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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

New nonlinear control algorithms for multiple robot arms

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Tarn, T. J.↗
NASA NTRS1989

A new adaptive control approach for aerospace vehicles with parameter uncertainties

A new stochastic adaptive control structure is developed for the problem of combined parameter estimation and control of aerospace vehicles with changing parameters. Parameter uncertainties are modeled as first-order Gauss-Markov processes, and are introduced to the system dynamics through a small parameter. It is assumed that an accurate inertial measurement unit gives perfect measurements of the state variables. Since the stochastic system is assumed to be Gauss-Markov, the density function of the parameters given these measurements is conditionally Gaussian. Based on this conditionally Gaussian density, the problem of minimizing a quadratic cost over an infinite time horizon can be set up within the framework of stochastic optimal control theory. The optimal feedback control law is derived from a straightforward expansion of the Hamilton-Jacobi-Bellman equation, based on the LQG solution. The resulting nonlinear controller is applied to the pitch axis control of a space platform with uncertain moments of inertia and is shown to produce marked improvement over a fixed controller.

Hahn, Yungsun↗
NASA NTRS1996

Aerodynamic shape optimization using control theory

Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.

Reuther, James↗
NASA NTRS1987

Optimal control concepts in design sensitivity analysis

A close link is established between open loop optimal control theory and optimal design by noting certain similarities in the gradient calculations. The resulting benefits include a unified approach, together with physical insights in design sensitivity analysis, and an efficient approach for simultaneous optimal control and design. Both matrix displacement and matrix force methods are considered, and results are presented for dynamic systems, structures, and elasticity problems.

Belegundu, Ashok D.↗
NASA NTRS1973

Optimality of incompletely measurable active and passive attitude control systems

Passive attitude control systems and active systems with incomplete state measurements are only suboptimal systems in the sense of optimal control theory, since optimal systems require complete state measurements or state estimations. An optimal system, then, requires additional hardware (especially in the case of flexible spacecraft) which results in higher costs. Therefore, it is a real engineering problem to determine how much an optimal system exceeds the suboptimal system, or in other words, what is the suboptimal system's degree of optimality. The problem will be treated in three steps: (1) definition of the degree of optimality for linear, time-invariant systems; (2) a computation method using the quadratic cost functional; (3) application to a gravity-gradient stabilized three-body satellite and a spinning flexible satellite.

Schiehlen, W.↗
NASA NTRS1989

Digital robust control law synthesis using constrained optimization

Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.

Mukhopadhyay, Vivekananda↗
NASA NTRS1989

Control law synthesis and optimization software for large order aeroservoelastic systems

A flexible aircraft or space structure with active control is typically modeled by a large-order state space system of equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics and gust spectra. The control law of this multi-input/multi-output (MIMO) system is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented on an onboard digital microprocessor. A software package for performing an analog or digital control law synthesis for such a system, using optimal control theory and constrained optimization techniques is described.

Mukhopadhyay, V.↗
NASA NTRS1981

Integrated Application of Active Controls (IAAC) technology to an advanced subsonic transport project: Current and advanced act control system definition study, volume 1

An active controls technology (ACT) system architecture was selected based on current technology system elements and optimal control theory was evaluated for use in analyzing and synthesizing ACT multiple control laws. The system selected employs three redundant computers to implement all of the ACT functions, four redundant smaller computers to implement the crucial pitch-augmented stability function, and a separate maintenance and display computer. The reliability objective of probability of crucial function failure of less than 1 x 10 to the -9th power per flight of 1 hr can be met with current technology system components, if the software is assumed fault free and coverage approaching 1.0 can be provided. The optimal control theory approach to ACT control law synthesis yielded comparable control law performance much more systematically and directly than the classical s-domain approach. The ACT control law performance, although somewhat degraded by the inclusion of representative nonlinearities, remained quite effective. Certain high-frequency gust-load alleviation functions may require increased surface rate capability.

Hanks, G. W.↗
NASA NTRS1995

A comparison of design variables for control theory based airfoil optimization

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work in the area it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using either the potential flow or the Euler equations with either a conformal mapping or a general coordinate system. We have also explored three-dimensional extensions of these formulations recently. The goal of our present work is to demonstrate the versatility of the control theory approach by designing airfoils using both Hicks-Henne functions and B-spline control points as design variables. The research also demonstrates that the parameterization of the design space is an open question in aerodynamic design.

Reuther, James↗
NASA NTRSDate not supplied

Optimal Angle of Attack Control for Aerocapture Maneuvers

Recent investigations of aerocapture maneuvers have considered direct force control as a promising alternative to bank angle control. By modulating the angle of attack and sideslip angle independently, the longitudinal and lateral channels can be decoupled and thus solved separately. However, the optimal angle of attack profile for minimizing post-atmospheric propellant expenditure was previously unknown. This research applies principles of optimal control theory to numerically solve for the optimal angle of attack profile for control of the longitudinal channel. Direct methods are first employed to discretize the angle of attack profile and show that an optimal solution follows a nearly bang-bang (full lift up then full lift down) structure under a variety of conditions along the flight path angle corridor. To corroborate these results, indirect methods were also applied to scope the Optimal Control Problem (OCP) as a Two Point Boundary Value Problem (2P-BVP) which could then be solved numerically. The indirect optimization results aligned closely with the direct results, providing further evidence that a bang-bang structure provides a good approximation for the optimal angle of attack profile for aerocapture maneuvers using direct force control.

aerocapture↗