Control of Uncertain Nonlinear Multibody Mechanical Systems

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Thanapat Wanichanon
Keyword(s):  
Closed Form ◽  
Error Bounds ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Real Life ◽  
Reference Trajectory ◽  
Control Force ◽  
Control Laws ◽  
Nominal System ◽  
The Face

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.

Comparison of Methods for Tracking Control of Nonlinear Uncertain Multi-Body Mechanical Systems

2012 ◽  
Author(s):  
F. E. Udwadia ◽  
T. Wanichanon
Keyword(s):  
Tracking Control ◽  
Mechanical Systems ◽  
Real Life ◽  
Reference Trajectory ◽  
Sliding Surface ◽  
Nominal System ◽  
Damping Control ◽  
Multi Body ◽  
Tracking Signal ◽  
Damping Controller

This paper presents a comparison of several alternative approaches to obtaining tracking control of a nonlinear uncertain system. A real-life multi-body system is in general highly nonlinear and is intrinsically error-prone due to uncertainties in the modeling system. The uncertainty which is time-varying, unknown but bounded, is therefore assumed in this paper, whereby it may arise from two general sources: uncertainty in the knowledge of the physical system and/or uncertainty in the ‘given force’ applied to the system. In this paper, the use of a new, generalized nonlinear controller is illustrated incorporating two control laws—generalized sliding surface control and generalized damping control. The generalized damping control law also provides two control approaches, one with an uncertainty bound and one without the bound on uncertainty. This leads to three sets of closed-form controllers that can guarantee, regardless of the uncertainty, a tracking signal of a desired reference trajectory of the nominal system, which we refer to as our best assessment of the actual real-life situation. A comparison of the use of the proposed three control designs is demonstrated using an example of a control problem in multi-body dynamics. Both the generalized sliding surface controller and the generalized bound damping controller require knowledge of the bound on uncertainty in order to guarantee a tracking signal of a desired reference trajectory within a desired error bound. In contrast, when using the generalized no-bound damping controller, tracking of the nominal system trajectory can be obtained regardless of the knowledge of the uncertainty’s bound. However, the tracking results from the generalized no-bound damping controller are the least optimal when compared with those obtained from the other two controllers. With simplicity and accuracy obtained, all three control approaches can be implemented for a wide range of complex multi-body mechanical systems.

Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss’s Principle

1993 ◽  
Vol 60 (3) ◽  
pp. 662-668 ◽  
Author(s):  
R. E. Kalaba ◽  
F. E. Udwadia
Keyword(s):  
Dynamical Systems ◽  
Closed Form ◽  
Programming Problem ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Closed Form Solution ◽  
Nonholonomic Constraints ◽  
Form Solution ◽  
Constrained Motion ◽  
Constraint Forces

In this paper we develop an analytical set of equations to describe the motion of discrete dynamical systems subjected to holonomic and/or nonholonomic Pfaffian equality constraints. These equations are obtained by using Gauss’s Principle to recast the problem of the constrained motion of dynamical systems in the form of a quadratic programming problem. The closed-form solution to this programming problem then explicitly yields the equations that describe the time evolution of constrained linear and nonlinear mechanical systems. The direct approach used here does not require the use of any Lagrange multipliers, and the resulting equations are expressed in terms of two different classes of generalized inverses—the first class pertinent to the constraints, the second to the dynamics of the motion. These equations can be numerically solved using any of the standard numerical techniques for solving differential equations. A closed-form analytical expression for the constraint forces required for a given mechanical system to satisfy a specific set of nonholonomic constraints is also provided. An example dealing with the position tracking control of a nonlinear system shows the power of the analytical results and provides new insights into application areas such as robotics, and the control of structural and mechanical systems.

Modal self-excitation in a class of mechanical systems by nonlinear displacement feedback

2016 ◽  
Vol 24 (4) ◽  
pp. 784-796 ◽  
Author(s):  
Anindya Malas ◽  
Shyamal Chatterjee
Keyword(s):  
Degrees Of Freedom ◽  
Research Work ◽  
Mechanical Systems ◽  
Nonlinear Function ◽  
Control Force ◽  
Nonlinear Feedback ◽  
Control Cost ◽  
Control Laws ◽  
Filter Output ◽  
Excited Oscillation

Many devices and processes utilize self-excited oscillation to enhance performance. Recently, much research work has been devoted to the induction of self-excited oscillation in mechanical systems by nonlinear feedback. The present paper investigates the efficacy of a displacement feedback technique in generating self-excited oscillation at the desired mode(s) in a multiple degrees-of-freedom mechanical system. The controller couples the system with a bank of second-order filters and generates the required control force as a nonlinear function of the filter output. The describing function method theoretically explores the dynamics of the system with the control law. The control cost of the controller is studied for the proper choice of the filter parameters. The analytical results are substantiated by the numerical simulation results. The present study reveals that the proposed control laws, if used in an appropriate way, can generate self-excited oscillation in the system at the desired mode(s).

scholarly journals A Discussion of Low-Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
Dan Negrut ◽  
Laurent O. Jay ◽  
Naresh Khude
Keyword(s):  
Numerical Experiments ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Real Life ◽  
Flexible Multibody Dynamics ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Integration Formulas ◽  
Impact Phenomena ◽  
Low Order

The premise of this work is that the presence of high stiffness and/or frictional contact/impact phenomena limits the effective use of high order integration formulas when numerically investigating the time evolution of real-life mechanical systems. Producing a numerical solution relies most often on low-order integration formulas of which the paper investigates three alternatives: Newmark, HHT, and order 2 BDFs. Using these methods, a first set of three algorithms is obtained as the outcome of a direct index-3 discretization approach that considers the equations of motion of a multibody system along with the position kinematic constraints. The second batch of three algorithms draws on the HHT and BDF integration formulas and considers, in addition to the equations of motion, both the position and velocity kinematic constraint equations. Numerical experiments are carried out to compare the algorithms in terms of several metrics: (a) order of convergence, (b) energy preservation, (c) velocity kinematic constraint drift, and (d) efficiency. The numerical experiments draw on a set of three mechanical systems: a rigid slider-crank, a slider-crank with a flexible body, and a seven body mechanism. The algorithms investigated show good performance in relation to the asymptotic behavior of the integration error and, with one exception, result in comparable CPU simulation times with a small premium being paid for enforcing the velocity kinematic constraints.

scholarly journals Formulating Modes of Cooperative Leaning for Education for Sustainable Development

2021 ◽  
Vol 13 (6) ◽  
pp. 3465
Author(s):  
Jordi Colomer ◽  
Dolors Cañabate ◽  
Brigita Stanikūnienė ◽  
Remigijus Bubnys
Keyword(s):  
Sustainable Development ◽  
Real Life ◽  
Education For Sustainable Development ◽  
Professional Life ◽  
Global Challenges ◽  
Life Problems ◽  
The Face ◽  
Contemporary Education ◽  
The Impact

In the face of today’s global challenges, the practice and theory of contemporary education inevitably focuses on developing the competences that help individuals to find meaningfulness in their societal and professional life, to understand the impact of local actions on global processes and to enable them to solve real-life problems [...]

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Examining the interplay between face mask usage, asymptomatic transmission, and social distancing on the spread of COVID-19

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adam Catching ◽  
Sara Capponi ◽  
Ming Te Yeh ◽  
Simone Bianco ◽  
Raul Andino
Keyword(s):  
Social Distance ◽  
Large Fraction ◽  
Real Life ◽  
Virus Transmission ◽  
Face Mask ◽  
Social Distancing ◽  
Viral Spread ◽  
The Face ◽  
Asymptomatic Individuals ◽  
High Virus

AbstractCOVID-19’s high virus transmission rates have caused a pandemic that is exacerbated by the high rates of asymptomatic and presymptomatic infections. These factors suggest that face masks and social distance could be paramount in containing the pandemic. We examined the efficacy of each measure and the combination of both measures using an agent-based model within a closed space that approximated real-life interactions. By explicitly considering different fractions of asymptomatic individuals, as well as a realistic hypothesis of face masks protection during inhaling and exhaling, our simulations demonstrate that a synergistic use of face masks and social distancing is the most effective intervention to curb the infection spread. To control the pandemic, our models suggest that high adherence to social distance is necessary to curb the spread of the disease, and that wearing face masks provides optimal protection even if only a small portion of the population comply with social distance. Finally, the face mask effectiveness in curbing the viral spread is not reduced if a large fraction of population is asymptomatic. Our findings have important implications for policies that dictate the reopening of social gatherings.

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