• Journal of Institute of Control, Robotics and Systems
• /
• v.17 no.10
• /
• pp.1006-1013
• /
• 2011

In this paper, we propose an optimal posture control law for an unmanned bicycle by deriving linear bicycle model from fully nonlinear differential equations. We calculate each equilibrium point of a bicycle under any given turning radius and angular speed of rear wheel. There is only one equilibrium point when a bicycle goes straight, while there are a lot of equilibrium points in case of turning. We present an optimal equilibrium point which makes the leaning input minimum when a bicycle is turning. As human riders give rolling torque by moving center of gravity of a body, many previous studies use a movable mass to move center of gravity like humans do. Instead we propose a propeller as a new leaning input which generates rolling torque. The propeller thrust input makes bicycle model simpler and removes input magnitude constraint unlike a movable mass. The proposed controller can hold optimal equilibrium points using both steering input and leaning input. The simulation results on linear control for circular motion are demonstrated to show the validity of the proposed approach.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.123-139
• /
• 1994

In this paper we are concerned with optimal control problems whose costs are quadratic and whose states are governed by linear delay differential equations and general boundary conditions. The basic new idea of this paper is to introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.27.4-27
• /
• 2001

A stabilizing control method for linear systems with model uncertainties and hard input constraints is developed, which does not require on-line optimizations. This work is motivated by the constrained robust MPC(CRMPC) approach [3] which adopts the dual mode prediction strategy (i.e. free control moves and invariant set) and minimizes a worst case performance criterion. Based on the observation that, a feasible control sequence for a particular state can be found as a linear combination of feasible sequences for other states, we suggest a stabilizing control algorithm providing sub-optimal and feasible control sequences using pre-computed optimal sequences for some canonical states. The on-line computation of the proposed method reduces to simple matrix multiplication.

• International Journal of Aeronautical and Space Sciences
• /
• v.11 no.3
• /
• pp.206-220
• /
• 2010

This paper proposes optimal control techniques for determining translational and rotational maneuvers that facilitate proximity operations and docking. Two candidate controllers that provide translational motion are compared. A state-dependent Riccati equation controller is formulated from nonlinear relative motion dynamics, and a linear quadratic tracking controller is formulated from linearized relative motion. A linear quadratic Gaussian controller using star trackers to provide quaternion measurements is designed for precision attitude maneuvering. The attitude maneuvers are evaluated for different final axis alignment geometries that depend on the approach distance. A six degrees-of-freedom simulation demonstrates that the controllers successfully perform proximity operations that meet the conditions for docking.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.97-113
• /
• 2004

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.

• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.717-730
• /
• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.127-146
• /
• 2004

In this paper we consider a heat flow in an inhomogeneous. body without internal source. There exists special initial and boundary conditions in this system and we intend to find a convenient coefficient of heat conduction for this body so that body cool off as much as possible after definite time. We consider this problem in a general form as an optimal control problem which coefficient of heat conduction is optimal function. Then we replace this problem by another in which we seek to minimize a linear form over a subset of the product of two measures space defined by linear equalities. Then we construct an approximately optimal control.

• Journal of the Korean Society for Precision Engineering
• /
• v.21 no.10
• /
• pp.109-114
• /
• 2004

A combined optimal design problem of structural and control systems is discussed by taking a 3-D flexible structure as an object. We consider a minimum weight design problem for structural system and disturbance suppression problem for the control system. The conditions for the existence of controller are expressed in terms of linear matrix inequalities (LMI). By minimizing the linear sum of the normalized structural objective function and control objective function, it is possible to make optimal design by which the balance of the structural weight and the control performance is taken. We showed in this paper the validity of combined optimal design of structural and control systems.

• Journal of Institute of Control, Robotics and Systems
• /
• v.14 no.6
• /
• pp.515-518
• /
• 2008

Organic light emitting diode(OLED) is one of the most promising type of future flat panel display. A linear source is used to deposite organic vapor to a large size OLED substrate. An electric heater which is attached on the side of linear source heats the organic powder for the sublimation. The nozzle of heater, which is attached at the top of the linear source has an optimal temperature. An numerical analysis has been performed to find optimal heater position for the optimal nozzle temperature. A commercial CFD program, FLUENT, is used on the analysis. Two-dimensional and three-dimensional analysis have been performed. The analysis showed that the heater should be attached at the outer side of crucible wall rather than inner side of housing, which was original design. Eighteen milimeter from the top of the linear source was suggested as the optimal position of heater. Improving thermal performance of linear source not only helps the uniformity of organic vapor deposition on the substrate but also increase productibity of vapor deposition process.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.341-341
• /
• 2000

This paper presents a sliding mode control(SMC) design method for single input linear systems with uncertainties and time delay in the state. We define a sliding surface for the augmented system with a virtual state which is defined from the nominal system. We make a virtual state from optimal control input using LOR(Linear Quadratic Regulator) and the states of the nominal system. We construct a controller that combines SMC with optimal controller. The proposed sliding mode controller stabilizes on the overall closed-loop system.