Ravindra Munje

Discrete-Time Sliding Mode Spatial Control of Advanced Heavy Water Reactor

This brief presents the design of a discrete-time sliding mode control (DSMC) for spatial power stabilization of advanced heavy water reactor (AHWR). Mathematical model of AHWR is represented by 90 first-order nonlinear differential equations with 18 outputs and five inputs. The linear model is obtained by linearizing nonlinear equations over the rated power. This linear model is found to be highly ill conditioned and is possessing three-time-scale property. Initially, the linear model is transformed into block diagonal form to separate slow, fast 1, and fast 2 subsystems and then DSMC is designed using slow subsystem alone since fast 1 and fast 2 subsystems are stable. The proposed DSMC strategy is designed using the constant plus proportional rate reaching law with matched disturbance. Finally, the nonlinear multivariable model of AHWR is simulated with the designed controller and the results are generated under different transients. The efficacy of the proposed DSMC is demonstrated with the comparison of prevalent controllers in the literature and the performance is evaluated under the same transient levels.

Periodic Output Feedback for Spatial Control of AHWR: A Three-Time-Scale Approach

This paper presents a novel technique of designing Periodic Output Feedback (POF) based controller for three-timescale systems. This design method is investigated for spatial control of Advanced Heavy Water Reactor (AHWR). The numerically ill-conditioned system of AHWR is first decomposed into three subsystems, namely, slow, fast1 and fast 2 by direct block-diagonalization and then a composite controller is designed which provides an output injection gain. This output injection gain has been used to compute POF gain, which is then applied to the vectorized nonlinear model of AHWR to achieve spatial control. This controller is tested via simulations carried out under different transient conditions and the results of simulation are presented.

Multirate output feedback based controllers for non-linear inverted pendulum system

Multirate output feedback (MROF) techniques have attracted the interest of many researchers for the design of controller, as these methods are based on output feedback and are at the same time capable of assigning arbitrary dynamical characteristics to the closed loop system. Fast output sampling (FOS) is a kind of MROF, in which the states of the system can be computed from the output of the system. In this paper, different techniques of FOS based controllers are investigated for non-linear system of inverted pendulum (IP). Control laws are designed using linear model of IP system. The first control law is constructed based on past output observations. In second control law, past output observations alongwith past input is used for design purpose. However, in third case, discrete-time sliding mode control (DSMC) in combination with FOS feedback, presented in second control law, is formulated. Simulations have been carried out using non-linear model of IP system developed in MatLab/Simulink environment. From simulations it is observed that, the performance of FOS feedback based DSMC is comparatively better than other control techniques.

Investigation of Spatial Control Strategies for AHWR: A Comparative Study

Large nuclear reactors such as the Advanced Heavy Water Reactor (AHWR), are susceptible to xenon-induced spatial oscillations in which, though the core average power remains constant, the power distribution may be nonuniform as well as it might experience unstable oscillations. Such oscillations influence the operation and control philosophy and could also drive safety issues. Therefore, large nuclear reactors are equipped with spatial controllers which maintain the core power distribution close to desired distribution during all the facets of operation and following disturbances. In this paper, the case of AHWR has been considered, for which a number of different types of spatial controllers have been designed during the last decade. Some of these designs are based on output feedback while the others are based on state feedback. Also, both the conventional and modern control concepts, such as linear quadratic regulator theory, sliding mode control, multirate output feedback control and fuzzy control have been investigated. The designs of these different controllers for the AHWR have been carried out using a 90th order model, which is highly stiff. Hence, direct application of design methods suffers with numerical ill-conditioning. Singular perturbation and time-scale methods have been applied whereby the design problem for the original higher order system is decoupled into two or three subproblems, each of which is solved separately. Nonlinear simulations have been carried out to obtain the transient responses of the system with different types of controllers and their performances have been compared.

Periodic Output Feedback

This chapter examines periodic output feedback (POF) control scheme for spatial control of Advanced Heavy Water Reactor (AHWR) based on three-time-scale decomposition. The numerically ill-conditioned system of AHWR is first decoupled into three subsystems of lower order, namely, slow, fast 1, and fast 2 by three-stage linear transformation and then a composite controller is designed which provides an output injection gain. Output injection matrix is then used to calculate POF gain, which is applied to the vectorized nonlinear system of AHWR to attain control of spatial power. Effectiveness of the presented control scheme is evaluated via simulations generated under various transient situations. Performance of this scheme is also compared with the fast output sampling control scheme.

Comparison of Spatial Control Techniques

Large nuclear reactors are prone to xenon oscillations in which despite the fact that the total power remains constant, the power distribution in the core may be nonuniform as well as it might experience unstable oscillations. Such oscillations affect the operation and control philosophy of core and could also drive issues related to safety. Thus, spatial control is required. In this chapter, several types of spatial controllers have been examined for Advanced Heavy Water Reactor (AHWR). Some of these designs are based on output feedback whereas the others are based on state feedback and both the conventional and modern control concepts have been investigated. The designs of controllers have been carried out using a 90th order model of AHWR, which is extremely stiff. As a result, straight forward application of these methods suffers with numerical ill-conditioning. Singular perturbation and time-scale methods have been applied whereby the design problem for the original high order system is decoupled into two or three subproblems, each of which is worked out independently. Nonlinear simulations have been carried out to get the transient responses of the system with all the controllers and their performances have been evaluated on the similar time scale.

Fast Output Sampling Technique

In this chapter, spatial control of Advanced Heavy Water Reactor (AHWR) is achieved by fast output sampling (FOS) based control strategy. State feedback control designed using two time-scale approach is realized using FOS feedback gain. As a result, the system states are not needed for feedback. The effectiveness of the controller has been confirmed by nonlinear simulation of transient behavior of AHWR system. Overall controller performance is observed to be acceptable.

Sliding Mode Control

In this chapter, sliding mode control (SMC) is designed for spatial control of Advanced Heavy Water Reactor (AHWR). Nonlinear system of AHWR has 90 states, 18 outputs, and 5 inputs. When linearized, the model is observed to be highly stiff. Therefore, direct application of the control method to the full-order system results into numerical ill-conditioning. Hence, full-order system of AHWR is separated into slow and fast subsystems of dimensions 73 and 17, respectively, by direct block diagonalization and sliding mode controller design is carried out using simply slow subsystem states. Afterward, SMC for full-order system is formulated by straightforward linear transformation matrices. In this, it is also demonstrated that slow subsystem SMC results in a sliding mode motion for full-order system. Nonlinear dynamic simulations have been carried out to show efficacy and robustness of the technique.

Discrete-Time Sliding Mode Control

In this chapter, design of discrete-time sliding mode control (DSMC) for spatial stabilization of Advanced Heavy Water Reactor (AHWR) is demonstrated. AHWR system is represented by 90 first-order nonlinear differential equations with 18 outputs and 5 inputs. Initially, highly ill-conditioned linear system of AHWR is transformed into block diagonal form to have separate slow, fast 1, and fast 2 subsystems. Fast 1 and fast 2 subsystems are observed to be stable, hence DSMC is designed using slow subsystem alone. The constant plus proportional rate reaching law and power rate reaching law are used for design purpose. This nonlinear multivariable model of AHWR is simulated with the designed controls and results are generated. Performances are compared under the same transient conditions.

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 17, respectively, by two-stage linear transformation. As the fast subsystem is observed to be stable, controller is designed only for the slow subsystem and then composite controller is derived for the original system. Vectorized nonlinear model of AHWR is simulated with presented composite controller and performance is tested under various transient conditions. It is noticed that xenon oscillations are effectively suppressed and performance is found to be acceptable.