Decentralised control of nonlinear dynamical systems

2015

Nonlinear Dyn

Self Cite

The explicit equations of motion for a general n-body planar pendulum are derived in a simple and concise manner. A new and novel approach for obtaining these equations using mathematical induction on the number bodies in the pendulum system is used. Assuming that the parameters of the system are precisely known, a simple method for its control that is inspired by analytical dynamics is developed. The control methodology provides closed-form nonlinear control and makes no approximations/linearizations of the nonlinear system. No a priori structure is imposed on the controller. Globally, asymptotic Lyapunov stability is achieved along with the minimization of a userprovided control cost at each instant of time. This control methodology is then extended to include uncertainties in the parameters of the system through the use of an additional continuous controller. Simulations showing the simplicity and efficacy of the approach are provided for a 10-body pendulum system whose model is only known imprecisely. The ease with which the uncertain system can be controlled to move from any initial

Section: Sliding Mode Controller For Uncertain Pendulum Systemmentioning

confidence: 99%

“…Equation (28) can be rewritten for further notational convenience as Mθ =−{S θ 2 +Cθ + D+ F} + Q C := Q + Q C (29) where we have suppressed the arguments of the various quantities.…”

Section: Explicit Control Of N-body Pendulummentioning

confidence: 99%

Dynamics and control of a multi-body planar pendulum

2015

Nonlinear Dyn

Self Cite

“…The approach is based on recent (exact) results from analytical dynamics [36][37][38][39][40][41]. First, the control requirements are framed as constraints on the nonlinear dynamical system.…”

Section: Equations Of Motion Of Controlled System: Explicit Determentioning

confidence: 99%

Dynamics and Precision Control of Tumbling Multibody Systems

Journal of Guidance, Control, and Dynamics

2017

Self Cite

Tumbling is an inherently nonlinear phenomenon, and this paper uses a generic model of a tumbling multibody system made up of a rigid body to which discrete masses are attached; it obtains the equations of motion of the system explicitly, exhibiting the highly nonlinear nature of the dynamics. Particularizations of the generic model used here are useful in applications such as liquid sloshing in rockets, biodynamics, and capture and refurbishing of space debris. It is assumed that the mathematical description of the system is accurately known. A uniform analytical dynamics-based approach is used to obtain both the equations of motion of the system as well as the requisite control torques and forces to satisfy control requirements. No linearizations or approximations of the nonlinear dynamics are made, and closed-form controls are obtained that precisely track user-specified time-dependent control requirements on the tumbling multibody system. The methodology is demonstrated using two examples of tumbling systems with internal degrees of freedom in a constant gravity field that possess significant nonlinear internal motions. Precision tumbling control of such tumbling-vibrating multibody systems is achieved with considerable ease, making the approach presented herein useful for real-time control.

“…Applications to the control of systems with complex and highly nonlinear dynamics such as the formation flight of spacecraft in nonuniform gravity fields illustrate the simplicity and effectiveness of the closed-form approach [10][11][12]. Current extensions to dynamical systems subjected to (generalized) forces that are only imprecisely known and/or to systems whose description is only imprecisely known can be found in [13][14][15][16]. Also, stable full-state control of a general nonlinear, nonautonomous mechanical system has been achieved by casting the objective of realizing asymptotically stable control as a Lyapunov constraint on the system [5,6,15,16].…”

Section: Introductionmentioning

confidence: 99%

Unified Approach to Modeling and Control of Rigid Multibody Systems

Journal of Guidance, Control, and Dynamics

2016

Self Cite

A unified approach is developed to model complex multibody mechanical systems and design controls for them. The characterization of such complex systems often requires the use of more coordinates than the minimum number to describe their configurations and/or the use of modeling constraints to capture their proper physical descriptions. When required to satisfy prescribed control requirements, it becomes necessary that the generalized control forces they are subjected to exactly satisfy these modeling constraints so that their physical descriptions are correctly preserved. The control requirements imposed can always be interpreted as a set of additional control constraints, and they may or may not be consistent with the modeling constraints that describe the physical system. This paper considers both the cases when the control constraints are consistent with the modeling constraints and when they are inconsistent. Such inconsistencies can arise when dealing with underactuated systems. A user-prescribed control cost is minimized at each instant of time in both cases. No linearizations/approximations of the nonlinear mechanical systems are made throughout. Insights into the control methodology are afforded through its geometric interpretation. Numerical examples with full-state control and underactuated control are considered, demonstrating the simplicity of the approach, its ease of implementation, and its effectiveness.