Sharif Digital Repository

The necessity of dynamic equivalents for power system analysis has been well known since the expansion of large interconnected power networks, and has been discussed during the last decades. The present paper proposes a new method for constructing dynamic equivalents of power systems. In this method, at the first step the "study system" is modeled completely via a single machineinfinite bus modeling procedure. Then the "external system" is identified as a MIMO feedback block of this model in such a manner that can include dynamic effects of the latter on the behavior of the former. The method is successfully experimented on a part of the Iranian southern network. Copyright © 2007 The... 

This paper deals with the impulsive formation control of spacecraft in the presence of constraints on the position vector and time. Determining a set of path constraints can increase the safety and reliability in an impulsive relative motion of spacecraft. Specially, the feasibility problem of the position norm constraints is considered in this paper. Under assumptions, it is proved that if a position vector be reachable, then the reach time and the corresponding time of impulses are unique. The trajectory boundedness of the spacecraft between adjacent impulses are analyzed using the Gerschgorin and the Rayleigh-Ritz theorems as well as a finite form of the Jensen's inequality. Some... 

A system is called prescribed-time attractive if its solution converges at an arbitrary user-defined finite time. In this note, necessary and sufficient conditions are developed for the prescribed-time attractivity of linear time-varying (LTV) systems. It is proved that the frozen-time eigenvalues of a prescribed-time attractive LTV system have negative real parts when the time is sufficiently close to the convergence moment. This result shows that the ubiquitous singularity problem of prescribed-time attractive LTV systems can be avoided without instability effects by switching to the corresponding frozen-time system at an appropriate time. Consequently, it is proved that the time-varying... 

Feed-in tariff (FiT) is one of the most efficient ways that many governments throughout the world use to stimulate investment in renewable energies (REs) technology. For governments, financial management of the policy could be challenging as it needs a considerable amount of budget to support RE producers during the long remuneration period. In this paper, it has been illuminated that the early growth of REs capacity could be a temporary boost. And the socio-economic structure of the system will backlash the policy if some social mechanisms are not considered. Social tolerance for paying REs tax and potential investors’ trust emanated from budget-related mechanisms -which have rarely been... 

Delaminated composite beam under general edge loading conditions is studied. Based on a technical engineering theory an analytical procedure for calculation of strain energy release rate and its separation into modes I and II of delamination is presented. By choosing a suitable displacement field based on second-order shear-thickness deformation theory and using the principle of minimum total potential energy, the equations of equilibrium are obtained along with the appropriate boundary conditions. The J integral and its definition for different modes of fracture is used for calculation of strain energy release rate and its separation into different modes. Double cantilever beam (DCB)... 

A fault detection and isolation method for satellite rate gyros is proposed based on using the satellite-to-satellite measurements such as relative position beside orbit parameters of the primary satellite. By finding a constant of motion, it is shown that the dynamic states in a relative motion are restricted in such a way that the angular velocity vector of primary satellite lies on a quadratic surface. This constant of motion is then used to detect the gyroscope faults and estimate the corresponding scale factor or bias values of the rate gyros of the primary satellite. The proposed algorithm works even in time variant fault situations as well, and does not impose any additional... 

This article introduces a class of time-varying controllers for Euler-Lagrange systems such that the convergence occurs at an arbitrary finite time, independently of initial conditions, and free of chattering. The proposed controller is based on a mapping technique and is designed in two steps: First, a conventional (obstacle avoidance) asymptotically stable controller is specified for the nominal system; then, by a simple substitution, a prescribed-time (obstacle avoidance) controller is achievable for the perturbed system. It is proved that the proposed scheme is uniformly prescribed-time stable for unperturbed systems and prescribed-time attractive for perturbed systems as it rejects... 

This letter presents a unified framework for the design of prescribed-time controllers under time-varying input and state constraints for normal-form unknown nonlinear systems with uncertain input gain. The proposed approach is based on a time-domain mapping method by which any infinite-time system can be corresponded to a prescribed-time system and vice versa. It is shown that the design of a constrained nonasymptotic prescribed-time controller can be reduced to the asymptotic control design for an associated constrained infinite-time system. Faà di Bruno’s formula and Bell polynomials are used for a constructive representation of the associated infinite-time system. The presented results... 

This paper introduces a class of time-varying controllers for Euler-Lagrange systems such that the convergence occurs at an arbitrary finite time, independently of initial conditions, and free of chattering. The proposed controller is based on a mapping technique and is designed in two steps: First, a conventional (obstacle avoidance) asymptotically stable controller is specified for the nominal system; then, by a simple substitution, a prescribed-time (obstacle avoidance) controller is achievable for the perturbed system. It is proved that the proposed scheme is uniformly prescribed-time stable for unperturbed systems and prescribed-time attractive for perturbed systems as it rejects... 

In this letter, a new notion of stability is introduced, which is called triangular stability. A system is called triangularly stable if the norm of its state vector is bounded by a decreasing linear function of time such that its intersection point with the time axis can be arbitrarily commanded by the user. Triangular stability implies prescribed-time stability, which means that the nonlinear system is converged to zero equilibrium at an arbitrary finite time. A prescribed-time controller with guaranteed triangular stability is developed for normal form nonlinear systems with uncertain input gain, which is able to reject the disturbances and unmodeled dynamics. Numerical simulations are... 

This letter presents a unified framework for the design of prescribed-time controllers under time-varying input and state constraints for normal-form unknown nonlinear systems with uncertain input gain. The proposed approach is based on a time-domain mapping method by which any infinite-time system can be corresponded to a prescribed-time system and vice versa. It is shown that the design of a constrained nonasymptotic prescribed-time controller can be reduced to the asymptotic control design for an associated constrained infinite-time system. Faà di Bruno's formula and Bell polynomials are used for a constructive representation of the associated infinite-time system. The presented results... 

Natural frequencies and mode shapes of two joined isotropic conical shells are presented in this study. The joined conical shells can be considered as the general case for joined cylindrical-conical shells, joined cylinder-plates or cone-plates, conical and cylindrical shells with stepped thicknesses and also annular plates. Governing equations are obtained using thin-walled shallow shell theory of Donnell and Hamilton's principle. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved assuming trigonometric response in circumferential and series solution in meridional directions and all... 

In this study, the buckling of two joined isotropic conical shells under axial compression and simply supported boundary conditions is investigated. The governing equations are obtained using thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved by assuming trigonometric response in circumferential and series solution in meridional direction. The results are validated in comparison with the available results in the literature. Effects of semi-vertex angles and meridional lengths on the buckling load... 

In the present study, a simple analytical method is introduced for determination of natural frequencies of generally laminated conical and cylindrical shells with arbitrary boundary conditions. The governing equations of motion employed are those of thin-walled shell theory of Donnell. The free-vibration equations are solved using state space method and series solution in meridional direction. The results are compared and validated with the available especial results in the literature. The effects of bending-stretching coupling, semi-vertex angle, meridional length, shell thickness, fiber directions of composite plies, and lamination sequences on the natural frequency of conical and... 

This study presents a motion planning algorithm to generate a feasible periodic solution for a hybrid system describing running by a three-dimensional (3-D), three-link, three-actuator, monopedal robot. In order to obtain a symmetric running gait along a straight line, the hybrid system consists of two stance phases and two flight phases. The motion planning algorithm is developed on the basis of a finite-dimensional optimisation problem with equality and inequality constraints. By extending the concept of hybrid zero dynamics to running, the authors propose a time-invariant control scheme that is employed at two levels to locally exponentially stabilise the generated periodic solution for... 

Presented is a novel approach for online trajectory modification of joint motions to transfer a free open kinematic chain, undergoing flight phase, from a specified initial configuration to a specified final configuration. Formally, it is assumed that a nominal trajectory, computed offline, can reorient the kinematic chain (reconfiguration problem) for a given angular momentum on a time interval. A modification algorithm of body joints, based on optimal control, is developed such that for different angular momentums and time intervals, the same reconfiguration problem can be solved online. This approach can be utilised for space robotics applications and online computation of planar running... 

This study presents an online motion planning algorithm for generating reference trajectories during flight phases of a planar monopedal robot to transfer the configuration of the mechanical system from a specified initial pose to a specified final one. The algorithm developed in this research is based on the reachability and optimal control formulations of a time-varying linear system with input and state constraints. A two-level control scheme is developed for asymptotic stabilisation of a desired period-one orbit during running of the robot. Within-stride controllers, including stance and flight phase controllers, are employed at the first level. The flight phase controller is a feedback... 

This paper presents an analytical approach to design a continuous time-invariant two-level control scheme for asymptotic stabilization of a desired period-one trajectory for a hybrid model describing walking by a planar biped robot with noninstantaneous double-support phase and point feet. It is assumed that the hybrid model consists of both single- and double-support phases. The design method is based on the concept of hybrid zero dynamics. At the first level, parameterized continuous within-stride controllers, including single- and double-support-phase controllers, are employed. These controllers create a family of 2-D finite-time attractive and invariant submanifolds on which the dynamics... 

Presented is a novel approach for designing continuous-time update laws to update the parameters of stabilising controllers during continuous phases of bipedal walking such that (i) a general cost function, such as the energy of the control input over single support, can be minimised in an online manner, and (ii) the exponential stability of the corresponding limit cycle for the closed-loop impulsive system is not affected. Formally, a class of update laws with a radial basis step length is developed to minimise a cost function in terms of the stabilising controller parameters and initial states of the mechanical system  

The general goal of the facility layout problem is to arrange a given number of facilities to minimize the total cost associated with the known or projected interactions between them. One of the special classes of the facility layout problem is the Single Row Facility Layout Problem (SRFLP), which consists of finding an optimal linear placement of rectangular facilities with varying dimensions on a straight line. This paper first presents and proves a theorem to find the optimal solution of a special case of SRFLP. The results obtained by this theorem prove to be very useful in reducing the computational efforts when a new algorithm based on tabu search for the SRFLP is proposed in this...