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NASA NTRS1973

Digital flight control design using implicit model following.

A design procedure for determining the control gains of a discrete-time ('digital') control system is presented. The method is separable into four distinct steps: (1) the definition of closed-loop response criteria, (2) the choice of a discrete-time model which provides the desired response, (3) the determination of control gains which implicitly force the actual system to follow the desired response, and (4) the reduction of the measurement state by the introduction of an 'observer' (a form of integral-differential compensation). It is shown that a single desired response does not completely define the 'ideal' system. The response criterion generally leaves some parameters of the model unspecified, allowing two courses for improving the model: (1) definition of additional response criteria, or (2) redefinition of the discrete-time model for improved implicit model-following with the actual closed-loop system.

Stengel, R. F.↗

NASA NTRSDate not supplied

Estimation With Range Depended Sensor Model

This paper focuses on the improvement of object detection accuracy taking into account the sensor’s reading degradation as the relative range increases. The approach is based on the assumption that range measurement error depends on the actual range. Specifically, we model the measurement error as a proportional to the actual range term plus a zero-mean, Gaussian distributed, and uncorrelated process. The tracking problem is considered in a mixed continuous-discrete time domain, where the target dynamics is in continuous-time and the measurements are in discrete-time, which is an optimal choice in many tracking and navigation applications. We adopt a commonly used continuous time coordinate-uncoupled white-noise acceleration model for a point object to describe the target motion, and use Extended Kalman Filter (EKF) framework to estimate the target's state and the unknown proportionality coefficient.

Vahram Stepanyan↗

NASA NTRS1991

Hybrid state-space self-tuning control using dual-rate sampling

This paper presents a hybrid state-space self-tuning control scheme using dual-rate sampling for suboptimal digital adaptive control of linear time-invariant continuous-time multivariable stochastic systems with unknown parameters. An equivalent fast-rate discrete-time state-space innovation model (with estimated states) of the continuous-time system is constructed by using the estimated system parameters and Kalman gain. To utilize the existing optimal regional-pole assignment method developed in the continuous-time domain, the constructed fast-rate discrete-time model is converted into an equivalent continuous-time model for the development of a state-feedback optimal control law with pole placement in a specific region. The developed analog optimal control law is then converted into an equivalent pseudo-slow-rate digital control law via the proposed digital redesign technique, which can be realized via slow-rate digital electronics. The proposed method enables the development of a digitally implementable advanced control algorithm for digital adaptive control of continuous-time multivariable stochastic systems which may be unstable and/or have nonminimum phase.

Shieh, Leang S.↗

NASA NTRS2009

Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

Nixon, Douglas D.↗

NASA NTRS1988

Multirate digital control system design

Methods for multirate digital control system design are discussed. A simple method for sampling rate selection based on control bandwidths is proposed. Methods for generating a discrete-time state model of a sampled-data plant and a discrete-time equivalent to an analog cost function for a sampled-data plant are described. The succesive loop closures and linear quadratic Gaussian synthesis methods are reviewed, and a constrained optimization synthesis method is introduced. The proposed sampling rate selection, discretization, and synthesis methods are applied to two example design problems. Multirate and single-rate compensators synthesized by the different methods are compared, based on closed-loop responses, with compensators having the same real-time computation load.

Berg, Martin C.↗

NASA NTRS1985

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Gibson, J. S.↗

NASA NTRS1987

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

Gibson, J. S.↗

NASA NTRS1988

Stabilization and robustness of non-linear unity-feedback system - Factorization approach

The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.

Desoer, C. A.↗

NASA NTRS1988

Finite-dimensional modeling of network-induced delays for real-time control systems

In integrated control systems (ICS), a feedback loop is closed by the common communication channel, which multiplexes digital data from the sensor to the controller and from the controller to the actuator along with the data traffic from other control loops and management functions. Due to asynchronous time-division multiplexing in the network access protocols, time-varying delays are introduced in the control loop, which degrade the system dynamic performance and are a potential source of instability. The delayed control system is represented by a finite-dimensional, time-varying, discrete-time model which is less complex than the existing continuous-time models for time-varying delays; this approach allows for simpler schemes for analysis and simulation of the ICS.

Ray, Asok↗

NASA NTRS1989

Computational fluid dynamic control

A general technique is presented for modeling fluid, or gas, dynamic systems specifically for the development of control systems. The numerical methods which are generally used in computational fluid dynamics are borrowed to create either continuous-time or discrete-time models of the particular fluid system. The resulting equations can be either left in a nonlinear form, or easily linearized about an operating point. As there are typically very many states in these systems, the usual linear model reduction methods can be used on them to allow a low-order controller to be designed. A simple example is given which typifies many internal flow control problems. The resulting control is termed computational fluid dynamic control.

Hartley, Tom T.↗

NASA NTRS1990

Polynomial Compensation, Inversion, And Approximation

New criterion introduced for design of discrete-time compensator. Method devised for polynomial compensation, inversion, and approximation of discrete-time linear systems. Involves quadratic measure of difference between response of compensated system and desired response. Impulse response of compensated system improves as degree of polynomial increases. Compensator emphasizes matching of large initial response. Compensators used in variety of applications, including navigation systems for spacecraft, aircraft, ships, and automated manufacturing equipment.

Baram, Yoram↗

NASA NTRS1989

Integrated control-system design via generalized LQG (GLQG) theory

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.

Bernstein, Dennis S.↗

NASA NTRS1992

Model reduction using new optimal Routh approximant technique

An optimal Routh approximant of a single-input single-output dynamic system is a reduced-order transfer function of which the denominator is obtained by the Routh approximation method while the numerator is determined by minimizing a time-response integral-squared-error (ISE) criterion. In this paper, a new elegant approach is presented for obtaining the optimal Routh approximants for linear time-invariant continuous-time systems. The approach is based on the Routh canonical expansion, which is a finite-term orthogonal series of rational basis functions, and minimization of the ISE criterion. A procedure for combining the above approach with the bilinear transformation is also presented in order to obtain the optimal bilinear Routh approximants of linear time-invariant discrete-time systems. The proposed technique is simple in formulation and is amenable to practical implementation.

Hwang, Chyi↗

NASA NTRS1992

A parameterization of minimal plants

The authors present the input-normal Riccati parameterization which allows a minimal plant (A, B, C, D) to be represented completely by its B, C, and D matrices. In addition to the basic parameterization, they present useful gradient expressions for a cost functional J(A, B, C, D) when the plant is restricted to the input-normal Riccati form. The parameterization is valid for both stable and unstable, and continuous-time and discrete-time systems.

Davis, L.↗

NASA NTRS2002

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Freed, Alan D.↗

NASA NTRS1991

Alternative smoothing algorithms for on-line estimation problems

In recent years, much emphasis has been placed on the Kalman filter to solve on-line estimation problems. Smoothers, which determine state estimates at a certain time t using measurements between 0 and T, have been used primarily in off-line estimation schemes. This paper presents alternative forms of smoothers that can be used for on-line estimation problems. The alternative smoothing algorithms provide state estimates which are more refined than Kalman filtered state estimates. The alternative smoothing algorithms are illustrated in two examples. The first example considers a linear discrete-time system while the second example considers a nonlinear continuous-time system with discrete-time measurements.

Baumgartner, Eric T.↗

NASA NTRS1976

On the optimal minimum order observer-based compensator and the limited state variable feedback controller

Four design problems are considered: two on the optimal minimum order observer-based compensator design and two on the optimal limited state variable feedback controller. The problem of designing an optimal discrete time linear time-invariant observer-based compensator for the regulation of an n dimensional linear discrete time time-invariant plant with m independent outputs is considered. This is a stochastic design problem to the extent that the initial plant state is assumed to be a random vector with known first and second order statistics. The compensator parameters are obtained by minimizing the expectation, with respect to the initial conditions, of the standard cost, quadratic in the state and control vectors with the inclusion of cross terms.

Llorens-Ortiz, B.↗

NASA NTRS2010

Probabilistic Round Trip Contamination Analysis of a Mars Sample Acquisition and Handling Process Using Markovian Decompositions

A method for evaluating the probability of a Viable Earth Microorganism (VEM) contaminating a sample during the sample acquisition and handling (SAH) process of a potential future Mars Sample Return mission is developed. A scenario where multiple core samples would be acquired using a rotary percussive coring tool, deployed from an arm on a MER class rover is analyzed. The analysis is conducted in a structured way by decomposing sample acquisition and handling process into a series of discrete time steps, and breaking the physical system into a set of relevant components. At each discrete time step, two key functions are defined: The probability of a VEM being released from each component, and the transport matrix, which represents the probability of VEM transport from one component to another. By defining the expected the number of VEMs on each component at the start of the sampling process, these decompositions allow the expected number of VEMs on each component at each sampling step to be represented as a Markov chain. This formalism provides a rigorous mathematical framework in which to analyze the probability of a VEM entering the sample chain, as well as making the analysis tractable by breaking the process down into small analyzable steps.

Hudson, Nicolas↗