Search

The optimal attitude maneuver control problem without control constraints is studied in the quaternion statement for an axially symmetric spacecraft as a rigid body under arbitrary boundary conditions on angular position and angular velocity of a spacecraft. The performance criterion is given by a functional combining the time and energy used for the attitude maneuver. Using substitutions of variables, the original problem is simplified (in terms of dynamic Euler equations) to the optimal slew problem for a rigid body with a spherical mass distribution. The simplified problem contains one additional scalar differential equation. In the class of generalized conical motions, the traditional optimal slew problem is modified to obtain analytical solutions for motion equations. The solutions contain arbitrary constants and two arbitrary scalar functions (generalized conical motion parameters). The proposed approach fits well with the Poinsot concept that any arbitrary angular motion of a rigid body around a fixed point can be considered as some generalized conical motion of a rigid body. Moreover, for the cases of analytic solvability of the classical problem of optimal reversal spherically symmetric spacecraft, when restrictions are imposed on the edge conditions of the problem (plane Euler turn, conical motion) solutions of the classical and modified tasks are completely the same. An optimization problem is formulated and solved with respect to these functions, the second derivatives of which serve as controls in the optimization problem. The resulting analytical solution of the modified problem can be treated as an approximate (quasioptimal) solution of the traditional optimal slew problem under arbitrary boundary conditions. The quasioptimal algorithm of the optimal turn of a spacecraft is given. Numerical example showing the closeness of the solutions of the traditional and modified optimal slew problems for an axially symmetric spacecraft is given.

The subject of research is an influence pattern of quasioptimal quick acting movement control of lifting cranes with a load flexible suspension on dynamic movement characteristics. The purpose of the work lies in the synthesis of quasioptimal crane movement control when its accelerating with the elimination of load fluctuations, as well as in the study of the crane movement dynamics at the quasioptimal control. The paper proposed to switch from an optimal control of crane movements to control, which is described by a continuous function. In order to achieve specified final conditions of movement by the system “crane-load” an algebraic system of transcendental equations was composed, which was leaded to the target of minimizing the complex function of three arguments. By using the particle swarm method points in time were found at which there was a change in the control character (the driving force of the crane actuator). Simulation of crane movements at quasioptimal control made it possible to find its basic dynamic characteristics during acceleration. Comparative analysis of the data showed a significant reduction of dynamic loads in the crane elements. The transitional regime duration of the crane movement in comparison with the optimal control increases slightly. Thus, by increasing the duration of the crane`s non-essential movement cycle (for tens of seconds) an increase in the durability of the crane steel structures, mechanical gears, motor, power inverter, and other elements is achieved. The obtained results should be used for the development and modernization of movement control systems for lifting equipment, which require a significant productivity, energy efficiency and durability (for example, cranes that are extensively exploited in ports, metallurgical and machine-building enterprises, construction sites, warehouses).

The proximity is estimated of a resource quasioptimal control to the optimal control. We give a method for subdividing the bounded region of initial conditions into subregions and bringing the quasioptimal control closer to the resource optimal control. [ABSTRACT FROM AUTHOR]

For linear systems with constrained control and fixed transition time, we propose two methods for solving the resource consumption minimization problem approximately. We prove that the switching moments of resource-quasioptimal controls are independent of the initial conditions and constant for autonomous systems. Some region of the initial conditions is found for which the constraints on the control are never violated. [ABSTRACT FROM AUTHOR]

A simple algorithm for developing a quasioptimal control over resource consumption is considered. The control is used as an initial approach to an iterative procedure of computing an optimal control. A system of linear algebraic equations is derived which approximately relate increments of initial conditions of an adjoint system to increments of amplitudes of a quasioptimal control with respect to ultimate values. Local convergence of the computing process with a quadratic rate is proved, and the convergence radius is found. A condition for global convergence of the method is specified. [ABSTRACT FROM AUTHOR]