Department of Electrical Engineering

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We deal with the design of robust controllers for linear time invariant uncertain singularly perturbed systems using Periodic Output Feedback. The singularly perturbed uncertain system is represented using interval matrix representation. The fast and slow subsystems are obtained using interval arithmetic. The fast modes are assumed to be stable. The periodic output feedback gain is obtained for slow subsystem. The reduced control obtained from the slow subsystem is shown to stabilize the original uncertain system. A numerical example illustrates the proposed method. © 2006 IEEE.

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Proceedings of the American Control Conference

Robust control for uncertain singularly perturbed systems using periodic output feedback

Nuclear reactors of small and medium size are generally described by point kinetics model, however, this model is not valid in case of a large reactor, because in that flux shape under-goes appreciable variation with time. The behaviour of large reactor core can be explained with reasonable accuracy by spatial model like nodal model, which considers the reactor to be divided into number of regions or nodes. The thermal feedbacks which introduce nonlinearity into the problem, should be considered for realistic modeling. The spatial model of 540-MWe PHWR developed in [4] is augmented with the dynamics of coolant and fuel temperatures and a 72nd-order model is obtained. As working with such a large model is difficult from the point of view of numerical computations, the new model having 14 inputs and 14 outputs, is suitably reduced by aggregation technique to obtain a 26th-order reduced model, which is more suitable to handle. The design of spatial controller by a state feedback based on reduced model needs the availability of all the states of the system for feedback purpose. As all the states of the reactor are not accessible for measurement, one has to resort to output feedback. Also, as the stability is not guaranteed by static output feedback, here the spatial controller is designed by periodic output feedback which is static in nature and at the same time guarantees complete closed-loop pole assignability. The various zones in a large reactor are coupled and a change in the control input to any zone causes respective change in the neutron flux of the other neighbouring zones, which may not be desirable. Therefore, a decentralized controller would serve as a better option, as it ensures that the input to any zone affects corresponding zone only and other zones are not affected by it. The above idea of periodic output feedback controller design yields a gain matrix with large magnitude, which amplifies measurement noise and is difficult to implement practically. Hence, it is desirable to keep the gain low. This objective is suitably expressed as LMI problem and putting appropriate design constraints, a better gain is obtained. The nonlinear model of the 540-MWe PHWR with the controller as above is tested for the reactivity transient simulation and the results of such a simulation are presented. © 2006 IEEE.

IEEE Transactions on Nuclear Science

Spatial control of a large PHWR by decentralized periodic output feedback and model reduction techniques

In recent years, the study of sliding mode control for systems with time delay in its state dynamics has received consideration. The delays present in a system can be broadly categorized into three categories. The input delay, state delay and output delay. Input delay is caused by the transmission of a control signal over a long distance. State delay is due to transmission or transport delay among interacting elements in a dynamic system. The output delay is to delay due to sensors. A lumped function based approach is adopted in [50] to design a sliding mode control law for systems with state delay. An added uncertainty is handled in [13]. In [78], a control law has been proposed for systems where delay is present in both state and input. A state feedback discrete-time sliding mode controller for time-delay system has also been investigated in [54]. In [58], an observer based sliding mode algorithm has been proposed. The algorithm handles systems with computational delay. © Springer-Verlag Berlin Heidelberg 2006.

Lecture Notes in Control and Information Sciences

4 Multirate output feedback based discrete-time quasi-sliding mode control of time delay systems

Though continuous-time sliding mode control has a variety of desirable properties, its discrete-time counterpart does not guarantee the same performance. This is due to the fact that most of the discrete-time sliding mode control algorithms are based on reaching laws that are only approximations of continuous-time reaching laws and thus may not give a performance close to continuous-time sliding mode control. This paper presents a method of multirate output feedback based discrete-time control design which guarantees the closest possible performance for a pre-designed continuous-time sliding mode control algorithm. © 2006 IEEE.

Proceedings of the 2006 International Workshop on Variable Structure Systems, VSS'06

Multirate output feedback based digital redesign of sliding mode control algorithms

This chapter introduces various techniques of multirate output feedback based discrete-time sliding mode control of LTI systems with uncertainty. Systems satisfying the so-called matching condition [19] would be studied first. Linear systems that do not satisfy this condition would be handled next in the chapter. Finally the chapter would present a discrete-time version of the integral sliding-mode [76] control technique. This technique can be used to impart robustness to a controller structure. © Springer-Verlag Berlin Heidelberg 2006.

3 Multirate output feedback bassed discrete-time sliding mode in LTI systems with uncertainty

Several algorithms for discrete-time quasi-sliding mode control of time-delay systems with different delay and disturbance structures are proposed. Four different delay structures are considered. All the algorithms are based on multirate output feedback. Hence, they are more practical than state feedback and are less complex compared with observer-based control strategies.

IEE Proceedings: Control Theory and Applications

Output feedback discrete-time sliding mode control for time delay systems

In terminal sliding-mode control, the system states are brought to the origin in finite time using the concept of sliding-mode control. Though the theory of terminal sliding mode is well studied for continuous time systems, a discrete-time terminal sliding mode concept has not been investigated. This note analyses the applicability of terminal sliding-mode control in the discrete-time framework and discusses the problems involved in the discretization of continuous-time terminal sliding mode. The note also suggests a method to approach the discrete-time terminal sliding-mode control problem. © 2006 IEEE.

IEEE Transactions on Automatic Control

On discretization of continuous-time terminal sliding mode

This paper presents a context-based predictive coding method for lossless compression of video. For this method, we propose a model to estimate level of activity in the prediction context of a pixel. This is measured in terms of slope and the same is optimally classified to results in a small number of slope bins. After finding the slope bins, we propose a LS based method to find switched predictors to be associated with the various bins. The set of the predictors are found on a frame-by-frame basis and when it is incorporated in CALIC frame work, the proposed method results in, on an average, a better compression performance than that is obtained using recently published methods - LOPT and M-CALIC. The proposed codec has higher coding complexity but much lower decoding complexity, which is necessary for real-time video decoding. The proposed method of coding, however, has much lower complexity as compared to the LOPT method, which has same order of high coding and decoding complexity. © 2007 IEEE.

Proceedings - International Conference on Image Processing, ICIP

Least-squares based switched adaptive predictors for lossless video coding

A reaching law based discrete sliding mode control is designed for piezoelectric actuated structures to suppress the vibration in the presence of disturbance. Recursive least square method is used to identify the model and the states are estimated using Kalman filter. The performance of the controller for vibration suppression and disturbance rejection is demonstrated through simulation and experimental results.

Proceedings of the IEEE International Conference on Industrial Technology

Discrete time sliding mode control for piezoelectric actuated structures

Though continuous-time sliding mode control has a variety of desirable properties, its discrete-time counterpart does not guarantee the same performance. This is due to the fact that most of the discrete-time sliding mode control algorithms are based on reaching laws that are only approximations of continuous-time reaching laws and thus may not give a performance close to continuous-time sliding mode control. This paper presents a method for digital redesign of sliding mode control using saturation function based on state feedback. The method is extended to multirate output feedback case. It is shown that performance of the proposed controller is close to the performance of a pre-designed continuous-time sliding mode control algorithm. The method is illustrated by a numerical example. © 2006 IEEE.