State Feedback Control Using Pole Placement
In this chapter, a state feedback-based control technique is explored for spatial control of Advanced Heavy Water Reactor (AHWR). The AHWR model with 90 state, 18 output, and 5 input variables is decomposed into slow and fast subsystems of orders 73 and 1
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State Feedback Control Using Pole Placement
3.1 Introduction Singularly perturbed systems are the systems that possess small time constants or similar ‘parasitic’ parameters which usually are neglected in simplified modeling. When those small quantities are taken into consideration, the order of the model is increased and the computation needed for control design can be time-consuming and even ill-conditioned. Singular perturbation methods have been developed for years to address the stability and robustness of those systems. Singularly perturbed systems, more generally multi-time-scale systems, often occur naturally in mathematical models due to the presence of small time constants, masses, large feedback gains, weak coupling [3, 6], etc. It was recognized long ago that the singular perturbations are present in most classical and modern control schemes based on reduced order models, and it led to the development of time-scale methods for a variety of applications including state feedback, output feedback, filter, and observer design [9, 12]. Controllers for the large-scale system are effectively designed by splitting the original system into slow and fast subsystems using singular perturbation techniques [3]. The system decoupling, achieved either by quasi-steady-state method [2] or by direct block diagonalization [4, 6, 7], results in reduction in order. For quite a small perturbation parameter ε, the quasi-steady-state is an efficient technique for decoupling. On the other hand, for systems like nuclear reactor, the perturbation parameter is not zero. Consequently, the eigenvalues of the slow and fast subsystems are no longer in the same position as the eigenvalues of the full-order system, when quasi-steady-state method is used. For that reason, block diagonalization process [6, 7] can be utilized. In this technique, accurate decoupling is accomplished. Control law synthesis for such systems may be carried out for each individual subsystem and then outcomes are merged to get a composite feedback control for the original system. The state feedback control cases are discussed in [1, 7, 8, 11]. In [1]; the technique for singularly perturbed linear system is developed using linear quadratic
© Springer Nature Singapore Pte Ltd. 2018 R. Munje et al., Investigation of Spatial Control Strategies with Application to Advanced Heavy Water Reactor, Energy Systems in Electrical Engineering, https://doi.org/10.1007/978-981-10-3014-7_3
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3 State Feedback Control Using Pole Placement
optimal design, in which a cost functional of the subsystems is taken out from the cost functional for the full-order system. Further, it is shown that a composite controller is stabilizing and is near-optimal with the optimal cost. Suzuki [11] has revealed that controllability and stabilizability features of the slow subsystem are invariant about the feedback from fast subsystem. This feature is again investigated in [8]. Furthermore, two-stage eigenvalue placement via two-stage decomposition is presented in [7]. In Chap. 2, mathematic
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