Thanapat Wanichanon

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 ...

Control of Uncertain Nonlinear Multibody Mechanical Systems

Descriptions of real-life complex multibody mechanical systems are usually uncertain. Two sources of uncertainty are considered in this paper: uncertainties in the knowledge of the physical system and uncertainties in the “given” forces applied to the system. Both types of uncertainty are assumed to be time varying and unknown, yet bounded. In the face of such uncertainties, what is available in hand is therefore just the so-called “nominal system,” which is our best assessment and description of the actual real-life situation. A closed-form equation of motion for a general dynamical system that contains a control force is developed. When applied to a real-life uncertain multibody system, it causes the system to track a desired reference trajectory that is prespecified for the nominal system to follow. Thus, the real-life system’s motion is required to coincide within prespecified error bounds and mimic the motion desired of the nominal system. Uncertainty is handled by a controller based on a generalization of the concept of a sliding surface, which permits the use of a large class of control laws that can be adapted to specific real-life practical limitations on the control force. A set of closed-form equations of motion is obtained for nonlinear, nonautonomous, uncertain, multibody systems that can track a desired reference trajectory that the nominal system is required to follow within prespecified error bounds and thereby satisfy the constraints placed on the nominal system. An example of a simple mechanical system demonstrates the efficacy and ease of implementation of the control methodology. [DOI: 10.1115/1.4025399]

Decentralised control of nonlinear dynamical systems

In this paper, we provide a simple novel approach to decentralised control design. Each subsystem of an interconnected interacting system is controlled in a decentralised manner using locally available information related only to the state of that particular subsystem. The method is developed in two steps. In the first step, we define what we call a ‘nominal system’, which consists of ‘nominal subsystems’. The nominal subsystems are assumed to be acted upon by forces that can be computed using only locally available information. We obtain an asymptotically stable control for each nominal subsystem which minimises a suitable, desired norm of the control effort at each instant of time. In the second step, we determine the control force that needs to be applied to the actual (interconnected) subsystem in addition to the control force calculated for the nominal subsystem, so each actual subsystem tracks the state of the controlled nominal subsystem as closely as desired. This additional compensating controller is obtained using the concept of a generalised sliding surface control. The design of this additional controller needs as its input an estimate of the bound on the mismatch between the nominal and the actual subsystems. Examples of non-autonomous, nonlinear, distributed systems are provided that demonstrate the efficacy and ease of implementation of the control method.

Hamel's paradox and the foundations of analytical dynamics

This paper deals with an explanation of a paradox posed by Hamel in his 1949 book on Theoretical Mechanics. The explanation deals with the foundations of mechanics and points to new insights into analytical dynamics.

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

Explicit Equation of Motion of Constrained Systems

This chapter develops a new, simple, general, and explicit form of the equations of motion for general nonlinear constrained mechanical systems that can have holonomic and/or nonholonomic constraints that may or may not be ideal, and that may contain either positive semi-definite or positive definite mass matrices. This is done through the replacement of the actual unconstrained mechanical system, which may have a positive semi-definite mass matrix, with an unconstrained auxiliary system that is then subjected to the same holonomic and/or nonholonomic constraints as those applied to the actual unconstrained mechanical system. The unconstrained auxiliary system is subjected to the same “given” force as the actual mechanical system, and its mass matrix is appropriately augmented to make it positive definite so that the so-called fundamental equation can then be directly and simply applied to obtain the closed-form acceleration of the actual constrained mechanical system. Furthermore, it is shown that by appropriately augmenting the “given” force that acts on the actual unconstrained mechanical system, the auxiliary system directly provides the constraint force that needs to be imposed on the actual unconstrained mechanical system so that it satisfies the given holonomic and/or nonholonomic constraints. Thus, irrespective of whether the mass matrix of the actual unconstrained mechanical system is positive definite or positive semi-definite, a simple, unified fundamental equation results that give a closed-form representation of both the acceleration of the constrained mechanical system and the constraint force. The results herein provide deeper insights into the behavior of constrained motion and open up new approaches to modeling complex, constrained mechanical systems, such as those encountered in multi-body dynamics. Several examples are provided.

A New Approach to the Tracking Control of Uncertain Nonlinear Multi-body Mechanical Systems

This chapter presents a new approach for the tracking control of uncertain mechanical systems. Real-life multi-body systems are in general highly nonlinear and modeling them is intrinsically error prone due to uncertainties related to both their description and the description of the various forces that they may be subjected to. As such, in the modeling of such systems one only has in hand the so-called nominal system—a model based upon our best assessment of the system and our best assessment of the generalized forces acting on it. Uncertainties that are time-varying, unknown but bounded, are assumed in this chapter, and a new approach to the development of a closed-form controller is developed. The approach uses the concept of a generalized sliding surface. Its closed-form approach can guarantee, regardless of the uncertainty, that the uncertain system can track a desired reference trajectory that the nominal system is required to follow. An example of a simple multi-body system whose description is known only imprecisely is illustrated showing the simplicity of the approach and its efficacy in tracking the trajectory of the nominal system. The approach is easily implemented for a wide range of complex multi-body mechanical systems.