Results for “POLE PLACEMENT METHOD” — Page 3

NASA NTRS1989

Overview of Krylov subspace methods with applications to control problems

An overview of projection methods based on Krylov subspaces are given with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Span and seek an approximate solution the the original problem from this subspace. Thus, the original matrix problem of size N is approximated by one of dimension m typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now just becoming popular for solving nonlinear equations. It is shown how they can be used to solve partial pole placement problems, Sylvester's equation, and Lyapunov's equation.

Saad, Youcef↗

NASA NTRS1987

IECON '87: Industrial applications of control and simulation; Proceedings of the 1987 International Conference on Industrial Electronics, Control, and Instrumentation, Cambridge, MA, Nov. 3, 4, 1987

Recent advances in control-system design and simulation are discussed in reviews and reports. Among the topics considered are fast algorithms for generating near-optimal binary decision programs, trajectory control of robot manipulators with compensation of load effects via a six-axis force sensor, matrix integrators for real-time simulation, a high-level control language for an autonomous land vehicle, and a practical engineering design method for stable model-reference adaptive systems. Also addressed are the identification and control of flexible-limb robots with unknown loads, adaptive control and robust adaptive control for manipulators with feedforward compensation, adaptive pole-placement controllers with predictive action, variable-structure strategies for motion control, and digital signal-processor-based variable-structure controls.

Hartley, Tom T.↗

NASA NTRSDate not supplied

Innovative Features of NASA's Celestial Mapping System to Support Exploration in the Lunar South Pole

Introduction: NASA's Celestial Mapping System (CMS) is developed to address the need for 3D tools for planetary science investigations, mission planning, in-situ operations, in a 3D-first design constructed around a unified view of a planetary globe. At present CMS provides many critical functionalities that include 1) Equipment planning and optimized placement on Lunar surface 2) Line of sight (visibility ) analysis 3) Powerful measurement tools based on 3D terrain with realistic 3D models to represent rovers, astronauts and equipment 4) Visualization of de-rived mapping products (e.g. resource maps), and 5) Data engine for hosting new observations that are not available in other contemporary lunar data tools. CMS is built on the foundation of powerful NASA WorldWind globe engines. In near future, users will be able to simultaneously deploy CMS onto multiple hardware configurations and platforms such as Windows, Linux, iOS and Android. The users will also have the flexibility to update to the latest imagery and terrain datasets as they are being acquired (in real time) before and/or during the exploration mission. CMS is also capable of consumption and analysis of data from locally hosted and external sources. It supports Open Geospatial Consorti-um (OGC) data and file standards, with current integrations of datasets from the Astrogeology Science Center of USGS which include global and local data acquired from NASA (LRO, Clementine, Lunar Orbiter) and JAXA (SELENE/Kaguya) with the capability of integrating more datasets. With development experience in both the end-user application and planetary engine side, CMS is also able to adapt to newer Lunar cartography standards as they develop and become recognized by international geospatial panels. Overcoming Polar Distortions: 3D geospatial applications traditionally suffer from significant distortion of imagery at the poles due to following reasons – 1) distortions in the source imagery 2) Incompatible tessellation algorithm on the poles 3) map projections. In the lunar context, with the focus on the South pole, this is not acceptable. The CMS team is researching ways to address polar distortion of imagery with new tessellation algorithms and by reprojecting the data using projections that are more accurate in polar scenarios. Figure1 shows the potential error introduced by different tessellation methods, represented by the red and green circles for Shoemaker crater. There is ~2 Km difference in the placement of the crater. Line of Sight Analysis and Traverse Planning: We have developed a built-in line of sight analysis (LOS) tool in CMS that analyzes the terrain profile and obstructions and provides the visibility of a given terrain for a remote observer. Figure 2 shows the viewshed analysis on the PSR in Nobile region. The PSR was created with help of HORUS generated images. The yellow pin shows the observer location outside the PSR. The yellow area shows the visible part of PSR. The obstructed area with no visibility for the observer is shown in red. This analysis was ex-tended further to set different heights for various observers and then perform the viewshed analysis. Combining the different visibility profiles can help designing improved traverses within the crater.

Geospatial Mapping↗

NASA NTRSDate not supplied

Innovative Features of NASA's Celestial Mapping System to Support Exploration in the Lunar South Pole

Introduction: NASA's Celestial Mapping System (CMS) is developed to address the need for 3D tools for planetary science investigations, mission planning, in-situ operations, in a 3D-first design constructed around a unified view of a planetary globe. At present CMS provides many critical functionalities that include 1) Equipment planning and optimized placement on Lunar surface 2) Line of sight (visibility ) analysis 3) Powerful measurement tools based on 3D terrain with realistic 3D models to represent rovers, astronauts and equipment 4) Visualization of de-rived mapping products (e.g. resource maps), and 5) Data engine for hosting new observations that are not available in other contemporary lunar data tools. CMS is built on the foundation of powerful NASA WorldWind globe engines. In near future, users will be able to simultaneously deploy CMS onto multiple hardware configurations and platforms such as Windows, Linux, iOS and Android. The users will also have the flexibility to update to the latest imagery and terrain datasets as they are being acquired (in real time) before and/or during the exploration mission. CMS is also capable of consumption and analysis of data from locally hosted and external sources. It supports Open Geospatial Consorti-um (OGC) data and file standards, with current integrations of datasets from the Astrogeology Science Center of USGS which include global and local data acquired from NASA (LRO, Clementine, Lunar Orbiter) and JAXA (SELENE/Kaguya) with the capability of integrating more datasets. With development experience in both the end-user application and planetary engine side, CMS is also able to adapt to newer Lunar cartography standards as they develop and become recognized by international geospatial panels. Overcoming Polar Distortions: 3D geospatial applications traditionally suffer from significant distortion of imagery at the poles due to following reasons – 1) distortions in the source imagery 2) Incompatible tessellation algorithm on the poles 3) map projections. In the lunar context, with the focus on the South pole, this is not acceptable. The CMS team is researching ways to address polar distortion of imagery with new tessellation algorithms and by reprojecting the data using projections that are more accurate in polar scenarios. Figure1 shows the potential error introduced by different tessellation methods, represented by the red and green circles for Shoemaker crater. There is ~2 Km difference in the placement of the crater. Line of Sight Analysis and Traverse Planning: We have developed a built-in line of sight analysis (LOS) tool in CMS that analyzes the terrain profile and obstructions and provides the visibility of a given terrain for a remote observer. Figure 2 shows the viewshed analysis on the PSR in Nobile region. The PSR was created with help of HORUS generated images. The yellow pin shows the observer location outside the PSR. The yellow area shows the visible part of PSR. The obstructed area with no visibility for the observer is shown in red. This analysis was ex-tended further to set different heights for various observers and then perform the viewshed analysis. Combining the different visibility profiles can help designing improved traverses within the crater.

Geospatial Mapping↗

NASA NTRS2011

Dawn Statistical Maneuver Design for Vesta Operations

In July of 2011 the Dawn spacecraft is scheduled to begin orbital operations at Vesta, a large main-belt asteroid. Dawn is a NASA Discovery mission that uses solar-electric low-thrust ion propulsion for both interplanetary cruise and orbital operations. Navigating between the Dawn project's four targeted science orbits at Vesta requires a plan that accounts for uncertainties not only in thrust execution, orbit determination, and other spacecraft forces, but also large uncertainties in characteristics of Vesta - such as the asteroid's gravity field and pole orientation. Accommodating these uncertainties requires strategic use of low-thrust maneuvers reserved for statistical trajectory corrections. This paper describes the placement and evaluation of low-thrust statistical maneuvers during two key phases of the Vesta mission along with a discussion of the tools, constraints, and methods used to plan those maneuvers.

Solar Electric Propulsion↗

NASA NTRS1982

Pole placement and order reduction in two-time-scale control systems through Riccati iteration

A transformation of variables taken from singular perturbations may be applied to two-time-scale linear systems in state space form to reduce the system to block-diagonal form with slow and fast modes decoupled. The transformation is easily computed by applying the new Riccati iteration. The iteration yields a solution to the nonsymmetric algebraic Riccati equation obtained by partitioning the original system matrix A. The numerical procedure is initiated with the trivial iterate L(0) = 0, and is globally convergent to the desired unique time scale decoupling solution. After transformation, the decoupled system may be used in controller design to achieve exact closed loop pole placement in the slow subsystem without altering the poles of the fast subsystem. The decoupled form may also be used to reduce system order by wetting a small parameter to zero. Provided the fast subsystem is stable, the order reduction can be expected to yield a good approximation to the original system. These methods are demonstrated using the 16th order linear model of a turbofan engine.

Anderson, L. R.↗

NASA NTRS1985

Eigenvalue Placement and Stabilization by Constrained Optimization

A pole placement algorithm is proposed which uses constrained nonlinear optimization techniques on a finite dimensional model of a linear n degree of freedom system. Low order feedback control is assumed where r poles may be assigned; r being the rank of the sensor coefficient matrix. It is shown that by combining feedback control theory methods with optimization techniques, one can ensure the stability characteristics of a system, and can alter its transient response.

Decaro, S. M.↗

NASA NTRS1988

Linear quadratic regulators with eigenvalue placement in a specified region

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

Shieh, Leang S.↗

NASA NTRS1986

Design of multivariable controllers for robot manipulators

The paper presents a simple method for the design of linear multivariable controllers for multi-link robot manipulators. The control scheme consists of multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and achieves pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. The two controllers are independent of each other and are designed separately based on the linearized robot model and then integrated in the overall control scheme. The proposed scheme is simple and can be implemented for real-time control of robot manipulators.

Seraji, H.↗

NASA NTRS1983

Experimental implementation of parameter adaptive control on a free-free beam

A method for identifying modal parameters has been integrated with a modal control scheme and implemented on an experimental beam at the NASA Langley Research Center. This work is the culmination of several studies to develop adaptive control schemes for large flexible spacecraft. The identification scheme is an equation-error technique which generates modal frequency and damping estimates on-line from a set of distributed displacement measurements. The control law is a modal pole placement technique with the objective of vibration suppression. Integration of the identification and control schemes is achieved through a series of tests which validate the identified parameters before they are used for control gain updating. Results using a low order controller show that control gains can be updated in real time based on the validated parameters to improve the performance of the closed loop system. Important factors in the implementation are the test criterion and the a priori assumption of mode shapes.

Williams, J. P.↗

NASA NTRS1988

An approach to simultaneous system design. II - Nonswitching gain and dynamic feedback compensation by algebraic geometric methods

This paper studies structured uncertainty problems in feedback system design, considers a compact parameterization of the space of linear dynamical systems and introduces 'base points' and 'critical points' as two algebraic-geometric objects that have significance in sensitivity and robustness studies, respectively. Using the Nevanlinna-Pick interpolation theory, the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one-parameter family of plants. A recent result due to Kharitonov, on the simultaneous stability of a parameterized family of polynomials, leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants. Furthermore, the author considers 'simultaneous pole placement' of an r-tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system. The concept of 'nondegenerate' and 'twisted' r-tuples of plants is introduced as the pole placement problem is studied via Schubert enumerative geometry as an intersection problem on the associated Grassmannian. Various other design problems, viz., the strong stabilization problem and the dead beat control problem, are also considered.

Ghosh, Bijoy K.↗

NASA NTRS1992

Numerical analysis of right-half plane zeros for a single-link manipulator

The purpose of this research is to further develop an understanding of how nonminimum phase zero location is affected by structural link design. As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links become more of an issue in controls problems. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. The research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixes, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to inverse dynamic algorithms currently under development at Georgia Tech.

Girvin, Douglas Lynn↗

NASA NTRS1991

Numerical analysis of nonminimum phase zero for nonuniform link design

As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links becomes more of an issue in control. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. This research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixed, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to the inverse dynamic algorithms that are currently under development.

Girvin, Douglas L.↗