A new perspective on the tracking control of nonlinear structural and mechanical systems (original) (raw)
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Constrained Dynamics and Tracking Control of Structural and Mechanical Systems
2000
Based on recent results from analytical dynamics, this paper develops a class of tracking controllers for controlling general, non-linear, structural and mechanical systems. Unlike most control methods that perform some kind of linearization and/or cancellation, the methodology developed herein obtains a class of control forces that 'exactly' maintain the nonlinear system along a certain trajectory, which, in general, may be
Constrained Motion of Mechanical Systems and Tracking Control of Nonlinear Systems
Springer Proceedings in Mathematics & Statistics, 2014
This paper aims to expose the connections between the determination of the equations of motion of constrained systems and the problem of tracking control of nonlinear mechanical systems. The duality between the imposition of constraints on a mechanical system and the trajectory requirements for tracking control is exposed through the use of a simple example. It is shown that given a set of constraints, d'Alembert's principle corresponds to the problem of finding the optimal tracking control of a mechanical system for a specific control cost function that Nature seems to choose. Furthermore, the general equations for constrained motion of mechanical systems that do not obey d'Alembert's principle yield, through this duality, the entire set of continuous controllers that permit exact tracking of the trajectory requirements. The way Nature seems to handle the tracking control problem of highly nonlinear systems suggests ways in which we can develop new control methods that do not make any approximations and/or linearizations related to the nonlinear system dynamics, or its controllers. More general control costs are used and Nature's approach is thereby extended to general control problems.
Tracking Control Design in Nonlinear Multivariable Systems: Robotic Applications
Mathematical Problems in Engineering
In this work, a controller design technique called linear algebra based controller (LABC) is presented. The controller is obtained following a systematic procedure that is summarized in this work. In addition, the influence of additive uncertainty on the tracking error is analyzed, and a solution using integrators is proposed. A mobile robot is used as a benchmark to test the performance of the proposed algorithms. In addition, implementation to other systems such as marine vessel is referenced. In this work, the design of controllers in continuous and discrete time is included and experimental and simulation results are shown in a Pioneer 3AT mobile robot. Comparisons are also shown with other controllers proposed in the literature.
This paper aims to expose the connections between the determination of the equations of motion of constrained systems and the problem of tracking control of nonlinear mechanical systems. The duality between the imposition of constraints on a mechanical system and the trajectory requirements for tracking control is exposed through the use of a simple example. It is shown that given a set of constraints, d'Alembert's principle corresponds to the problem of finding the optimal tracking control of a mechanical system for a specific control cost function that Nature seems to choose. Furthermore, the general equations for constrained motion of mechanical systems that do not obey d'Alembert's principle yield, through this duality, the entire set of continuous controllers that permit exact tracking of the trajectory requirements. The way Nature seems to handle the tracking control problem of highly nonlinear systems suggests ways in which we can develop new control methods that do not make any approximations and/or linearizations related to the nonlinear system dynamics, or its controllers. More general control costs are used and Nature's approach is thereby extended to general control problems.
A New Approach to the Tracking Control of Uncertain Nonlinear Multi-body Mechanical Systems
Nonlinear Approaches in Engineering Applications 2, 2013
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.
Tracking Control of Robotic Multi-Body Systems
This paper presents a simple methodology for obtaining the entire set of continuous controllers that cause a nonlinear dynamical system to exactly track a given trajectory. The trajectory is provided as a set of algebraic differential equations that may or may not be explicitly dependent on time. The method provided is inspired by results from analytical dynamics and the close connection between nonlinear control and analytical dynamics is explored. The results provided in this paper here yield new and explicit methods for the control of highly nonlinear systems. The paper is based on previous work of the authors.