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MODAL CONTROL TECHNIQUE
DEVELOPMENT OF OPTIMAL CONTROLLER
3 other sections not shown
20-actuator active optics actuator and sensor actuator forces analyzer astronomical telescopes coefficient matrices complex conjugate computer results computer runs conjugate transpose contour maps control channels control matrix control system described eigenvalues eigenvectors equation 22 error curve error distribution number error number evaluated flexibility matrix force-transformation compensation matrix function of number grid point 88 H nn identity matrix invert matrix Langley Research Center location of actuators matrix see eq matrix Snn mirror displacements mirror surface modal and optimal modal control law modal control loop modal control technique modal-displacement coefficients modal-displacement vector mode shapes mode-analyzer designs NASA NASTRAN number of actuators number of modes number of sensors numerical analysis observed optimal control law paper Percent of rms perfect figure-error sensor performance index potential energy primary mirror rms error left sensor points state-space differential steady-state error Substituting equation tions total number tt nn uncontrolled modes