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Sridhar, B.

Publications and source records attributed to Sridhar, B..

33 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.

Patel, R. V.↗
NASA NTRS1977

Robustness in linear quadratic feedback design with application to an aircraft control problem

Some new results concerning robustness and asymptotic properties of error bounds of a linear quadratic feedback design are applied to an aircraft control problem. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed based on Linear Quadratic (LQ) theory and the results developed in this paper. The variation of the error bounds to changes in the weighting matrices in the LQ design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable error bound for variations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.

Patel, R. V.↗
NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Patel, R. V.↗
NASA NTRS1976

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

Toda, M.↗
NASA NTRS1974

Investigation of rank 2 and higher output feedback for pole placement

A common feature of several pole placement techniques is discussed and the use of a dyadic feedback matrix is presented. The limitation of this design is examined and a design involving output feedback matrices of Rank greater than one is developed as a logical extension of the dyadic feedback design. An example is presented to illustrate the design procedure.

Sridhar, B.↗
NASA NTRS1974

On the use and computation of the Jordan canonical form in system theory

This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.

Sridhar, B.↗
NASA NTRS1973

Pole-placement with constant gain output feedback

Davison (1970) has demonstrated that it is possible to assign max (m, p) poles of a linear time-invariant controllable and observable multivariable system arbitrarily close to desired locations by using constant gain output feedback. A new proof of Davison's theorem on pole placement is developed, and a system design procedure is described which offers some advantages over Davison's method. It is shown that in some cases more than max (m, p) poles can be assigned arbitrarily, and a least square design procedure is proposed to approximate the desired pole locations when it is not possible to place all the poles.

Sridhar, B.↗
NASA NTRS1973

An efficient algorithm for calculation of the Luenberger canonical form.

A new algorithm is presented to obtain the Luenberger canonical form for multivariable systems. A distinct feature of the method is that the canonical form is obtained directly and, if necessary, the similarity transformation can be computed. There is a substantial reduction in the amount of computation compared to Luenberger's method. The reduced computations along with Gaussian techniques lend greater inherent accuracy and the ability to refine the solution with additional computations. An example is presented to illustrate the technique.

Jordan, D.↗
NASA NTRS1973

Pole and zero placement in multivariable control systems

A method is proposed for designing multivariable systems based on an alternate derivation of Davison's theorem on pole placement and the solution of the nonlinear equations for the feedback gains by the least square error method. Output feedback is used to control a complex dynamical system. The freedom in design, after allocating poles, is used to place zeros and/or satisfy other design objectives. This method results in algorithms which are computationally attractive. However, this is done at a considerable sacrifice in terms of the design freedom available. For a system with m inputs and p outputs only m + p variables are available instead of mp variables.

Sridhar, B.↗
NASA NTRS1973

An algorithm for calculation of the Jordan canonical form of a matrix

Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.

Sridhar, B.↗
NASA NTRS1973

Application of pole-placement theory to helicopter stabilization systems.

This paper is concerned with the problem of designing a controller for a complex dynamical system using output feedback. The system selected for the study is the Boeing-Vertol CH-46 tandem rotor helicopter. Feedback gains are obtained by a least square solution of the nonlinear equations derived from pole-placement theory.

Sridhar, B.↗
NASA NTRS1972

An efficient algorithm for calculation of the Luenberger canonical form

An algorithm is suggested to obtain the Luenberger canonical form for multivariable systems. The method computes the canonical form directly without having to compute the transformation matrix. In addition, there is a large reduction in the number of calculations. The reduced computations along with Gaussian techniques lend to greater inherent accuracy and the ability to refine the solution with additional computations.

Jordan, D.↗
NASA NTRS1972

Pole placement with constant gain output feedback

Given a linear time invariant multivariable system with m inputs and p outputs, it was shown that p closed loop poles of the system can be preassigned arbitrarily using constant gain output feedback provided (A circumflex, B circumflex) is controllable. These data show that if (A circumflex, B circumflex, C circumflex) is controllable and observable, and Rank B circumflex = m, Rank C circumflex = p, then max (m,p) poles of the system can be assigned arbitarily using constant gain output feedback. Further, it is shown that in some cases more than max (m,p) poles can be arbitrarily assigned. A least square design technique is outlined to approximate the desired pole locations when it is not possible to place all the poles.

Sridhar, B.↗
NASA NTRS1972

A note on pole assignment

It is shown that for a controllable, linear time invariant multivariable system at least max (m,p) poles can be assigned arbitrarily. In certain cases more than max (m,p) oikes can be assigned. This result is particularly useful in designing systems for high integrity in the event of transducer failure. In such an event this design takes advantage of the unequal number of inputs and outputs so as to assure no loss in pole assignability.

Sridhar, B.↗