Investigation of Spatial Control Strategies with Application to Advanced Heavy Water Reactor by Ravindra Munje Balasaheb Patre & Akhilanand Tiwari

Author:Ravindra Munje, Balasaheb Patre & Akhilanand Tiwari
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

4.2.1 Linear State Feedback Control

For convenience, system (4.2)–(4.4) is again given in the following form:

(4.11)

(4.12)

where is the dimensional state vector and recall that

In particular, it is considered to minimize the quadratic performance index

(4.13)

where and are, respectively, and matrices. The solution to the problem (4.13) is the optimal linear feedback

(4.14)

where matrix in (4.14) can be obtained by solving the Riccati equation

(4.15)

The simultaneous presence of the slow and fast phenomena in the system results in ill-conditioning of the system so that it becomes difficult to solve (4.15) for finding . However, by application of singular perturbation approach, the original higher order ill-condition system is decomposed in two subsystems and the linear regulator design is carried out for two separate subsystems individually. Finally, separately designed regulators are combined to obtain control given by (4.14). For design purpose, the matrices and are assumed to be partitioned as

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