An application of eigenspace methods to symmetric flutter suppression

An eigenspace assignment approach to the design of parameter insensitive control laws for linear multivariable systems is presented. The control design scheme utilizes flexibility in eigenvector assignments to reduce control system sensitivity to changes in system parameters. The methods involve use of the singular value decomposition to provide an exact description of allowable eigenvectors in terms of a minimum number of design parameters. In a design example, the methods are applied to the problem of symmetric flutter suppression in an aeroelastic vehicle. In this example the flutter mode is sensitive to changes in dynamic pressure and eigenspace methods are used to enhance the performance of a stabilizing minimum energy/linear quadratic regulator controller and associated observer. Results indicate that the methods provide feedback control laws that make stability of the nominal closed loop systems insensitive to changes in dynamic pressure

Root locii for systems defined on Hilbert spaces

The root locus is an important tool for analysing the stability and time constants of linear finite-dimensional systems as a parameter, often the gain, is varied. However, many systems are modelled by partial differential equations or delay equations. These systems evolve on an infinite-dimensional space and their transfer functions are not rational. In this paper a rigorous definition of the root locus for infinite-dimensional systems is given and it is shown that the root locus is well-defined for a large class of infinite-dimensional systems. As for finite-dimensional systems, any limit point of a branch of the root locus is a zero. However, the asymptotic behaviour can be quite different from that for finite-dimensional systems. This point is illustrated with a number of examples. It is shown that the familiar pole-zero interlacing property for collocated systems with a Hermitian state matrix extends to infinite-dimensional systems with self-adjoint generator. This interlacing property is also shown to hold for collocated systems with a skew-adjoint generator

Flutter suppression using eigenspace freedoms to meet requirements

A constrained optimization methodology has been developed which allows specific use of eigensystem freedoms to meet design requirements. A subset of the available eigenvector freedoms was employed. The eigenvector freedoms associated with a particular closed-loop eigenvalue are coefficients of basis vectors which span the subspace in which that closed-loop vector must lie. Design requirements are included as a vector of inequality constraints. The procedure was successfully applied to develop an unscheduled controller which stabilizes symmetric flutter of an aeroelastic vehicle to a dynamic pressure 44 percent above the open-loop flutter point. The design process proceeded from full-state feedback to the inclusion of a full-order observer to the selection of an eighth-order controller which preserved the full-state sensitivity characteristics. Only a subset of the design freedoms was utilized (i.e., assuming full-state feedback only four out of 26 eigenvectors were used, and no variations were made in the closed-loop eigenvalues). Utilization of additional eigensystem freedoms could further improve the controller

A new momentum management controller for the space station

A new approach to CMG (control moment gyro) momentum management and attitude control of the Space Station is developed. The control algorithm utilizes both the gravity-gradient and gyroscopic torques to seek torque equilibrium attitude in the presence of secular and cyclic disturbances. Depending upon mission requirements, either pitch attitude or pitch-axis CMG momentum can be held constant: yaw attitude and roll-axis CMG momentum can be held constant, while roll attitude and yaw-axis CMG momentum cannot be held constant. As a result, the overall attitude and CMG momentum oscillations caused by cyclic aero-dynamic disturbances are minimized. A state feedback controller with minimal computer storage requirement for gain scheduling is also developed. The overall closed-loop system is stable for + or - 30 percent inertia matrix variations and has more than + or - 10 dB and 45 deg stability margins in each loop

Using deflation in the pole assignment problem with output feedback

A direct algorithm is suggested for the computation of a linear output feedback for a multi input, multi output system such that the resultant closed-loop matrix has eigenvalues that include a specified set of eigenvalues. The algorithm uses deflation based on unitary similarity transformations. Thus researchers hope the algorithm is numerically stable; however, this has not been proven as yet

Theoretical constraints in the design of multivariable control systems

The research being performed under NASA Grant NAG1-1361 involves a more clear understanding and definition of the constraints involved in the pole-zero placement or assignment process for multiple input, multiple output systems. Complete state feedback to more than a single controller under conditions of complete controllability and observability is redundant if pole placement alone is the design objective. The additional feedback gains, above and beyond those required for pole placement can be used for eignevalue assignment or zero placement of individual closed loop transfer functions. Because both poles and zeros of individual closed loop transfer functions strongly affect the dynamic response to a pilot command input, the pole-zero placement problem is important. When fewer controllers than degrees of freedom of motion are available, complete design freedom is not possible, the transmission zeros constrain the regions of possible pole-zero placement. The effect of transmission zero constraints on the design possibilities, selection of transmission zeros and the avoidance of producing non-minimum phase transfer functions is the subject of the research being performed under this grant

Optimum linear adaptive design of dominant type systems with large parameter variations

Optimum design of compensating feedback control system with parameter variation