Sharif Digital Repository

This paper concerns the delay margin achievable using fractional order Proportional_Integral_Derivative controllers for linear time- invariant systems subject to variable, unknown time delays. The basic issue under investigation addresses the question: What is the largest range of time delay so that there exists a single fractional order Proportional_Integral_Derivative controller to stabilize the delay plants within the entire range? Delay margin is a fundamental measure of robust stabilization against uncertain time delays and poses a fundamental, longstanding problem that remains open except in simple, isolated cases. In this research, we develop explicit expressions of the exact delay... 

In this thesis, various fractional order controllers (FOCs), e.g., FO-PID, FO-TID, CRONE and FO-Lead/Lag, are implemented using PLC. For this purpose first, several methods are used to approximate the differentiator and integral operators. Based on these methods, the equivalent rational transfer functions of the fractional order controllers are obtained. Then, using STEP7 software, the FOCs are implemented in Siemens PLC. Moreover, to facilitate the use of the implemented FOCs in the industry and to take full advantage of the controllers, WinCC software as an interface between human and machine (HMI) is used. The WinCC software enables the operator to access the PLC through a computer (PC)... 

In this study, some of robust and exact tuning methods for fractional order PD and PI controllers are investigated in order to extract their solution existence conditions. Using aforementioned methods needs solving a set of nonlinear equations to obtain desired controller parameters which satisfy the control objectives. Hence, one of the aims of this study is to find necessary and sufficient condition on tuning specifications which guarantee the applicability of the aforementioned methods. The achievable performance region of the methods is obtained through the extracted necessary and sufficient conditions. The other aim of this work is to investigate the uniqueness of the methods... 

In the present thesis, first of all we consider a particular class of fractional order plants which have uncertainty in their time constant.In order to make the closed loop system robust against variations of the aforementioned parameter, a robust fractional order controller will be designed and the corresponding tuning rule will be expressed. By using the proposed controller, phase margin of the system will be preserved on a desired value for any value of the uncertain parameter and also gain crossover frequency of the system, in the nominal case, will be adjustable.Also another class of fractional order system will be considered. For these systems, the problem is the same as the former... 

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... 

In this thesis, a new method has been developed for tuning of fractional PI ( ) and fractional [PI] ( ) controllers for the first order plus dead-time ( ) systems. By using the performance-map method ( ) and based on phase and gain margins' criteria, a formula which is function of fractional order ( ) and normalized dead-time ( ) has been proposed for the proportional and integral coefficients. In addition, an equation has been given for the fractional order of controller to minimize the integrated absolute error ( ) index. Moreover, overshoot and settling-time of the step response of the system have been improved by dynamic setpoint weighting. Simulation results have shown that proposed... 

The main effort of this thesis is to present a numerical method to simulate and implement a special type of controllers, called proportional-weighted integral (PWI) controllers. For this purpose, at first mathematical equations of the fractional order proportional-integral controllers have been investigated in the time domain, and then by generalization of these controllers, the PWI controllers are achieved. Next the discretization of these controllers are carried out and the performance of the controllers are simulated by means of this discretization and comparison between these controllers and the conventional PI controllers has been held. After that a method for estimation of these... 

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... 

Distributed order dynamic systems are studied in this thesis. These systems incorporate distributed order operators to describe physical phenomena that naturally occur in diffusion, relaxation and viscoelasticity. Hence, the exact solutions of distributed order system of differential equations are derived analytically which are described by what we later call distributed order mittag-leffler functions. Then robust stability of distributed order LTI continuous time systems with uncertain weight functions and dynamic matrices is investigated and some sufficient conditions for stability/instability are introduced in this matter. Also, after discussing some of the properties of stability... 

Due to the simplicity and generality, design of feedback control systems in the frequency domain is among the most prominent topics in the control systems engineering. The problem of compensation means properly adjusting the loop frequency response at critical frequencies. Considering the point that the traditional methods usually use trial and error procedures for compensation, analytical design of fixed-structure controllers for exactly adjusting such values has great importance. Benefitting from the capability of fractional-order dynamics, the compensation problem is studied from three aspects in this thesis. At first according to the importance of adjusting the system frequency response... 

A servomechanism is a system with the objective of to controlling the position or velocity of a mechanical device. In many servomechanisms, one of the major performance measures is tracking the reference input in the shortest time possible. In practice, due to reasons such as modeling error and existence of disturbances, time-optimal control strategy, which is obtained using the classical calculus of variations methods, leads to the undesirable chattering phenomenon. The Proximate Time-Optimal Servomechanism control method is among the practical approaches proposed to obtain responses arbitrarily close to time-optimal, and at the same time avoid chattering. This methodology has found... 

Multi-agent systems have been attracting much attention in various fields due to their enormous potential applications, such as network control, distributed control, surveillance, etc. One of the most important issues in multi-agent systems is consensus, which refers to the problem that an agreement state is reached as a result of local communication.In order to reducing the necessary computations and the number of communications between agents, the event-triggered control was introduced and this excellent control scheme has received considerable attention of researchers.Time delay in multi-agent systems cannot be avoided duo to the signal processing and propagation. Hence, it is natural... 

Linear controllers have become popular in the industry because they have a simple structure and are easily implemented. But, they have fundamental limitations like waterbed effect and Bode’s phase gain relation. To overcome these limitations, other types of controllers have to be used like nonlinear controllers and reset ones. The hybrid integrator-gain system (HIGS) is one of these systems that has been able to overcome these limitations very well.Partial resetting and achieving variable phase in output are essential features in reset systems that have not been developed in HIGS. Here we are interested in generalizing HIGS to accomplish these features.Calculating higher-order harmonics is... 

This thesis deals with output feedback control design, adaptive output feedback control design, and adaptive actuator compensation for input-affine nonlinear systems on the basis of contraction metrics. In Section I, some necessary backgrounds on Riemannian geometry and contraction analysis are presented. In Section II, firstly, an observer for the considered class of nonlinear systems is proposed. Then, it is shown that by combining the introduced observer with state-feedback controllers in a suitable way, output tracking can be achieved. Moreover, the obtained results are extended to be used for adaptive output feedback stabilization of uncertain nonlinear systems. The introduced... 

Time delay and bandwidth limitations are common characteristics of communication channels that cause problems in direct use of classic control strategies in networked control systems. As networked systems become larger in scale and the need to share communication channels by multiple processes and controllers, this issue becomes more apparent. In recent decades, the stabilization of time-delay systems has attracted much attention. One of the most common control methods in such cases is based on the use of predictor feedback controllers. Predictor feedback controllers apply a delay-dependent or delay-independent control signal to the system. On the other hand, event-based control has many... 

Event-triggered control is used in various systems because of its capacity to optimize resources, improve responsiveness, and increase efficiency. Unlike the old time-based approaches, event-based control executes the necessary actions only when certain events or conditions occur, leading to the desired response. This strategy is used in scenarios where events occur irregularly, or are difficult to predict, and allows the system to conserve resources by maintaining the current state until the control signal needs to be updated. An event-triggered control strategy implemented using a secret sharing scheme enhances security across multiple systems; Especially in scenarios where sensitive... 

Today, the fractional-order systems are widely used in the system identification and design and implementation of control systems. By production of electrical elements with fractional-order relationship between voltage and current of their terminals, implementation of fractional-order functions with passive elements is possible. Fractional order capacitors are one of these elements. It was shown that necessary and sufficient condition for the implementation of an integer order function by passive elements is positive realness of such a function.
Like systems with integer-order, in this thesis the aim is to find corresponding conditions for implementation of fractional-order functions... 

A new generation of physical and industrial systems is evolving towards communication and information technology as communication and information technologies progress. Cyber-Physical Systems, or CPSs, are physical systems situated in a cyber environment and use communication and information technology to improve efficiency. A CPS is an integrated synthesis of the principles of "control," "communication," and "computation" from an engineering point of view, attempting to provide a comprehensive framework in which all aspects of these three fields are covered. One of the capabilities of CPSs is the ability to deal with and implement a large scale system. A group of control missions in large... 

Synchronous machines is one of the most popular machines in industry and in power plants. Because the dynamic of this machine is nonlinear, it can exhibit complex behaviors. In this project we have studied a special case in Permanent Magnet Synchronous Machines. A case in which speed of rotor, frequency, currents amplitude and voltages amplitude change in an irregular manner. This special case is called chaos. Chaos occurs for some specific values of parameters and inputs. In this study in the first step, we have tried to find the chaotic area of parameters of system (Prediction of chaos). Then in the next step, we have designed some controllers which can eliminate chaos in the system. The... 

The present thesis introduces a new method to design non-fragile controllers. The idea of design is to set the centroid of the stability region as the tuning point of two-parameter controllers. This ideahas been motivated by the fact that the centroid of a convex region belongs to a set of pointsthat have farthest distance from its boundary. In case that stability region is not convex, a correction may be needed because the centroid of non-convex region may be very near to or out of its boundary. One modified version of design method when stability region is not convex, is to find maximum convex sub-area inside stability region and set its centroid as the tuning point of controller...