongoing program in neural network control technology targeted toward real time flight demonstrations using a modified F-15 which permits direct inner loop control of actuators, rapid switching between alternative control designs, and substitutable processors. An important part of this program is the ACTIVE flight project which is examining the feasibility of using neural networks in the design, control, and system identification of new aircraft prototypes. This paper discusses two research applications initiated with this objective in mind: utilization of neural networks for wind tunnel aircraft model identification and rapid learning algorithms for on line reconfiguration and control. The first application involves the identification of aerodynamic flight characteristics from analysis of wind tunnel test data. This identification is important in the early stages of aircraft design because complete specification of control architecture's may not be possible even though concept models at varying scales are available for aerodynamic wind tunnel testing. Testing of this type is often a long and expensive process involving measurement of aircraft lift, drag, and moment of inertia at varying angles of attack and control surface configurations. This information in turn can be used in the design of the flight control systems by applying the derived lookup tables to generate piece wise linearized controllers. Thus, reduced costs in tunnel test times and the rapid transfer of wind tunnel insights into prototype controllers becomes an important factor in more efficient generation and testing of new flight systems. NASA Ames Research Center is successfully applying modular neural networks as one way of anticipating small scale aircraft model performances prior to testing, thus reducing the number of in tunnel test hours and potentially, the number of intermediate scaled models required for estimation of surface flow effects.
Jorgensen, C. C.↗
Advanced EVA Suit Camera System Development Project
The National Aeronautics and Space Administration (NASA) at the Johnson Space Center (JSC) is developing a new extra-vehicular activity (EVA) suit known as the Advanced EVA Z2 Suit. All of the improvements to the EVA Suit provide the opportunity to update the technology of the video imagery. My summer internship project involved improving the video streaming capabilities of the cameras that will be used on the Z2 Suit for data acquisition. To accomplish this, I familiarized myself with the architecture of the camera that is currently being tested to be able to make improvements on the design. Because there is a lot of benefit to saving space, power, and weight on the EVA suit, my job was to use Altium Design to start designing a much smaller and simplified interface board for the camera's microprocessor and external components. This involved checking datasheets of various components and checking signal connections to ensure that this architecture could be used for both the Z2 suit and potentially other future projects. The Orion spacecraft is a specific project that may benefit from this condensed camera interface design. The camera's physical placement on the suit also needed to be determined and tested so that image resolution can be maximized. Many of the options of the camera placement may be tested along with other future suit testing. There are multiple teams that work on different parts of the suit, so the camera's placement could directly affect their research or design. For this reason, a big part of my project was initiating contact with other branches and setting up multiple meetings to learn more about the pros and cons of the potential camera placements we are analyzing. Collaboration with the multiple teams working on the Advanced EVA Z2 Suit is absolutely necessary and these comparisons will be used as further progress is made for the overall suit design. This prototype will not be finished in time for the scheduled Z2 Suit testing, so my time was also spent creating a case for the original interface board that is already being used. This design is being done by use of Creo 2. Due to time constraints, I may not be able to complete the 3-D printing portion of this design, but I was able to use my knowledge of the interface board and Altium Design to help in the task. As a side project, I assisted another intern in selecting and programming a microprocessor to control linear actuators. These linear actuators will be used to move various increments of polyethylene for controlled radiation testing. For this, we began the software portion of the project using the Arduino's coding environment to control an Arduino Due and H-Bridge components. Along with the obvious learning of computer programs such as Altium Design and Creo 2, I also acquired more skills with networking and collaborating with others, being able to multi-task because of responsibilities to work on various projects, and how to set realistic goals in the work place. Like many internship projects, this project will be continued and improved, so I also had the chance to improve my organization and communication skills as I documented all of my meetings and research. As a result of my internship at JSC, I desire to continue a career with NASA, whether that be through another internship or possibly a co-op. I am excited to return to my university and continue my education in electrical engineering because of all of my experiences at JSC.
Mock, Kyla↗
A frequency domain solution for the linear attitude-control problem of spacecraft with flexible appendages
Linear interaction problem between spacecraft attitude control and flexible appendages solved in frequency domain using Fourier transform
Trubert, M. R.↗
Direct computation of optimal control of forced linear system
It is known that the optimal control of a forced linear system may be reduced to that of tracking the system without forces. The solution of the tracking problem is available via the costate variables method. This procedure is computationally expensive for large order systems. It requires solution of matrix Riccati equation and two final value problems. An alternate approach is outlined for the direct computation of the optimal control. Instead of Riccati equation, a matrix Volterra integral must be solved. For this purpose two computational schemes are described, and an illustrative example is given. The results compare favorably with the classical solution. This alternative approach may be especially useful for the control of large space structure where large order models are required.
Utku, S.↗
Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing
A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.
Childs, A. G.↗
Analysis, modelling and simulation of the large-angle magnetic suspension test fixture
The large-angle magnetic suspension test fixture (LAMSTF) research project is described which is based on a sophisticated finite element computer program, VF/GFUN, for calculating magnetic fields. The LAMSTF design includes eddy current paths the effect of which on system dynamics is being studied to modify the system dynamic model and the digital controller. Linearized equations of motions have been developed for system modelling and analysis of controllers.
Britcher, Colin P.↗
On the Design of P-I-D Controllers Using Optimal Linear Regulator Theory
Design of proportional-integral-derivative controllers using optimal linear regulator theory
Athans, M.↗
Parameter uncertainties in control system design.
Development of a design method for including the effects of parameter uncertainties in the design of linear control systems. The approach taken to this problem may be classified as a special case of the stochastic control problem. Thus the formulation is based on the minimization of the expected value of a quadratic performance index defined in terms of the system state vector. The uncertainty in the value of the performance index is the result of the statistical nature of the system parameters rather than a random input signal. It is shown that the expected value of the performance index may be written as a sum of two terms under the assumption of first-order variations of the system state. The first of these terms expresses the nominal performance of the system when the system parameters assume their mean values. The second term represents the effect of the uncertainties on the expected value of the performance index, and is interpreted as an index of system sensitivity.
Palsson, T.↗
Small motion experiments on a large flexible arm with strain feedback
Initial experiments on state-space feedback control of a large flexible manipulator with a parallel linkage drive are described. A linear controller using joint angle and strain measurements has been designed to minimize a quadratic performance index with a prescribed stability margin. It is based on a simplified model that accounts for the constraints of the parallel linkage kinematically rather than through constraint forces. The results show substantial improvement over a simple proportional-derivative joint control.
Yuan, B. S.↗
Vibration control by limiting the maximum axial forces in space trusses
Proposed here is a method of vibration control based on limiting the maximum axial forces in the active members of an adaptive truss. The actuators simulate elastic rigid-plastic behavior and consume the vibrational energy as work. The method is applicable to both statically determinate as well as indeterminate truss structures. However, for energy efficient control of statistically indeterminate trusses extra actuators may be provided on the redundant bars. An energy formulation relating the various control parameters is derived to get an estimate of the control time. Since the simulation of elastic rigid-plastic behavior requires a piecewise linear control law, a general analytical solution is not possible. Numerical simulation by step-by-step integration is performed to simulate the control of an example truss structure. The problems of application to statically indeterminate trusses and optimal actuator placement are identified for future work.
Chawla, Vikas↗
Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers
Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.
Molusis, J. A.↗
A minimum time control algorithm for linear and nonlinear systems
The minimum time control problem with bounded control has long been of interest to control engineers. Much of the theoretical study of this problem has been limited to linear systems and the results are usually problem-specific. This paper presents a new computational method for solving the minimum-time control problem when the control action is assumed to be bang-bang. A gradient-based algorithm is developed where the switching times are updated to minimize the final state missed distance. The algorithm is applicable to linear and nonlinear problems, including multi-input systems.
Wen, J.↗
Nonlinear compensation techniques for magnetic suspension systems
In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation.
Trumper, David L.↗
Introduction to time optimal control of stationary linear systems
Loci points of state space determination in time optimal control of stationary linear systems
TIME OPTIMAL CONTROL↗
A Case Study on the Application of a Structured Experimental Method for Optimal Parameter Design of a Complex Control System
This report documents a case study on the application of Reliability Engineering techniques to achieve an optimal balance between performance and robustness by tuning the functional parameters of a complex non-linear control system. For complex systems with intricate and non-linear patterns of interaction between system components, analytical derivation of a mathematical model of system performance and robustness in terms of functional parameters may not be feasible or cost-effective. The demonstrated approach is simple, structured, effective, repeatable, and cost and time efficient. This general approach is suitable for a wide range of systems.
Torres-Pomales, Wilfredo↗
A note on the transformation to canonical /phase-variable/ form
Phase-variable canonical form for single input linear dynamical systems applied to linear control theory
CANONICAL PROBLEM↗
Decoupling control of a long flexible beam in orbit
The paper presents a method of control for large flexible systems using state variable feedback, with a long flexible beam given as an example. These feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping and (2) by applying the linear regulator problem to the individual modal coordinates separately. It is shown that the linear control law thus obtained are then evaluated by numerical integration of the non-linear system equations. Also included are results showing the effects (control spillover) on the uncontrolled modes when the number of controllers is less than the number of modes, and the effects of inaccurate knowledge of the control influence coefficients which lead to errors in the calculated feedback gains.
Reddy, A. S. S. R.↗