Affine Parameterization of Cascade Control with Time Delays

The cascade control architecture is a standard solution in control engineering practice for industrial plants with considerable time delays. In this paper, the set of all stabilizing cascade controllers in parametric form is presented for such plants. The parameterization is based on the use of the so-called RQ meromorphic functions expressing the time delay character of the plant and the controller. The parameter enters any closed-loop transfer function in an affine manner. The performance is specified in terms of disturbance rejection and the “slave” controller gain is considered as the key parameter of the affine parameterization. Unlike in most literature on the subject, the primary controlled output is not considered to be directly dependent on the secondary controlled variable. The disturbance rejection potentials are discussed for various options of controlled plants with delays and the varying role of the secondary controlled output option is investigated.