Sharif Digital Repository

As a subset of hybrid systems, piecewise affine (PWA) systems are capable of approximating the behavior of a wide range of nonlinear systems. Considering the preliminaries regarding these systems and the vast literature gathered around them, the main contributions of the current study are presented in two separate sections. In the first section a class of uncertain piecewise affine systems subject to additive noise are studied. The problem of minimizing the bound on the variance of the steady response of these systems, by means of a piecewise affine observer-controller, is formulated as an optimization problem subject to a number of constraints in the form of matrix inequalities. Then the... 

Microrobots are the robots which manufactured or operated in micro dimentions. High accuracy, compatibility with harsh situations and caring or assembling in micro dimensions are the most important advantages of these robots. Manufacturing new microrobots with higher speed or increasing the velocity of existed microrobots is the discussion of these days.An A-shape microrobot designed and manufacturared before. The goal of this thesis is to model, identify the friction and observe the velocity of the A-shape microrobot. In low speeds both legs of microrobots are on the ground; it walks with the stick-slip motion principle. Increasing the velocity of the microrobot causes separation of one or... 

One of the issues in the design and synthesis of the state or output feedback controller is the issue of fragility as the existence of disturbance in the coefficients of the designed controller causes instability in the controlled closed-loop system or leads to deterioration of its performance. The need to consider this point results in some novel approaches for designing the non-fragile controllers. Accordingly, defining criteria for measuring fragility is crucial.As well, due to the considered practical problems in the implementation of ordinary designed robust and optimal controllers, non-reachability of all the states of dynamical systems, and the boundedness for the quantity of the... 

In this thesis, computational load reduction in linear matrix inequality based model predictive control for nonlinear multi-input systems is studied. The main idea is decomposing the system into several smaller interacting subsystems and computing each control input separately. The main challenge is how to consider the effects of interactions among subsystems in the control design. Three approaches are investigated in this thesis. In the first approach, a static approximation of the effects of other subsystems is augmented in the local model of each subsystem, to improve the closed loop performance than fully decentralized methods. In the second approach, considering the mutual interactions... 

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... 

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... 

Due to the prominence of low-order controllers in industry, this thesis intends to improve the common design algorithms in this field. In this regard, the main challenge is that this problem is NP-hard due to the non-convex rank constraint which appears in the formulation. The existing algorithms mostly solve this problem by obtaining a convex sub-space for this constraint and using output feedback convex optimization methods.Two of common algorithms are non-iterative. These methods two main steps; first to obtain the full-order Lyapunov matrices related to the controller, and then, to fix the null-space of the matrices which have rank constraint. One of the advantages of the algorithm... 

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... 

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... 

Order reduction is a very important issue in Control Theory. A growing need for order reduction models in different fields such as simulation, identification, and design of control system shows this significance. Actually, a high-order system makes a great deal of complexity in designing hardware of control system, debugging, and implementation. Till nowadays, many repetitive as well as nonrepetitive methods with various criteria have been introduced to find low-order models. In this research, order reduction of linear time invariant system models is analyzed. The selected criterion for measuring error between original system and reduced order system is the norm of H1 because it is not only... 

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... 

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... 

One of the most common problems encountered in multivariable systems is the interactions between the system inputs and outputs. Interaction causes difficulties in control of these systems. Hence reduction of interaction in multivariable systems is an important design objective. One way to do this is to employ a pre-compensator in the open loop systems. Several approaches with different design methods and optimization criterions have been proposed thus far. In this study the problem of interaction reduction for a square stable system is considered and a pre-compensator matrix is designed which reduces interactions in the interacting multivariable system.In this case the purpose is to use... 

Wheeled mobile robots form a subcategory of mobile robots and are usually accompanied with geometric constraints on their velocities. These constraints do not allow the robots to move in any path that only does not collide with obstacles, in order to move from one point to another. On the other hand, the nonlinear nature of these systems make their control difficult. A general approach in motion planning and control for mobile robots is using standard forms equivalent to their state equations; Usually, solving motion planning and control problems for these forms is easier than that of the original system. Also,the mentioned problems are more prospective to have a systematic solution for... 

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... 

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... 

In this thesis the problem of optimal robust fault detection has been studied. Optimal Fault Detection Filter (FDF) design, by using a Linear Matrix Inequality (LMI) structure for both linear systems with polytopic uncertainties and nonlinear Lipschitz systems has been considered. In this regard, a novel LMI is introduced which is capable of calculating the maximum lower bound of H− index with great accuracy.Then, based on the parameter-dependent Lyapunov function and the property of having convexity in combination of certain state space equations, the result is extended to polytopic uncertain systems. Afterward the design of an optimal observer-based residual generator, in the sense of... 

The constrained nonlinear systems with large operating regions have attracted great attention due to their correspondence with the most practical systems. There are several tools such as gain scheduling and Nonlinear Model Predictive Control (NMPC) to control them. Gain scheduling, with ability to provide stability guarantees between the estimated stability regions overlapping each other and to cover a large space of the allowable operating range of the system, is an attractive practical approach to control the systems with large operating regions. But this strategy do not account for constraints explicitly by online optimization. On the contrary, NMPC handles constraints on the manipulated... 

A robust decentralized control strategy for the islanded operation of a microgrid is proposed in this thesis. The microgrid consists of the parallel connection of several electronically-coupled distributed generation (DG) units. All DG units are connected to a point of common coupling (PCC) where a passive load is also connected. It is shown that the islanded microgrid can be modeled by an interconnected composite system comprising equal number of subsystems (to the DGs). Moreover, it is shown that the overall islanded microgrid can be controlled by only the local controllers about the individual subsystems. In this case, one of the DGs, referred to as the Master DG, is responsible for... 

The LQG theory made its appearance in the fifties and sixties. It has now become one of the standard methods for compensator design. Despite the existing powerful tools in modern control, there seems to be few or no systematic approaches proposed for determining the weighting and root matrices which are the free parameters of the compensator. These matrices are often found by trial-and-error. Initially, this thesis presents an iterative algorithm for determining the compensator parameters. The algorithm is based upon making corrections to the singular values graphs in order to enhance closed-loop performance and robustness. This is how the traditional intuitive trial-and-error approach is...