Stability of nonlinear vehicle systems
Nonlinear effects of liquid motion in fixed and moving containers on stability and control of liquid rocket powered missiles and spacecraft
LIQUID PROPELLANT↗
SEARCH · Engineering Papers
Results for “Nonlinear systems”
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Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations
A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.
Dieudonne, J. E.↗
Nonlinear systems approach to control system design
Consider some of the control system design methods for plants with nonlinear dynamics. If the nonlinearity is weak relative to the size of the operating region, then the linear methods apply directly. Fixed-gain design may be feasible even for significant nonlinearities. It may be possible to find a single gain which provides adequate control of the linear models at several perturbation points. If the nonlinearity is restricted to a sector, that fact may be used to obtain a fixed-gain controller. Otherwise, a gain may have to be associated with each perturbation point Pi. A gain schedule K(p(v)) is obtained by connecting the perturbation points by a function, say p(v), of the scheduling parameter v (i.e., speed). When the scheduling parameter must be multidimensional, this approach is difficult; the objective is to develop an easier procedure.
Meyer, G.↗
Newton's method and the optimization of nonlinear systems
Newton-Raphson method applied to solution of boundary value problems in trajectory optimization
TRAJECTORY OPTIMIZATION↗
Robust Stabilization of a Class of passive Nonlinear Systems
The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.
Joshi, Suresh M.↗
Identification of a nonlinear system using a combined algorithm
Parameter identification algorithm for nonlinear equations describing VTOL aircraft longitudinal response
Denery, D. G.↗
Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.
Data-driven model reduction↗
Periodic motion in nonlinear systems
In this paper it is shown how some basic ideas from system theory and differential geometry can be used to establish some new results on the existence of periodic motion in autonomous feedback systems. The conditions are expressed in terms of the frequency response characteristic of the open-loop system and certain general properties of the nonlinearities.
Williamson, D.↗
The Applicability of Nonlinear Systems Dynamics Chaos Measures to Cardiovascular Physiology Variables
Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).
Hooker, John C.↗
An algorithm for Liapunov stability analysis of complex nonlinear systems with application to the Orbiting Astronomical Observatory
Optimal quadratic Liapunov function generating algorithm for estimating domain of equilibrium attraction of nonlinear star tracker attitude control systems for OAO stability
Chomas, A.↗
Application of Nonlinear Systems Inverses to Automatic Flight Control Design: System Concepts and Flight Evaluations
A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.
Meyer, G.↗
Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints
The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.
Calise, A. J.↗
Evolving Systems: Nonlinear Adaptive Key Component Control with Persistent Disturbance Rejection
This paper presents an introduction to Evolving Systems, which are autonomously controlled subsystems that self-assemble into a new Evolved System with a higher purpose. Evolving Systems of aerospace structures often require additional control when assembling to maintain stability during the entire evolution process. This is the concept of Adaptive Key Component Control which operates through one specific component to maintain stability during the evolution. In addition this control must overcome persistent disturbances that occur while the evolution is in progress. We present theoretical results for the successful operation of Nonlinear Adaptive Key Component control in the presence of such disturbances and an illustrative example.
adaptive control↗
Optimal Energy Measurement in Nonlinear Systems: An Application of Differential Geometry
Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.
Nonlinear response↗
A tensor approach to modeling of nonhomogeneous nonlinear systems
Model following control methodology plays a key role in numerous application areas. Cases in point include flight control systems and gas turbine engine control systems. Typical uses of such a design strategy involve the determination of nonlinear models which generate requested control and response trajectories for various commands. Linear multivariable techniques provide trim about these motions; and protection logic is added to secure the hardware from excursions beyond the specification range. This paper reports upon experience in developing a general class of such nonlinear models based upon the idea of the algebraic tensor product.
Yurkovich, S.↗
Identification of nonlinear system parameters in joints using the force-state mapping technique
A procedure is presented for identifying the potentially strong nonlinear properties of structural members, such as joints, by expressing the force transmitted by the member as a function of its mechanical state. By explicitly including position and rate dependent effects, the surface of transmitted force versus state, the force-state map, has distinct, unique, superposable features for common structural nonlinearities, even those which appear to indicate hysteresis on a force-stroke presentation. An analysis is performed on the influence of true memory effects, transient response, and uncertainty in the measurements and system mass on the precision of the procedure. The successful identification of simulated data verifies the accuracy of the identification algorithm. Tests are then conducted on three actual joint models, with incomplete state measurements typical of an actual testing environment. The ability of the procedure to estimate the complete state vector and to analyze and reconstruct the measured nonlinear characteristics is demonstrated.
Crawley, E. F.↗
An approach to sub-optimal feedback control of non-linear systems.
Nonlinear system suboptimal feedback control technique based on method for determining approximate solutions for Hamilton-Jacobi- Bellman equation
OPTIMAL CONTROL↗
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.↗