Sharif Digital Repository

In this thesis, a new general state space form for uncertain LTI-fractional order system subjected to interval and polytopic uncertainties is introduced. Robust stability analysis and robust stabilization of presented system are investigated. Fractional derivative order assumed to be a known constant. Sufficient conditions in terms linear matrix inequalities (LMIs) are concluded to check the robust stability of the presented system. Then, these results are extended to derive some sufficient LMI conditions to design a state feedback controller in order to stabilize the mentioned uncertain system robustly. Effectiveness and correctness of presented sufficient conditions and application of... 

In this thesis, we derive the analytic condition that linear time invariant fractional order system being positive real. Also, by inspiration of positive real condition, we derive the analytic condition for linear time invariant fractional order system that their imaginary part of frequency response being negative. Intended conditions for single input single output systems are derived in the form of necessary conditions in one way and derived in the form of sufficient conditions in another way. However, intended conditions in multiple input multiple output are just derived in the form of sufficient conditions. Furthermore, an upper band for phase of oustaloup approximation frequency response... 

Magnetic bearings have been introduced in recent decades to overcome the problem of energy loses due to friction in bearings of rotating machinery. In magnetic bearings, the rotor is suspended by magnetic forces without any friction. These bearings are of the two types of passive and active. In Passive Magnetic Bearings (PMB), magnetic forces are generated by permanent magnets and have the ability to tolerate a small distribution. In Active Magnetic Bearings (AMB) magnetic forces are generated by electromagnets and have the ability to tolerate larger distributions than the PMB can. Since AMB is inherently unstable, it is necessary to use controllers to stabilize it. Due to the nonlinear... 

Robust model predictive control(RMPC) is a control strategy that has been widely adopted in industry and academic researches.In this project we have modified robust nonlinear model predictive control using SOS and dynamic feedback. In this control strategy we will linearize the nonlinear model of the system about it’s operating point. We will consider the error of linearization as an uncertainty and find an upper bound for uncertainty. Then we will change control objective to minimizing this upper bound. The most advantage of changing the control objective is that nonlinear system results a non-convex optimization problem but this strategy terminates a convex optimization problem. To find... 

Most of the robust or optimal controllers can produce extremely fragile controllers [1], in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed-loop control system. Modern control methods, including robust control, lead to high order controllers.Often times a reduced order controller is implemented. As a result, need for low order control design reducing controller’s ensitivity is tangible. Based on studies carried out, properties of normal matrices can be employed to define a fragility measure. In this thesis, a new convex criterion measuring controller fragility is defined. Then, a more resilient reduced order controller can... 

In this thesis we introduce a new methodology to solve the problem of multi-objective control design of linear output-feedback with a constraint on the order of controller. This problem can be formulated as a set of linear matrix inequalities and an additional rank constraint. This constraint is highly non-convex and makes this optimization problem NP-hard. The proposed methodology results in methods which are multi-step and in each step a convex optimization problem shall be solved. This methodology can consider any combination of different design objectives such as H2 performance, H1 performance, passivity and regional pole assignment. In the development of described methodology, a... 

Nowadays, the use of distributed generation (DG) units and microgrid systems is mainly limited to their operation in the grid-connected mode. In the grid-connected mode, a microgrid including its loads and DG units is connected to the main grid at the point of common coupling (PCC). In this case, the main grid provides fixed voltage and frequency for the microgird and each DG unit regulates its power components based on the conventional dqcurrent control strategy. Autonomous (islanded) operation of a microgrid, however, is not as straightforward as its operation in the grid-connected mode, i.e., control and power management of an islanded microgrid is very difficult due to the stochastic... 

Time-delay in measurement of the outputs is usually one of the important factors creating complexity in design of a robot controller such that ignoring the delay in controller design can cause instability or significant performance degradation in a robotic system. In this thesis, set-point regulation problem as well as the trajectory tracking problem for a rigid robotic manipulator in presence of constant and known delay in measurements have been investigated and in particular, three dynamically smooth controllers have been proposed:
1-A controller based on the “minimal” dynamic model of a robot manipulator that satisfies sufficient conditions in the form of Linear Matrix inequalities... 

An Ad-Hoc wireless network consists of a collection of geographically distributed nodes that communicate with each other over a wireless medium. These networks don’t use any infrastructure or base station to channel allocation. The important difference between wireless networks and wired networks is the broadcast nature of wireless communications. In these networks, each node transmits data to all of the nodes in the transmission range which may cause an increase in interference and data loss. On the other hand, due to mobility of users, fading the channel between them and change of routing, the probability of data loss increases. The extensive and successful employment of TCP variants in... 

First, stabilization problem of an integer order-nonlinear differential inclusion (IO-NDI) in the form of tracking problem is investigated and discussed while control inputs are subjected to the sector and dead-zone nonlinearities. Based on two the well-known theorems, the mentioned differential inclusion is modeled by a nonlinear system possessing polytopic uncertainties. For tackling the mentioned problem, sliding mode control (SMC) approach is applied and developed. Second, two issues including stability analysis and stabilization problem of a fractional order-linear differential inclusion (FO-LDI) are studied for both fractional order derivatives and separately. For solving these...