Sharif Digital Repository

The purpose of this thesis is presenting some decoupling methods for fractional-order two input-two outputs (TITO) systems in order to using in control applications. To achieve this purpose, some methods which have been proposed for decoupling of integer-order systems have been studied and then generalized to be used in decoupling of the fractional-order systems. These methods are classified in two classes: state space based methods and transfer function based methods. Also, in this thesis the proposed decoupling methods have been used in control of some fractional-order TITO systems  

Time delay generates exponential transcendental terms in characteristic equations. Subsequently, the applied methods are narrow to assess the stability map of delayed fractional-order systems with vanishing fractions. In this case, it is convenient to approximate these equations with its integer-order counterparts to design controllers or investigating features of the systems. But, delay can cause enormous differences between characteristic of these two equations. This study offers a method to survey analytically the stability of fractional-order time delayed linear time invariant systems with infinitesimal fractions. In this method, equations are transferred to an explicit expression which... 

In this thesis, some basic concepts in distributed order systems are rewieved. BIBO stability condition of these systems is introduced and stability boundary of distributed order systems in eigenvalue plane of system dynamic matrix is found. In next section, some basic properties of stability boundary are investigated. Stability boundary changes due to changes in distribution function discussed in next part. Furthermore, finding stability areas in cases which stability boundary divides plane of system dynamic matrix to several separated areas is done. A new method for identifying order distribution function by information obtained from stability boundary presented and after that, an... 

This thesis studies undamped oscillations generated by marginally stable fractional order linear time invariant (LTI) systems. In this study, the concept of integral curve is developed for fractional order LTI systems. The proposed concept is obtained based on equivalent integer order linear time varying (LTV) systems. Then, an analytical approach is proposed to be used for harmonic analysis of such oscillations in marginally stable commensurate order LTI systems. Also, it is shown that the Q-semi norm of the limit sets for a trajectory of these systems can be analytically determined based on the Q-semi norm of the initial condition, where Q is a specific matrix. Moreover, this result is... 

Using fractional order calculus to model complex phenomena with combined behavior (i.e., dissipative, capacitive and inertia behavior) is one of the most recent research fields in the world. These accurate models lead to better understanding of the phenomena. For example, consider viscoelastic materials. In early models, dissipative behavior is separated from capacitive behavior but by using fractional order models, these two behaviors are considered simultaneously thus the complexity of the model would be reduced. To use fractional order models in real-life engineering applications, it is important to investigate the dynamics of these systems. Unfortunately, there are a few proper... 

Stabilizing periodic orbit of fractional order chaotic system via linear state feedback is the subject of this research. Firstly, for detection of the unstable periodic orbits (UPO) in fractional order chaotic systems, the famous shooting method for integer order systems is extended to fractional order systems. After that, for stabilizing the fractional order system a hypothesis is stated and a theorem is proved in a specific condition. Besides the proven theorem, some examples are presented as evidences that verify the hypothesis. So, through the hypothesis, common methods for stabilizing integer order systems can be extended to the fractional order systems. Finally, for stabilizing the... 

The PID controller has been used for a long history in control engineering and is acceptable for many real applications due to its simplicity in architecture. Hence, in many real industrial applications, the PID controller is still widely used even though lots of new control techniques have been proposed. In recent years, by developing fractional calculus in control applications, using fractional order PID controller —which is simply called — was proposed by Podlubny. Up to now, several methods of tuning fractional order PID controller has been established for time invariant systems, but dynamics of real systems are mostly time varying. Because of this fact, using adaptive control and... 

The maximum number of oscillation frequencies which can be generated in a linear integer order system at the steady state is the half of its inner dimension. In this thesis, we seek the using of fractional order delayed systems with minimum order to produce maximum number of oscillation frequencies. We found a relation between the system parameters and the oscillation frequency and then adjust the system’s coefficients so that all the roots of the characteristic equation, except the roots on the imaginary axis, lie on the left-hand side of the imaginary axis. Taking into account the diagonal and triangular lower for the state space matrices of fractional order systems with one delay, we... 

Identifying fractional systems and designing controllers for these systems is one of the leading challenges due to their limitations. Systems can have constraints on output, input, and states. These constraints make it difficult to design a controller. In this project, controller design methods for fractional-order systems with output constraints are investigated. A controller is designed for a strict feedback nonlinear system with unknown dynamics subject to asymmetric and variable output constraints, unknown direction of the controller, and unmeasurable states. To design the controller, the direct and backstepping technique is used and the Lyapunov barrier function is applied for the first... 

Today, energy production as well as environmental damage caused by non-renewable fuels has become one of the serious challenges of Society. Thermoelectrics are among the systems that can be used as a new source for cooling and heating production as well as electric energy production.Thermoelectrics can be divided into two categories: Cooler/thermal thermoelectrics and thermoelectric generators. Cooler/thermal thermoelectrics can be used as a source for producing cooling and heating in various applications, among its advantages are the non-use of environment-hazardous refrigerants, suitable for use in small spaces, not heavy and complicated, easy maintenance and low cost. It is also possible...