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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

A Linear Programming Approach to Routing Control in Networks of Constrained Nonlinear Positive Systems with Concave Flow Rates

We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.

Positive Systems↗
NASA NTRS1976

Parameter estimating state reconstruction

Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and the system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a space shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.

George, E. B.↗
NASA NTRS1977

Parameter estimating state reconstruction

Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. These systems must be observable. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a Space Shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.

George, E. B.↗
NASA NTRS1988

Application of dynamical systems theory to nonlinear aircraft dynamics

Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

Culick, Fred E. C.↗
NASA NTRS1995

Dissipative rendering and neural network control system design

Model-based control system designs are limited by the accuracy of the models of the plant, plant uncertainty, and exogenous signals. Although better models can be obtained with system identification, the models and control designs still have limitations. One approach to reduce the dependency on particular models is to design a set of compensators that will guarantee robust stability to a set of plants. Optimization over the compensator parameters can then be used to get the desired performance. Conservativeness of this approach can be reduced by integrating fundamental properties of the plant models. This is the approach of dissipative control design. Dissipative control designs are based on several variations of the Passivity Theorem, which have been proven for nonlinear/linear and continuous-time/discrete-time systems. These theorems depend not on a specific model of a plant, but on its general dissipative properties. Dissipative control design has found wide applicability in flexible space structures and robotic systems that can be configured to be dissipative. Currently, there is ongoing research to improve the performance of dissipative control designs. For aircraft systems that are not dissipative active control may be used to make them dissipative and then a dissipative control design technique can be used. It is also possible that rendering a system dissipative and dissipative control design may be combined into one step. Furthermore, the transformation of a non-dissipative system to dissipative can be done robustly. One sequential design procedure for finite dimensional linear time-invariant systems has been developed. For nonlinear plants that cannot be controlled adequately with a single linear controller, model-based techniques have additional problems. Nonlinear system identification is still a research topic. Lacking analytical models for model-based design, artificial neural network algorithms have recently received considerable attention. Using their universal approximation property, neural networks have been introduced into nonlinear control designs in several ways. Unfortunately, little work has appeared that analyzes neural network control systems and establishes margins for stability and performance. One approach for this analysis is to set up neural network control systems in the framework presented above. For example, one neural network could be used to render a system to be dissipative, a second strictly dissipative neural network controller could be used to guarantee robust stability.

Gonzalez, Oscar R.↗
NASA NTRS1990

System Identification for Nonlinear Control Using Neural Networks

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.

Stengel, Robert F.↗
NASA NTRS1974

Analysis and synthesis of a fluid sonic pulse system

A nonlinear sonic system is described that includes a delay line. Short-lived pulses with a high repetition frequency circulate through the system. The analysis was carried out by defining the reflection factor at the load and then dividing the input pulse according to duration into sections of appropriate width. The response was determined for each section, the response to the whole pulse being given by the sum of the responses at the sections. This makes it possible to broach the synthesis of a sonic system that will give an output pulse of the desired form.

Boita, M.↗
NASA NTRS2000

Generalized Predictive and Neural Generalized Predictive Control of Aerospace Systems

The research work presented in this thesis addresses the problem of robust control of uncertain linear and nonlinear systems using Neural network-based Generalized Predictive Control (NGPC) methodology. A brief overview of predictive control and its comparison with Linear Quadratic (LQ) control is given to emphasize advantages and drawbacks of predictive control methods. It is shown that the Generalized Predictive Control (GPC) methodology overcomes the drawbacks associated with traditional LQ control as well as conventional predictive control methods. It is shown that in spite of the model-based nature of GPC it has good robustness properties being special case of receding horizon control. The conditions for choosing tuning parameters for GPC to ensure closed-loop stability are derived. A neural network-based GPC architecture is proposed for the control of linear and nonlinear uncertain systems. A methodology to account for parametric uncertainty in the system is proposed using on-line training capability of multi-layer neural network. Several simulation examples and results from real-time experiments are given to demonstrate the effectiveness of the proposed methodology.

Kelkar, Atul G.↗
NASA NTRS1981

Pulse control of single degree-of-freedom system

The possibility of using active control for structural and mechanical systems is examined. Open loop adaptive control of structural systems subjected to deterministic and stochastic excitations is considered by means of an algorithm for a single-degree-of-freedom oscillator. The algorithm is heuristic and requires continuous monitoring of the state variables, with a pulse control applied when some prespecified level of control is exceeded. The control algorithm is based on the principle that the gradual rhythmic increase of the structural response can be eliminated by applying a pulse of suitable magnitude in the proper direction, thereby avoiding the application of large forces over sustained periods of time. The optimum pulse magnitude is determined as the minimum rms response of the system. Application to linear and nonlinear systems, as well as in chatter suppression, are outlined.

Udwadia, F. E.↗
NASA NTRS1975

Time domain desensitized specific optimal system design

A digital computer algorithm for desensitized specific optimal system design for general time-invariant nonlinear systems is presented. The algorithm utilizes a technique of partitioning and uncoupling of the original specific closed-loop system state and sensitivity equations into linear, nonlinear, and control subsystems. Results of the application of the algorithm in the design of a Saturn V Launch Vehicle analog attitude control system and an LST image motion compensation digital controller are given.

Henson, T. F.↗
NASA NTRS1994

The Dynamics of Some Iterative Implicit Schemes

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations is analyzed using the theory of dynamical systems. With the aid of parallel Connection Machines (CM-2 and CM-5), the associated bifurcation diagrams as a function of the time step, and the complex behavior of the associated 'numerical basins of attraction' of these iterative implicit schemes are revealed and compared. Studies showed that all of the four implicit LMMs exhibit a drastic distortion and segmentation but less shrinkage of the basin of attraction of the true solution than standard explicit methods. The numerical basins of attraction of a noniterative implicit procedure mimic more closely the basins of attraction of the differential equations than the iterative implicit procedures for the four implicit LMMs.

Yee, H. C.↗
NASA NTRS1987

Response of joint dominated space structures

An efficient linearization method is presented for calculating the transient response of nonlinear systems due to initial disturbances. The method is an extension of the describing function approach in which the steady state response of the system is calculated by representing the nonlinear element, typically joints in the case of space structures, by impedances which are functions of the amplitude of response. Thus, the problem of solving the differential equation for the steady state response becomes one of solving a set of nonlinear algebraic equations involving the steady state amplitudes and phases of the system. It is shown that for the transient case the steady state impedances can be averaged over the range of responses in order to provide equivalent values of stiffness and damping that, for a given set of initial displacements, may be treated as being constant for purposes of calculating system response. Single degree of freedom system are used to demonstrate the method and to develop an approach for optimizing the joint's characteristics so as to minimize transient response times. The use of this method for response estimation and optimization in multiple degree of freedom systems is investigated.

Source record↗
NASA NTRS1994

Global Asymptotic Behavior of Iterative Implicit Schemes

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

Yee, H. C.↗