Reduced Order Modelling and Control Using Advanced Techniques

Abstract

In the present day of automated world, control system has become a very imminent research area. System modelling, stability testing, and controller design are the major aspects that have to be considered to obtain the desired control in the real-world applications. The control algorithms formulated using fix values of the system parameters, reveal an assured level of robustness, however, if the parameter values of the system go ahead a certain limit due to some external disturbance or some abnormal system behavior, the nominal controllers (i.e., controllers devised using fix parameter values) may at times become unsuccessful to stabilize the system or to maintain the system output at the required level. Fractional order control systems have emanated as a new control strategy in the recent literature which provides robust performance over conventional control techniques. Although a lot of research is being carried out in direction of using fractional calculus in system modelling and designing efficient control strategies for fractional controller design, however, still there is scope of development in this area. The available techniques are mathematically complex and have limited applicability. Hence in this work, an attempt has been made to carry out fractional system modelling and formulate simpler and robust controller design strategies. The analysis of any dynamical system requires a mathematical model. The real time behavior can be much easily approximated with the fractional modelling for large and complex systems. Hence, fractional order modelling of a liquid-liquid heat exchanger system has been carried out using various optimization techniques. The system has been modelled in fractional first and second order templates with time delay. Promising results have been achieved and obtained results demonstrate that the second order estimated models better fit the original data than the first order models. Higher order dynamics prove mathematically complex due to which controller design becomes a cumbersome task. Reduced order helps in simplifying the mathematical design procedure but it has to preserve the system’s prime characteristics at the same time. The reduced order modelling of a Pressurized Heavy Water Reactor (PHWR) of the sixth order has been carried out using Balanced Truncation technique. The reduced order model has been obtained by curtailing the states analogous to the smaller Hankel Singular Values (HSVs). This technique gave pronounced results to reduce the unstable sixth order PHWR system to a lower third order system while maintaining v the dominant characteristics of the higher order original system. This stride helped to concoct a controller for the higher order system with lesser intricacy. The fractional order PID controller has been designed for the higher (sixth) order model of the Pressurized Heavy Water Reactor using corresponding reduced (third) order model and stability boundary locus technique with specific gain-phase margin. The simulation results reveal that the proposed FOPID controller (designed with the reduced order model) works very well on the original higher order PHWR system. The existing controllers gave unstable results when applied to original higher order system whereas the proposed FOPID controller gave a stable response. Moreover, it has also been observed that the integer order PID controller has a higher settling time in comparison to the proposed FOPID controller. A reduction of almost 40% in the settling time has been obtained for all the operating conditions of PHWR with the proposed controller. Further, the new interval fractional order PID (INFOPID) controllers have been designed for perturbed PHWR and two area interconnected power system applications. The proposed controllers have been designed taking into account the parametric variations because most of the available controllers face performance precincts while working in an uncertain or dynamic environment. The fractional controller design has been carried out for the perturbed PHWR fractional order system using Stability Boundary Locus technique and Edge theorem. The proposed INFOPID controller has been designed for eight nuclear reactor models considering eight interval conditions (±50% variations in system parameters) for each reactor model of the PHWR. The performance of the proposed controller has been evaluated using different error criterion by comparing its performance with the existing methods. As observed from comparison, the proposed INFOPID controller provides the best performance under the given perturbed conditions as well as the varying step back operating conditions and is hence much more robust than the nominal controllers. Moreover, the proposed controller has a faster set point tracking ability as compared to existing controllers under different step back conditions. Similarly, the fractional controller design has been carried out using Kharitonov’s theorem and Stability boundary locus technique for frequency control in a perturbed two area interconnected power system. The analysis of the designed controller has been performed by changing system parameters such as governor constant, turbine time constant and step load perturbation (magnitude and location). Further, the performance of the controller has also been monitored under the effect vi of nonlinearities like Generation Rate Constraint (GRC) and Governor Dead Band (GDB). The simulation results show that proposed controller is capable of providing better performance under the given perturbed conditions than the nominal controllers. Therefore, the key objective of designing robust controllers capable of delivering improved performance under unsure operating conditions has been successfully achieved.