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Results for “linear quadratic regulator (LQR) control”

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.

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89 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Risk-Constrained Reinforcement Learning for Inverter-Dominated Power System Controls

Here, this paper develops a risk-aware controller for grid-forming inverters (GFMs) to minimize large frequency oscillations in GFM inverter-dominated power systems. To tackle the high variability from loads/renewables, we incorporate a mean-variance risk constraint into the classical linear quadratic regulator (LQR) formulation for this problem. The risk constraint aims to bound the time-averaged cost of state variability and thus can improve the worst-case performance for large disturbances. The resulting risk-constrained LQR problem is solved through the dual reformulation to a minimax problem, by using a reinforcement learning (RL) method termed as stochastic gradient-descent with max-oracle (SGDmax). In particular, the zero-order policy gradient (ZOPG) approach is used to simplify the gradient estimation using simulated system trajectories. Numerical tests conducted on the IEEE 68-bus system have validated the convergence of our proposed SGDmax for GFM model and corroborate the effectiveness of the risk constraint in improving the worst-case performance while reducing the variability of the overall control cost.

Frequency control↗
NASA NTRS1993

Load alleviation maneuvers for a launch vehicle

This paper addresses the design of a forward-looking autopilot that is capable of employing a priori knowledge of wind gusts ahead of the flight path to reduce the bending loads experienced by a launch vehicle. The analysis presented in the present paper is only preliminary, employing a very simple vehicle dynamical model and restricting itself to wind gusts of the form of isolated spikes. The main result of the present study is that linear quadratic regulator (LQR) based feedback laws are inappropriate to handle spike-type wind perturbations with large amplitude and narrow base. The best performance is achieved with an interior-point penalty optimal control formulation which can be well approximated by a simple feedback control law. Reduction of the maximum bending loads by nearly 50% is demonstrated.

Seywald, Hans↗
NASA NTRS1991

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

Hanks, Brantley R.↗
NASA NTRS1986

Design of Linear Quadratic Regulators and Kalman Filters

AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

Lehtinen, B.↗
NASA NTRS1987

Multi-input multi-output system control for experimental aircraft

Results from the synthesis of control laws for an advanced short takeoff aircraft in a low-speed approach flight condition are given. Two of four candidate synthesis techniques are reported: direct eigenspace assignment and explicit model following via a linear quadratic regulator (LQR) formulation. A fundamental objective of this work is to obtain low-order feedback compensators, synthesized via the above techniques, and the judicious use of state estimation, thus allowing the use of a reasonable number of sensors for feedback.

Schmidt, David K.↗
NASA NTRS1993

Controls-structures-interaction dynamics during RCS control of the Orbiter/SRMS/SSF configuration

During the assembly flights of the Space Station Freedom (SSF), the Orbiter will either dock with the SSF and retract to the final berthed position, or will grapple the SSF using the Shuttle Remote Manipulator System (SRMS) and maneuver the SRMS coupled vehicles to their final berthed position. The SRMS method is expected to take approximately one to one and a half hours to complete and require periodic attitude corrections by either the Orbiter or the SSF reaction control system (RCS) or continuous control by a control moment gyro (CMG) system with RCS desaturation as required. Free drift of the attached vehicles is not currently thought to be acceptable because the desired system attitude will quickly deteriorate due to unbalanced gravity gradient and aerodynamic torques resulting in power generation problems, thermodynamic control problems, and communications problems. This paper deals with the simulation and control of the SRMS during trunnion/latch interaction dynamics and during RCS maneuvers. The SRMS servo drive joints have highly non-linear elastic characteristics which tend to degrade sensitive control strategies. In addition the system natural frequencies are extremely low and depend on the drive joint deflections and SRMS geometric position. The lowest mean period of oscillation for the Orbiter/SRMS/SSF(MB6) system in brakes hold mode positioned near the final berthed position is approximately 120 seconds. A detailed finite element model of the SRMS has been developed and used in a newly developed SRMS systems dynamics simulation to investigate the non-linear transient response dynamics of the Orbiter/SRMS/SSF systems. The present SRMS control strategy of brakes only recommended by the Charles Draper Labs is contrasted with a robust controller developed by the authors. The robust controller uses an optimal inear quadratic regulator (LQR) to optimally place the closed-loop poles of a multivariable continuous-time system within the common region of an open sector with the sector angle plus or minus 45 degrees from the negative real axis, and the left-hand side of a parallel to the imaginary axis in the complex s-plane. This guarantees that the critical damping ratio for the desired control modes is equal to or in excess of 0.707. The matrix sign function is used for solving the Riccati equations which appear in the controller design procedure. Fast and stable algorithms have recently been developed for the computation of the matrix sign function. Simulation results are given which demonstrate the potential CSI involvement for the current SRMS control system and the proposed control system.

Schliesing, J. A.↗
DOE OSTI2021

Model-based and Model-free Designs for an Extended Continuous-time LQR with Exogenous Inputs

We present an extended linear quadratic regulator (LQR) design for continuous-time linear time-invariant (LTI) systems in the presence of exogenous inputs. We first propose a model-based solution with cost minimization guarantees for states and inputs using dynamic programming (DP). The control law consists of a combination of the optimal state feedback and an additional optimal term dependent on the exogenous inputs. The control gains for the two components are obtained by solving a set of matrix differential equations. We provide these solutions for both finite horizons and steady-state cases. In the second part of the paper, we formulate a reinforcement learning (RL) based algorithm which does not need any model information except the input matrix, and can compute an approximate steady-state LQR gain using measurements of the states, the control inputs, and the exogenous inputs. Both model-based and data-driven optimal control algorithms are tested with a numerical example under different exogenous inputs showcasing the effectiveness of the designs.

Mukherjee, Sayak↗
NASA NTRS1985

SUBOPT: A CAD program for suboptimal linear regulators

An interactive software package which provides design solutions for both standard linear quadratic regulator (LQR) and suboptimal linear regulator problems is described. Intended for time-invariant continuous systems, the package is easily modified to include sampled-data systems. LQR designs are obtained by established techniques while the large class of suboptimal problems containing controller and/or performance index options is solved using a robust gradient minimization technique. Numerical examples demonstrate features of the package and recent developments are described.

Fleming, P. J.↗
NASA NTRS1991

Application of modern control design methodology to oblique wing research aircraft

A Linear Quadratic Regulator synthesis technique was used to design an explicit model following control system for the Oblique Wing Research Aircraft (OWRA). The forward path model (Maneuver Command Generator) was designed to incorporate the desired flying qualities and response decoupling. The LQR synthesis was based on the use of generalized controls, and it was structured to provide a proportional/integral error regulator with feedforward compensation. An unexpected consequence of this design approach was the ability to decouple the control synthesis into separate longitudinal and lateral directional designs. Longitudinal and lateral directional control laws were generated for each of the nine design flight conditions, and gain scheduling requirements were addressed. A fully coupled 6 degree of freedom open loop model of the OWRA along with the longitudinal and lateral directional control laws was used to assess the closed loop performance of the design. Evaluations were performed for each of the nine design flight conditions.

Vincent, James H.↗
NASA NTRS1989

Convergence of infinite dimensional sampled LQR problems - Theory and numerical results

A theory is developed for the convergence of the closed-loop solution to infinite-dimensional discrete-time linear-quadratic regulator (LQR) problems on the infinite time interval to the solution of a corresponding continuous-time LQR problem as the length of the sampling interval tends toward zero. Convergence of solutions to the operator algebraic Riccati equation and corresponding optimal feedback control gains is guaranteed under appropriate uniform stabilizability and detectability conditions and consistent sampling. Also presented are numerical results involving the optimal LQ control of a heat or diffusion equation, a hereditary or delay differential equation, and a hybrid system of ordinary and partial differential equations describing the transverse vibration of a cantilevered Voigt-Kelvin viscoelastic beam with tip mass.

Rosen, I. G.↗
NASA NTRS1987

Proof-mass actuator placement strategies for regulation of flexure during the SCOLE slew

An analysis was performed in order to find the best placement for proof-mass actuators and to determine the importance of placement, i.e., what is the sensitivity of beam flexure to actuator placement. The analysis was performed by using the NASTRAN finite element model for a flexible beam with 21 grid points on beam, by using the nonlinear DISCOS simulation of 20 deg slew and the use of a closed-loop linear quadratic regulator (lqr). Some conclusions reached are: (1) proof-mass actuators can reduce flexure amplitude and damp oscillations; (2) amplitude of deformations during slew is relatively insensitive to placement of actuators; (3) damping factor of oscillations is sensitive to actuator placement; and (4) the degree of controllability method indicates most effective placement for actuators.

Fisher, Shalom (mike)↗
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 NTRS1976

Stimulation of a turbofan engine for evaluation of multivariable optimal control concepts

The development of control systems for jet engines requires a real-time computer simulation. The simulation provides an effective tool for evaluating control concepts and problem areas prior to actual engine testing. The development and use of a real-time simulation of the Pratt and Whitney F100-PW100 turbofan engine is described. The simulation was used in a multi-variable optimal controls research program using linear quadratic regulator theory. The simulation is used to generate linear engine models at selected operating points and evaluate the control algorithm. To reduce the complexity of the design, it is desirable to reduce the order of the linear model. A technique to reduce the order of the model; is discussed. Selected results between high and low order models are compared. The LQR control algorithms can be programmed on digital computer. This computer will control the engine simulation over the desired flight envelope.

Seldner, K.↗
NASA NTRS1986

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

Banks, H. T.↗
NASA NTRS2018

Dynamics and Control of Quadcopter in Uncertain Environment

We consider problem of dynamics, control, and uncertainty quantification for quadcopter. We use the 6DOF model of quadcopter dynamics, linear quadratic regulator and linear quadratic Gaussian control of quadcopter in the presence of dynamical disturbances, measurement noise, hidden dynamical variables, dashing GPS signal, and wind gusts to predict quadcopter trajectory. We identify key sources of uncertainties and report on progress in development of a system that estimates the probability of safety-critical events using a set of algorithms based on the trajectory predictions.

uncertainty quantification↗
NASA NTRSDate not supplied

Pterodactyl: 6-DOF Integration of Guidance and Control Algorithms in Genesis

The NASA-funded Pterodactyl project seeks to advance the current state-of-the-art for entry vehicles by developing novel guidance and control technologies for Deployable Entry Vehicles. This paper builds upon the Pterodactyl architecture that employed eight individually articulating flaps with two options for guidance, bank angle modulation with the Fully Numerical Predictor Corrector Entry Guidance (FNPEG) technique and angle of attack and sideslip modulation with FNPEG uncoupled range control. These, with a linear quadratic regulator controller, have previously been presented in separate 3-DOF trajectory simulations, one for translational motion and another for rotational dynamics. This work will show results for integrated 6-DOF simulations, leveraging recent advancements in trajectory simulation tools, namely the Julia-based Genesis flight simulation tool. Results show similar performance for both schemes when compared to the previously presented 3-DOF results once the controllers were adequately tuned. Angle of attack and sideslip angle modulation necessitated a controller designed at high dynamic pressure conditions, and bank angle modulation necessitated a controller designed at lower dynamic pressure conditions. Notably, the angle of attack and sideslip modulation approach could not achieve the parachute deploy point target Mach number of 2, when only tuning the controller gains, so future work will be needed to improve guidance and control tracking.

EDL↗
NASA NTRSDate not supplied

Pterodactyl: 6-DOF Integration of Guidance and Control Algorithms in Genesis

The NASA-funded Pterodactyl project seeks to advance the current state-of-the-art for entry vehicles by developing novel guidance and control technologies for Deployable Entry Vehicles. This paper builds upon the Pterodactyl architecture that employed eight individually articulating flaps with two options for guidance, bank angle modulation with the Fully Numerical Predictor Corrector Entry Guidance (FNPEG) technique and angle of attack and sideslip modulation with FNPEG uncoupled range control. These, with a linear quadratic regulator controller, have previously been presented in separate 3-DOF trajectory simulations, one for translational motion and another for rotational dynamics. This work will show results for integrated 6-DOF simulations, leveraging recent advancements in trajectory simulation tools, namely the Julia-based Genesis package. Results show similar performance for both schemes when compared to the previously presented 3-DOF results once the controllers were adequately tuned. Angle of attack and sideslip modulation necessitated a controller designed at high dynamic pressure conditions, and bank angle modulation necessitated a controller designed at lower dynamic pressure conditions. Notably, angle of attack and sideslip modulation could not achieve the parachute deploy point target Mach number of 2, when only tuning the controller gains, thus future work will be needed to tune guidance specific parameters to achieve acceptable range targeting and guidance command tracking.

DEV↗