Search NASA⌕ Search

SEARCH · Search NASA

Results for “linear quadratic regulator”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Accelerometer placement in active flutter suppression systems

An elementary study of the placement of accelerometers when used as sensors in active flutter suppression systems is presented. The model analyzed is a two-dimensional typical section with various combinations of leading- and trailing-edge controllers. The relationship between the control surface placement and accelerometer placement is examined. The results for the numerical examples presented show that accelerometers must be on the same side of the center of gravity as the control surface or right half-plane transmission zeros will arise. The detrimental effects of the right half-plane zeros are discussed in the context of linear-quadratic-regulator plus loop-transfer-recovered observer designs.

Liebst, Bradley S.↗
NASA NTRS1986

The design of a turboshaft speed governor using modern control techniques

The objectives of this program were: to verify the model of off schedule compressor variable geometry in the T700 turboshaft engine nonlinear model; to evaluate the use of the pseudo-random binary noise (PRBN) technique for obtaining engine frequency response data; and to design a high performance power turbine speed governor using modern control methods. Reduction of T700 engine test data generated at NASA-Lewis indicated that the off schedule variable geometry effects were accurate as modeled. Analysis also showed that the PRBN technique combined with the maximum likelihood model identification method produced a Bode frequency response that was as accurate as the response obtained from standard sinewave testing methods. The frequency response verified the accuracy of linear models consisting of engine partial derivatives and used for design. A power turbine governor was designed using the Linear Quadratic Regulator (LQR) method of full state feedback control. A Kalman filter observer was used to estimate helicopter main rotor blade velocity. Compared to the baseline T700 power turbine speed governor, the LQR governor reduced droop up to 25 percent for a 490 shaft horsepower transient in 0.1 sec simulating a wind gust, and up to 85 percent for a 700 shaft horsepower transient in 0.5 sec simulating a large collective pitch angle transient.

Delosreyes, G.↗
NASA NTRS1988

Flight penetration of wind shear: Control strategies

Wind shear is a dangerous condition where there is a sharp change in the direction and magnitude of the wind velocity over a short distance or time. This condition is especially dangerous to aircraft during landing and takeoff and can cause a sudden loss of lift and thereby height at a critical time. A numerical simulation showed the effective performance of the Linear Quadratic Regulator and the Nonlinear Inverse Dynamics controllers. The major conclusions are listed and discussed.

Joshi, Amit S.↗
NASA NTRS1988

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Rosen, I. G.↗
NASA NTRS1987

Linear quadratic stationkeeping on travelling ellipses

An automatic controller for Space Shuttle stationkeeping or formationkeeping is presented. The controller, which is a candidate for future on-orbit autopilot enhancement, uses a fuel 'optimized' limit cycle trajectory in a feedforward loop for precise control at nonequilibrium set points. Disturbance rejection is accomplished by a discrete time, linear quadratic regulator, which is employed for tracking of the feedforward model. Feedback gain selection is done to provide good limit cycling performance and low fuel consumption. Velocity correlations are carried out by use of a pseudo 6 degree-of-freedom jet selection scheme. Results indicate that 20 ft precision can be achieved using current sensors.

Adams, Neil J.↗
NASA NTRS1988

Structural tailoring and feedback control synthesis - An interdisciplinary approach

Structural tailoring provides an attractive method to optimize the performance of actively controlled space structures. However, the simultaneous optimization of control gains and structural properties often becomes prohibitively expensive for large systems and physical insight is often lost in the resulting control law. This paper presents a method for optimization of the closed loop structural system using only structural tailoring. Optimal Linear Quadratic Regulator (LQR) control theory is used with weighting matrices chosen based on physical considerations. The LQR control law depends only on two scalar gains and the structural properties. Hence, the closed loop-performance can be expressed in terms of the structural parameters. Results are given for a beam and a truss-beam to show the simplicity of the method and the importance of structural tailoring to increase dynamic performance and to reduce the control effort.

Belvin, W. Keith↗
NASA NTRS1988

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gibson, J. S.↗
NASA NTRS1988

Dynamic evaluation of a traction-drive joint for space telerobots

Presented is an analysis and evaluation of a prototype traction-drive joint for robotic manipulators, developed under NASA sponsorship. A dynamic model is developed using the Lagrange formulation. Controllability, observability, dynamic stability, and response characteristics of the joint to test inputs are studied. A linear quadratic regulator (LQR) is implemented on the joint model to determine a basis for evaluating the performance of the traction-drive joint under servo control. An evaluation of the results and directions for future investigations are presented.

Desilva, Clarence W.↗
NASA NTRS1989

Optimization of structure and control system

The objective of this study is the simultaneous design of the structural and control system for space structures. This study is focused on considering the effect of the number and the location of the actuators on the minimum weight of the structure, and the total work done by the actuators for specified constraints and disturbance. The controls approach used is the linear quadratic regulator theory with constant feedback. At the beginning collocated actuators and sensors are provided in all the elements. The actuator doing the least work is removed one at a time, and the structure is optimized for the specified constraints on the closed-loop eigenvalues and the damping parameters. The procedure of eliminating an actuator is continued until an acceptable design satisfying the constraints is obtained. The study draws some conclusions on the trade between the total work done by the actuators, and the optimum weight and the number of actuators.

Khot, N. S.↗
NASA NTRS1989

On the state estimation of structures with second order observers

The use of Linear Quadratic Regulator (LQR) control synthesis techniques implies the availability of full state feedback. For vibration control of structures, usually only a limited number of states are measured from which an observer model reconstructs the full state. It is shown that using second order observers is a viable technique for reconstructing the unmeasured states of structures under mildly restrictive conditions. Moreover, the computational advantages of the second order observer as compared to a first order observer indicate that significantly larger observer models may be utilized. Numerical examples are used to demonstrate the performance of second order observers. The implications of second order observers in the development of Controls-Structures Interaction (CSI) technology is discussed.

Belvin, W. Keith↗
NASA NTRS1987

Reducing model uncertainty effects in flexible manipulators through the addition of passive damping

An important issue in the control of practical systems is the effect of model uncertainty on closed loop performance. This is of particular concern when flexible structures are to be controlled, due to the fact that states associated with higher frequency vibration modes are truncated in order to make the control problem tractable. Digital simulations of a single-link manipulator system are employed to demonstrate that passive damping added to the flexible member reduces adverse effects associated with model uncertainty. A controller was designed based on a model including only one flexible mode. This controller was applied to larger order systems to evaluate the effects of modal truncation. Simulations using a Linear Quadratic Regulator (LQR) design assuming full state feedback illustrate the effect of control spillover. Simulations of a system using output feedback illustrate the destabilizing effect of observation spillover. The simulations reveal that the system with passive damping is less susceptible to these effects than the untreated case.

Alberts, T. E.↗
NASA NTRS1989

On the state estimation of structures with second order observers

The use of the linear quadratic regulator control synthesis techniques implies the availability of full state feedback. For vibration control of structures, usually only a limited number of states are measured from which an observer model reconstructs the full state. This paper shows that using second-order observers is a viable technique for reconstructing the unmeasured states of structures under mildly restrictive conditions. Moreover, the computational advantages of the second-order observer, as compared to a first-order observer, indicate that significantly larger observer models may be utilized. Numerical examples are used to demonstrate the performance of second-order observers. The implications of second-order observers in the development of the control/structures interaction technology is discussed.

Belvin, W. Keith↗
NASA NTRS1989

An adaptive guidance law for single stage to low earth orbit

An adaptive guidance algorithm based on a cubic spline representation of the ascent profile and imposition of a dynamic pressure constraint is studied for a single stage to low earth orbit. The flight path is divided into initial and terminal phases. In the initial phase, fully adaptive, and in the terminal phase, semi-adaptive, guidance schemes are used. The cubic spline paqrameters are determined by gradient optimization for maximum payload to orbit. In the terminal phase, a linear quadratic regulator is used to derive the optimal feedback gains to keep the vehicle close to the nominal path. The computational aspects of the guidance algorithm are examined and criteria are developed to ensure stability and convergence.

Pamadi, Bandu N.↗
NASA NTRS1989

Periodic-disturbance accommodating control of the Space Station for asymptotic momentum management

Periodic-disturbance accommodating control is investigated for asymptotic momentum management of control moment gyros used as primary actuating devices for the Space Station. The proposed controller utilizes the concepts of quaternion feedback control and periodic-disturbance accommodation to achieve oscillations about the constant torque equilibrium attitude, while minimizing the control effort required. Three-axis coupled equations of motion, written in terms of quaternions, are derived for roll/yaw controller design and stability analysis. The quaternion feedback controller designed using the linear-quadratic regulator synthesis technique is shown to be robust for a wide range of pitch angles. It is also shown that the proposed controller tunes the open-loop unstable vehicle to a stable oscillatory motion which minimizes the control effort needed for steady-state operations.

Warren, Wayne↗
NASA NTRS1989

Perturbation guidance for aerocruise with bounded control

A perturbation guidance algorithm is developed for the constant-altitude portion of the orbital-plane change maneuver, called aerocruise. It is obtained by solving a linear-quadratic regulator problem in terms of the perturbed state and control variables. The regulator problem with hard control-variable constraints is then studied. For the two-control-variable case, the simulation results show that the bounded-control algorithm gives better performance than that obtained using a limiter for the case where control variables exceed the bounds.

Hull, David G.↗
NASA NTRS1989

Periodic-disturbance accommodating control of the space station for asymptotic momentum management

Periodic-disturbance accommodating control is investigated for asymptotic momentum management of control moment gyros used as primary actuating devices for the Space Station. The proposed controller utilizes the concepts of quaternion feedback control and periodic-disturbance accommodation to achieve oscillations about the constant torque equilibrium attitude, while minimizing the control effort required. Three-axis coupled equations of motion, written in terms of quaternions, are derived for roll/yaw controller design and stability analysis. The quaternion feedback controller designed using the linear-quadratic regulator synthesis technique is shown to be robust for a wide range of pitch angles. It is also shown that the proposed controller tunes the open-loop unstable vehicle to a stable oscillatory motion which minimizes the control effort needed for steady-state operations.

Warren, Wayne↗
NASA NTRS1989

Guidance and Control strategies for aerospace vehicles

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Hibey, J. L.↗
NASA NTRS1989

Optimization of the structural and control system for LSS with reduced-order model

The objective is the simultaneous design of the structural and control system for space structures. The minimum weight of the structure is the objective function, and the constraints are placed on the closed loop distribution of the frequencies and the damping parameters. The controls approach used is linear quadratic regulator with constant feedback. A reduced-order control system is used. The effect of uncontrolled modes is taken into consideration by the model error sensitivity suppression (MESS) technique which modified the weighting parameters for the control forces. For illustration, an ACOSS-FOUR structure is designed for a different number of controlled modes with specified values for the closed loop damping parameters and frequencies. The dynamic response of the optimum designs for an initial disturbance is compared.

Khot, N. S.↗