Hancheol Cho

Methodology for Satellite Formation-Keeping in the Presence of System Uncertainties

A two-step formation-keeping control methodology is proposed that includes both attitude and orbital control requirements in the presence of uncertainties. Based on a nominal system model that provides the best assessment of the real-life uncertain environment, a nonlinear controller that satisfies the required attitude and orbital requirements is first developed. This controller allows the nonlinear nominal system to exactly track the desired attitude and orbital requirements without making any linearizations/approximations. In the second step, a new additional set of closed-form additive continuous controllers is developed. These continuous controllers compensate for uncertainties in the physical model of the satellite and in the forces to which it may be subjected. They obviate the problem of chattering. The desired trajectory of the nominal system is used as the tracking signal, and these controllers are based on a generalization of the concept of sliding surfaces. Error bounds on tracking due to the ...

New Approach to Satellite Formation-Keeping: Exact Solution to the Full Nonlinear Problem

This paper presents a new, simple, and exact solution to the formation keeping of satellites when the relative distance between the satellites is so large that the linearized relative equations of motion no longer hold. We employ a recently proposed approach, the Udwadia-Kalaba approach, which makes it possible to explicitly obtain the desired control function without making any approximations related to the nonlinearities in the underlying dynamics. We use an inertial frame of reference to describe the motion of a satellite and since no approximations are made, the results obtained apply to situations even when the distance between the satellites is arbitrarily large. The paper deals with a projected circular formation, but the methodology in this paper can be applied to any desired configuration or orbital requirements. Numerical simulations confirm the brevity and the accuracy of the analytical solution to the dynamical control problem developed herein.

Explicit Control Force and Torque Determination for Satellite Formation-Keeping with Attitude Requirements

A simple analytical approach for formation-keeping of satellites in the presence of both orbital and attitude requirements is developed. A leader satellite is assumed to be in a J2-perturbed circular reference orbit and each follower satellite is required to stay in its prescribed, desired orbit with respect to the leader satellite, and at the same time, to point to an arbitrarily chosen specific spot in space that may be time-varying. Nonlinear relative dynamics is considered in its entirety without any approximations, and nonlinear controllers are designed to exactly satisfy the desired orbital and attitude mission requirements for the formation. The analytical approach leads to a separation principle that points out when orbital control is completely unaffected by attitude control. In the presence of sensor measurement noise that leads to incorrect initial conditions at the start of the control maneuver the approach asymptotically satisfies both the orbital and attitude control requirements, at any des...

Application of Analytic Solution in Relative Motion to Spacecraft Formation Flying in Elliptic Orbit

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not requiredfor thesolution in the currentstudy. Itis verifiedthat the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.

Lagrangians for Damped Linear Multi-Degree-of-Freedom Systems

This paper deals with finding Lagrangians for damped, linear multi-degree-of-freedom systems. New results for such systems are obtained using extensions of results for single and two degree-offreedom systems. The solution to the inverse problem for an n-degree-of-freedom linear gyroscopic system is obtained as a special case. Multi-degree-of-freedom systems that commonly arise in linear vibration theory with symmetric mass, damping, and stiffness matrices are handled similarly in a simple manner. Conservation laws for these damped multi-degree-of-freedom systems are found using the Lagrangians obtained, and several examples are provided.

Some Further Remarks on Hamilton's Principle

The development of the equations of motion for a mechanical ystem from Hamilton’s principle can be viewed as a problem in he calculus of variations when the constraints on the system are olonomic and the forces are derivable from a potential function. endering stationary the integral of the Lagrangian over a fixed nterval of time taken between two fixed points in configuration pace, then, yields the equations of motion for the system. Howver, it is interesting to investigate the types of forces that can be ngendered through the use of an appropriately chosen function integrand whose integral when rendered stationary, yields the roper equations of motion even when the forces acting on a ystem do not arise from a potential, that is, when they are nononservative. In 1931, Bolza 1 gave a general procedure for finding such an ntegrand for a single degree-of-freedom system. This was folowed by Douglas 2,3 who obtained the necessary and sufficient onditions for the existence of an integrand for multidegree-ofreedom systems. However, it is difficult to obtain the integrands or given, specific forces. In a 1963 note, Leitmann 4 provided ome examples of such forces and the corresponding integrands or which a variational principle exists. A single degree-ofreedom system was considered and two examples were provided. ecently, the so-called semi-inverse method 5 has attracted uch attention due to its simplicity and applicability to certain ases. However, this method assumes a specific form for the funcion f , which needs to be obtained from experience, intuition, or oth, and utilizes a Lagrange multiplier type approach. In this paper, we extend the results in Ref. 4 to some more eneral nonpotential systems and provide a more systematic way f handling the inverse problem of the calculus of variations. The ain difficulties lie in performing the necessary integrations exlicitly, as will be seen. The examples given in Ref. 4 arise as pecial cases of the results provided herein. Finally, we apply the eneral results to some specific systems to indicate the nature of he nonpotential forces, which the results encompass.

New Solutions to the Exact Formation-keeping Control of Satellites with Attitude Constraints

This paper provides a new, exact controller for formation-keeping in the presence of attitude tracking requirements. Both orbital and attitude dynamics are simultaneously considered and continuous thrust propulsion systems are assumed. A leader satellite is assumed to be in a given Keplerian orbit around a central body and each follower satellite is required to stay in a prescribed, desired orbit with respect to the leader satellite, and at the same time, to exactly point to a specific spot in inertial space that may be fixed or time varying. The satellites are considered as rigid-bodies and for attitude dynamics quaternions are used to realize arbitrary orientations and avoid singularities. Unlike most studies, no linearizations and/or approximations are made in dynamics or the controllers. It is hoped that the novel controller provides a remarkable improvement over the current state-of-the-art in that the control force and torque to satisfy the given orbital and/or attitude constraints are obtained in completely closed form. This new, analytical solution can be easily used for on-orbit, real-time control with low computational burden. Furthermore, it is useful in estimating the magnitude of the required control inputs and results in some interesting consequences, including the separation principle, which describes when the orbital control can be completely decoupled from the attitudinal control required to be applied to the follower satellite. Extensive computational simulations are performed to demonstrate the simplicity of implementation and accuracy of the control method developed herein.

Satellite Formation-Keeping Using the Fundamental Equation in the Presence of Uncertainties in the System

Formation flying of satellites is considered as a key space technology because of its potential operational and/or financial benefits. In this paper a formation-keeping control scheme with attitude constraints is proposed in the presence of uncertainties in the masses and moments of inertia of the satellites. In formation-keeping, we assume that the satellites are to stay in their prescribed, desired orbits, and simultaneously, to point to a fixed target in space. In this study, we obtain the desired controller in a two-step process: we first obtain a controller for the nominal system, which is referred to the best assessment of the given real-life uncertain system. This controller can be analytically attained under the presumption that there are no uncertainties in the masses and moments of inertia of the satellites with the aid of a recent finding in analytical dynamics, called the fundamental equation. With this controller the system exactly follows the given constraint trajectories for the dynamical model assumed. Unlike previous studies, no approximations/linearizations are done related to the nonlinear nature of the system. However, this analytical result is correct only under the assumption that the modeling of the physical

Advanced Control Methods for Systems with Fast-Varying Disturbances and Applications

In most real applications, disturbances and uncertainties, which affect stability and performance of the controlled system, are unavoidable. Unfortunately, disturbances are not measurable or too expensive to measure. A typical approach is first to estimate the disturbances and then design an advanced control law based on this estimation. Although this approach has attracted much attention of numerous researchers in various fields of study, most estimation techniques rely on the assumption that the disturbance is slowly varying or its time derivative is zero. Note that the disturbances do not arise only from external environments; uncertainties such as modelling errors and parameter perturbations can also be considered as disturbances. Also, for the objects with unknown components and noises, a good approach is to use the system with learning capability to adapt its parameters to the samples measured from the given objects. From 36 submissions, 10 papers are accepted for publication in this special issue. Each paper was reviewed by at least one reviewer and revised according to review comments. The papers cover the following topics: time-varying noise estimation, search algorithm for minimizing the makespan, robust control for thyristor controlled series compensator (TCSC), robust technique for computing average consensus, sensorless control of uncertain PM-assisted SynRM, wind turbine frequency control in microgrid, optimization of power system stabilizer (PSS), adaptive sliding mode control (SMC) for hybrid synchronization of chaotic systems, model predictive control (MPC) for electric vehicles, and control of hydraulic turbine governing system.

Simple adaptive methodology for chattering-free sliding mode control

This paper presents a new adaptive methodology for sliding mode control of a nonlinear dynamical system in the presence of unknown, but bounded uncertainties. A continuous control law is first developed to compensate for the uncertainties and this Lyapunov-based approach eliminates chattering by replacing a discontinuous signum function with a continuous function. By investigating the relation between the estimated gain with respect to the real unknown uncertainties and the resultant sliding variable, a new adaptive tuning law is obtained to ensure that the gain update is performed in real time and the resulting error is bounded within a user-specified value. The proposed adaptive algorithm is simple and easy to implement, and an inverted pendulum problem serves to demonstrate the accuracy and effectiveness of the control methodology proposed herein.