Control Design of Approximated Systems using Feedback Analysis of States and Output

Abstract

Scientific demonstration is a fundamental component for the investigation and outline of a dynamical systems. For the most part, extensive and complex models are acquired from physical systems. A few illustrations are automated broadcast communications, mechanical and numerous other complex systems. These systems are administered by the fractional differential, Laplace and integro-differential equations and so forth. For the investigation and plan of such systems, diminished request models are alluring that give a decent estimation of the original systems. In most recent couple of decades, remarkable exploratory work has been done on various parts of approximation of original systems. Existing techniques of approximation of original systems are having some limitations to perform the approximation of systems and obtain the stable approximated systems. New techniques are proposed that reduce these 1-D systems into their reduced order form. The proposed technique ensures the stability of the reduced order system and also provides the low approximation error as compared to other existing stability preserving techniques. This thesis is also fulfilling the limitation of previous 1-D Lower Order Approximation Systems techniques incase of continuous and discrete Gramians based Lower Order Approximation Systems. Simulation results show the effectiveness of the proposed transformation along with 1-D stability preserving technique. This thesis is also fulfilling the instability issue of lower order approximation of original systems by introducing different algorithms, static state feedback controller of lower order approximated systems incase continuous time systems, static observer based state feedback controller for continuous time systems, static state feedback controller of lower order approximated systems incase discrete time systems, static observer based state feedback controller for discrete time systems. Lower Order Approximation Systems algorithms primarily based on spectral projection strategies are composed of primary matrix computations such as fixing linear systems, matrix products, and QR factorizations. The use of these libraries enhances both the reliability and portability of the Lower Order Approximation routines. The performance will depend on the efficiency of the underlying serial and parallel computational linear algebra libraries and the verbal exchange routines. In this thesis, control design of approximated models along with different examples among different techniques are presented which shows the effectiveness of the proposed techniques.