Multivariable-control-system design concepts in failure analysis of a class of nuclear-reactor spatial-control systems

Given a symmetrical sector-control configuration for the control of the azimuthal modes of a cylindrical nuclear-power reactor and a feedback-control design which produces the required stability and transient responses of each of the dominant spatial modes of that system, the problem of system reliability, in the sense of stability with respect to sensor or control-actuator failure in any one sector, must be investigated. This paper derives a simple relationship between transfer-function elements of the multivariable closed-loop system and the reliability of that system with respect to a class of failures which can be represented by a zero transmission path in one of the loops, together with some known system input. For example, a jammed control rod no longer has any effect on the dynamics of the system, but will introduce static effects. The use of the relationship as a constraint in the final closed-loop design is discussed by reference to an example.