Decoupling methods and controller design in fractional order multi input multi output systems

Interest in fractional order systems has recently increased with the development of fractional order calculus. The fact that fractional order models of real systems are more accurate than integer order models has increased the studies on fractional order modeling and controller design. Since many industrial systems consist of multiple-input multiple-output (MIMO) systems, the application of fractional order modeling to MIMO systems, which provides more accurate modeling, has emerged. In this thesis, decentralized controllers are designed by using fractional order models of two-input two-output (TITO) systems, which are simple structures of MIMO systems. The integer order approximation models of fractional order TITO (FOTITO) systems are obtained by using an integer-order approximation method. Obtained approximate models are decomposed into two different subsystems using simplified and inverted decoupling methods, and stability regions are calculated with Stability Boundary Locus (SBL) method. Different test points selected from the stability regions of the subsystems are used to design decentralized PI controllers. Considering the findings, it has been observed that the controller parameters selected from the intersections of the stability regions of these subsystems ensure the stability of both TITO and FOTITO systems. In addition, decentralized controllers are designed with the Coefficient Diagram Method (CDM) for FOTITO systems with and without time delay. For this, integer order approximate models of FOTITO systems are obtained but these models are not suitable for CDM-based decentralized controller design due to high orders. Accordingly, this problem is overcome by using a model reduction method. In the next step, reduced approximate integer order models are decoupled by using the simplified and the inverted decoupling methods to obtain subsystems. Then, CDM-based decentralized controllers aredesigned for FOTITO systems by using each subsystem.