Control Problems of Objects with Zeros of the Transfer Function

Zeros of the control objects are the cause of difficulties in control system design process. In particular, this effect takes place in direct drive servo with elastic coupling whose finite-dimensional models have zeros. In modern literature, these difficulties are associated with the attenuation of controllability and observability of the objects with zeros. This article shows that controllability and observability properties could not explain the problem of the control system design process for objects with zeros because these properties are not invariant to the choice of basis. It is proposed to consider the completeness property of the object instead of the controllability and observability properties. The proximity of the object to singularity or to a loss of the completeness determines the difficulty of the control system design process. The article analyzes one of the methods to regularize the control system synthesis procedure.